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Numerical and analytical modelling of advective travel times in realistic three-dimensional fracture networks
KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering. (Water Resources Engineering)
KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering. (Water Resources Engineering)
2011 (English)In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 47, no W02506, 16pp- p.Article in journal (Refereed) Published
Abstract [en]

Travel time distributions obtained from advective transport in multiple realisations of realistic discrete fracture network simulations are analysed using the truncated one-sided stable distribution, which has previously been shown to generalise both the advection-dispersion solution as well as one-sided stable distributions. Using this model it is shown that the Fickian assumption inherent in the advection-dispersion equation generally fails, despite that the first two moments of travel time essentially scale linearly with distance. It is also observed that the equally probable realisations drawn from the ensemble can produce a wide range of behaviour under the current configuration, such that Fickian conditions are almost obtained in some cases for increasing scales. Based on a small-scale calibration against particle breakthrough, the model is then shown to successfully predict limiting bounds of transport for a one order of magnitude increase in scale. Correlation in particle velocity is explicitly shown to be significant for scales close to the characteristic Lagrangian segment length. The network configuration is obtained from extensive site characterisation data at the Laxemar region in Sweden, and represents a block scale domain of reasonably sparse background fractures.

Place, publisher, year, edition, pages
2011. Vol. 47, no W02506, 16pp- p.
Keyword [en]
Fractured media; Transport; Advection; Fickian dispersion; One-sided stable densities; Stochastic simulation
National Category
Earth and Related Environmental Sciences Oceanography, Hydrology, Water Resources Other Environmental Engineering
Identifiers
URN: urn:nbn:se:kth:diva-11972DOI: 10.1029/2010WR009290ISI: 000287039900001Scopus ID: 2-s2.0-79851496854OAI: oai:DiVA.org:kth-11972DiVA: diva2:291684
Note
QC 20110209. Uppdaterad från "accepted" till "published"(20110209).Available from: 2010-02-02 Created: 2010-02-02 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Stochastic analysis of fluid flow and tracer pathways in crystalline fracture networks
Open this publication in new window or tab >>Stochastic analysis of fluid flow and tracer pathways in crystalline fracture networks
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Understanding groundwater flow systems and how these control transport is an essential part in assessing the suitability of subsurface environments as hosts for storage of toxic waste. Therefore it is important to be able to integrate knowledge obtained from field characterisation of the subsurface with methods which can be used to evaluate and predict possible impact on surrounding environments.In this thesis I investigate the characteristics of flow and transport in discrete fracture networks by analysing Eulerian and Lagrangian descriptions within a stochastic framework. The analysis is conducted through numerical flow and transport simulations configured according to available field data, combined with independent theoretical analytic and semi-analytic methods which are able to reveal insight to relevant constitutive properties. It is shown that numerical simulations conducted with the discrete fracture network approach can be both conditioned and confirmed against field measurable quantities, and the developed theoretical methods are evaluated against results obtained from simulation. Thereby, a methodology which can provide links between field measurable quantities and tracer discharge is presented, developed and evaluated. It is shown to be robust with respect to underlying assumptions used for flow configurations.In particular, a specific sampling algorithm for obtaining a Lagrangian description of transport based on a Eulerian description of flow is proposed, evaluated and shown to be robust for the cases considered, providing accurate replications. Also a generalisation of both the advection-dispersion solution and the one-sided stable distribution is shown to be able to evaluate advective transport quantities, and combined with a Lagrangian retention model it is shown to be a fairly accurate and robust method for upscaling distributions, enabling predictions of transport in terms of tracer discharge. Evaluation of transport is also conducted against the advective-dispersion assumption, where results indicate advective transport is generally non-Fickian for the fracture networks and domain scales considered, but not necessarily anomalous. Additionally, the impact certain model assumptions have on tracer discharge are analysed. For example, transport is evaluated for assumptions regarding injection mode, fracture network heterogeneity, relationship between aperture and transmissivity, relationship between transmissivity and size, as well as scale and modelling dimension. In relation to hydraulic testing and flow analysis, a method for conditioning fracture transmissivity from field measurements of flow by simulation is developed and evaluated against homogenisation assumptions commonly used in field applications. Results indicate the homogenisation assumption generally fails for current interpretations of field data.

Abstract [sv]

Miljökonsekvensbedömningar av toxiskt avfall i djupt bergförvar kräver engrundläggande förståelse av grundvattenströmning samt hur detta påverkartransportfenomet. Därför är det viktigt att kunna integrerafältundersökningsdata från berggrundsmätningar med metoder som kan användas föratt utvärdera och förutsäga potentiella konsekvenser på omgivningen.I denna avhandling undersöker jag flödes- och transportegenskaper i diskretaspricknätverk genom stokastisk analys av eulerska och lagrangeskafältbeskrivningar. Analysen sker genom en kombination av dels numeriska flödes-och transportsimuleringar som är konfigurerade enligt tillgänglig fältdata, samtdels med oberoende teoretiska analytiska och semi-analytiska metoder som gerdjupare insyn i relevanta konstitutiva egenskaper. Resultat visar att dennumeriska simuleringsmetoden för diskreta spricknätverk kan både konditionerastill fältdata och bestyrkas gentemot mätbara kvantiter. Detta är av betydelse dåde teoretiska metoderna i sin tur är främst evaluerade gentemotsimuleringsresultat. Därmed utvecklas en bestyrkt metodik som kansammanlänka och i viss mån omvandla fältdata till uppskattningar av mängdenspårämnen i ett utflöde. Resultat indikerar att denna metodik är robust avseendeflera antaganden som har används i simuleringskonfigurationen.En särskild urvalsalgoritm introduceras som kan erhålla en lagrangesktransportbeskrivning utifrån ett eulerskt strömningsfält. även denna utvärderasavseende vissa simuleringsantaganden och resultat tyder på att den är robust förde undersökta fallen. Vidare föreslås en viss generalisering av lösningen tillden advektiva-dispersionsekvationen samt av ensidigt stabila (one-sided stable)sannolikhetsfördelningar som metod för att prediktera advektiva kvantitetergenom upskalning av transportfördelningar i rummet. Denna modell kombineras meden tidigare utvecklad metod för transportretention för att uppskatta reaktivagenombrottsfördelningar. Således blir det möjligt att prediktera reaktivtransport d v s rumslig upskalning av genombrottstider för spårämnestransport.Metoden används också för att evaluera ett linärt dispersionsantagande, därresultat indikerar att även advektiv transport kan påvisa icke-linärt beteende.Transport i spricknätverk utvärderas bland annat för modellantaganden avseendeinjektionsmetod, heterogenitet i spricknätverk, konstitutiva relationer mellanapertur och transmissivitet samt mellan transmissivitet och spricklängd, ochmodelleringsskala samt dimension. Beträffande hydrauliska testmetoder ochflödesanalys introduceras en simuleringsmetod för att konditioneraspricktransmissivitet från flödesmätningar. Detta jämförs med etthomogeniseringsantaganden som inte sällan används i fältundersökningar för atttolka flödesmätningar till spricktransmissivitet, och resultat tyder på attdetta antagande kan betydligt undervärdera transmissivitet.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. xi, 62 p.
Series
Trita-LWR. PHD, ISSN 1650-8602 ; 1056
Keyword
Groundwater; Fractured media; Transport; Retention; Macrodispersion; Lagrangian formulation; Stochastic modelling
National Category
Earth and Related Environmental Sciences Oceanography, Hydrology, Water Resources Other Environmental Engineering
Identifiers
urn:nbn:se:kth:diva-11974 (URN)978-91-7415-560-0 (ISBN)
Public defence
2010-02-18, F3, Lindstedtsvägen 26, Kungl Tekniska högskolan, 10:00 (English)
Opponent
Supervisors
Available from: 2010-02-03 Created: 2010-02-02 Last updated: 2010-04-28

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