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A generalized approach for estimation of in-plane curvature in invasion percolation models for drainage in fractures
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
Center for Experimental Study of Subsurface Environmental Processes, Colorado School of Mines, Golden, CO, USA.
2012 (English)In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 48, no 9, W09507- p.Article in journal (Refereed) Published
Abstract [en]

In-plane interfacial curvature plays an important role in shaping the phase structure during quasi-static immiscible displacement in horizontal rough-walled fractures. Existing approaches used in percolation modeling require the use of a pre-defined globally representative length scale for calculating the in-plane curvature. This length scale is typically estimated using the geostatistics of fracture aperture variability. However, there has not been any rigorous and general derivation on how to obtain this length scale in the literature. This paper presents a general method referred to as adaptive circle fitting (ACF) approach to estimate in-plane curvature, recognizing that in some fractures the in-plane curvature along the fluid-fluid interface may exhibit various length scales due to the variability both in the locally averaged aperture and in the fracture wall roughness. The ACF involves nonlinear fitting of the interface to an osculating circle whose radius geometrically defines the inverse of the local curvature. This approach does not require pre-defining an empirical representative length scale. The influence length of the interface to which the circle is fitted is determined adaptively based on an acceptable threshold error.  We have implemented the ACF approach to an invasion percolation model and performed numerical simulations against experimental data on drainage processes in two horizontal rough-walled fractures. The observed invasion phase structures can be well reproduced using this generalized approach. In comparison to the previous approaches, it also demonstrates better performance in matching the experimental results of invasion phase distributions and fractal dimensions of the invasion clusters.

Place, publisher, year, edition, pages
2012. Vol. 48, no 9, W09507- p.
Keyword [en]
fracture, two-phase flow, curvature, invasion percolation, immiscible displacement
National Category
Oceanography, Hydrology, Water Resources
Research subject
Hydrology
Identifiers
URN: urn:nbn:se:uu:diva-180902DOI: 10.1029/2012WR011829ISI: 000310541400002OAI: oai:DiVA.org:uu-180902DiVA: diva2:552048
Funder
Swedish Research Council
Available from: 2012-09-12 Created: 2012-09-12 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Multiphase Contamination in Rock Fractures: Fluid Displacement and Interphase Mass Transfer
Open this publication in new window or tab >>Multiphase Contamination in Rock Fractures: Fluid Displacement and Interphase Mass Transfer
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Flerfasföroreningar i sprickigt berg : Utbredning och massöverföring mellan faser
Abstract [en]

Multiphase flow and transport in fractured rock is of importance to many practical and engineering applications. In the field of groundwater hydrology an issue of significant environmental concern is the release of dense non-aqueous phase liquids (DNAPLs) which can cause long-term groundwater contamination in fractured aquifers. This study deals with two fundamental processes – fluid displacement and interphase mass transfer – concerning the behavior of the multiphase contaminants in fractured media. The focus of this work has been placed on improving the current understanding of small-scale (single fracture) physics by a combined effort of numerical modeling analysis, laboratory experiments and model development. This thesis contributes to the improved understanding through several aspects. Firstly, the effect of aperture variability, as characterized by geostatistical parameters such as standard deviation and correlation length, on the DNAPL entrapment, dissolution and source-depletion behaviors in single fractures was revealed. Secondly, a novel, generalized approach (adaptive circle fitting approach) to account for the effect of in-plane curvature of fluid-fluid interfaces on immiscible fluid displacement was developed; the new approach has demonstrated good performance when applied to simulate previously published experimental data. Thirdly, the performance of a continuum-based two-phase flow model and an invasion percolation model was compared for modeling fluid displacement in a variable-aperture fracture and the dependence of fracture-scale capillary pressure – saturation relationships on aperture variability was studied. Lastly, through experimental studies and mechanistic numerical modeling of DNAPL dissolution, kinetic mass transfer characteristics of two different entrapment configurations (residual blobs and dead-end pools) were investigated. The obtained understanding from this thesis will be useful for predictive modeling of multiphase contaminant behavior at a larger (fracture network) scale.

Abstract [sv]

Flerfasflöde och ämnestransport i sprickigt berg är av betydelse för många praktiska och tekniska problem. Tunga, svårlösliga organiska vätskor (engelska: dense non-aqueous phase liquids: DNAPLs; t.ex. klorerade lösningsmedel) kan orsaka långvarig förorening av vattenresurser, inklusive akviferer i sprickigt berg, och utgör ett viktigt miljöproblem inom grundvattenhydrologin. Denna studie behandlar två fundamentala processer för spridning av flerfasföroreningar i sprickiga medier – utbredning av den organiska vätskan och massöverföring mellan organisk vätska och vatten. Arbetet har fokuserat på att förbättra nuvarande kunskap om de fysikaliska processerna på liten skala (enskilda sprickor) genom en kombination av numerisk modellering, laboratorieexperiment och modellutveckling. Avhandlingen har bidragit till utökad processförståelse i flera avseenden. För det första har arbetet belyst effekterna av sprickaperturens variabilitet, uttryckt med geostatistiska parametrar som standardavvikelse och rumslig korrelationslängd, på fastläggning och lösning av organiska vätskor i enskilda sprickor, samt utmattningsbeteendet hos dessa källor till grundvattenförorening. För det andra har en ny, generell metod (adaptiva cirkelpassningsmetoden) för att ta hänsyn till effekten av krökningen av gränsytan mellan organisk vätska och vatten i sprickplanet utvecklats; denna metod har visats fungera väl i simuleringar av tidigare publicerade experimentella data. För det tredje, har en jämförelse gjorts mellan en kontinuumbaserad tvåfasflödesmodell och en invasions-perkolationsmodell med avseende på hur väl de kan simulera tvåfasflöde i en spricka med varierande apertur. Här studerades även hur relationen mellan kapillärtryck och mättnadsgrad på sprickplansskala beror av variabiliteten i sprickapertur. Till sist undersöktes lösning av den organiska vätskan i grundvatten för två fastläggningsscenarier (fastläggning i immobila droppar och ansamling i fällor – ”återvändssprickor”) både genom experiment och mekanistisk numerisk modellering. Kunskapen som tagits fram i denna avhandling bedöms vara användbar även för att modellera spridningen av flerfasföroreningar på större (spricknätverks-) skalor.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 75 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 994
Keyword
multiphase flow; dissolution; mass transfer; invasion percolation; immiscible displacement; fractured media; groundwater contamination; non-aqueous phase liquid; curvature
National Category
Oceanography, Hydrology, Water Resources Environmental Sciences
Research subject
Hydrology
Identifiers
urn:nbn:se:uu:diva-183720 (URN)978-91-554-8531-3 (ISBN)
Public defence
2012-12-14, Hambergsalen, Geocentrum, Villavägen 16, Uppsala, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council
Available from: 2012-11-23 Created: 2012-10-31 Last updated: 2013-02-11Bibliographically approved

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Yang, ZhibingNiemi, AuliFagerlund, Fritjof

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