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Comparison of relative permeability-fluid saturation-capillary pressure relations in the modelling of non-aqueous phase liquid infiltration in variably saturated, layered media
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences. (Hydrologi)
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences. (Hydrologi)
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences. (Hydrologi)
2006 (English)In: Advances in Water Resources, ISSN 0309-1708, E-ISSN 1872-9657, Vol. 29, no 11, 1705-1730 p.Article in journal (Refereed) Published
Abstract [en]

The characteristic functions relating relative permeabilities and capillary pressures to fluid saturations (krSPc models) are of great importance for the modelling of sub-surface multi-phase flow and transport. In order to test their performance and to identify their important parameters, four well-known three-phase krSPc models have been tested against published experimental data on non-aqueous phase liquid (NAPL) migration in the unsaturated zone. Both homogenous systems and systems with embedded heterogeneities have been analysed.

The results show that although there are differences between predictions based on the different models, all models exhibit some common problems and it is not obvious that any one model is more accurate than the other three. However, with the inclusion of a non-linear NAPL tortuosity factor, both the Brooks–Corey–Burdine and van Genuchten–Mualem models yield excellent fits to experimental data.

For NAPLs with non-zero spreading coefficients no exact theory currently exists for scaling two-phase capillary pressure–saturation functions to three-phase systems. Different ways of applying the Parker et al. [Parker JC, Lenhard RJ, Kuppusamy T. A parametric model for constitutive properties governing multi-phase flow in porous media. Water Resour Res 1987;23:618–24] scaling method have therefore been tested. It was found that since the NAPL–gas capillary pressure function has the strongest influence on NAPL migration, the scaling procedure should focus on accuracy in this function.

Place, publisher, year, edition, pages
2006. Vol. 29, no 11, 1705-1730 p.
Keyword [en]
Relative permeability, Capillary pressure, Constitutive relations, Multi-phase flow, Modelling, NAPL, Tortuosity, Scaling
National Category
Earth and Related Environmental Sciences
URN: urn:nbn:se:uu:diva-95312DOI: 10.1016/j.advwatres.2005.12.007ISI: 000242192400011OAI: oai:DiVA.org:uu-95312DiVA: diva2:169481
Available from: 2006-12-20 Created: 2006-12-20 Last updated: 2011-05-11Bibliographically approved
In thesis
1. Experimental and Modelling Studies on the Spreading of Non-Aqueous Phase Liquids in Heterogeneous Media
Open this publication in new window or tab >>Experimental and Modelling Studies on the Spreading of Non-Aqueous Phase Liquids in Heterogeneous Media
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Spridning av flerfasföroreningar i heterogen mark : Studier med experiment och modellering
Abstract [en]

Non-Aqueous Phase Liquids (NAPLs) include commonly occurring organic contaminants such as gasoline, diesel fuel and chlorinated solvents. When released to subsurface environments their spreading is a complex process of multi-component, multi-phase flow. This work has strived to develop new models and methods to describe the spreading of NAPLs in heterogeneous geological media.

For two-phase systems, infiltration and immobilisation of NAPL in stochastically heterogeneous, water-saturated media were investigated. First, a methodology to continuously measure NAPL saturations in space and time in a two-dimensional experiment setup, using multiple-energy x-ray-attenuation techniques, was developed. Second, a set of experiments on NAPL infiltration in carefully designed structures of well-known stochastic heterogeneity were conducted. Three detailed data-sets were generated and the importance of heterogeneity for both flow and the immobilised NAPL architecture was demonstrated. Third, the laboratory experiments were modelled with a continuum- and Darcy’s-law-based multi-phase flow model. Different models for the capillary pressure (Pc) – fluid saturation (S) – relative permeability (kr) constitutive relations were compared and tested against experimental observations. A method to account for NAPL immobility in dead-end pore-spaces during drainage was introduced and the importance of accounting for hysteresis and NAPL entrapment in the constitutive relations was demonstrated.

NAPL migration in three-phase, water-NAPL-air systems was also studied. Different constitutive relations used in modelling of three-phase flow were analysed and compared to existing laboratory data. To improve model performance, a new formulation for the saturation dependence of tortuosity was introduced and different scaling options for the Pc-S relations were investigated. Finally, a method to model the spreading of multi-constituent contaminants using a single-component multi-phase model was developed. With the method, the migration behaviour of individual constituents in a mixture, e.g. benzene in gasoline, could be studied, which was demonstrated in a modelling study of a gasoline spill in connection with a transport accident.

Abstract [sv]

Flerfasföroreningar innefattar vanligt förekommande organiska vätskor som bensin, dieselolja och klorerade lösningsmedel. Spridningen av dessa föroreningar i mark är komplicerad och styrs av det samtidiga flödet av organisk vätska, vatten och markluft samt utbytet av komponenter (föroreningar) mellan de olika faserna. Detta arbete syftade till att utveckla nya metoder och modeller för att studera spridningen av flerfasföroreningar i mark:

(i) En metodik utvecklades för att i laboratorium noggrant och kontinuerligt mäta hur en organisk vätska är rumsligt fördelad i en tvådimensionell experimentuppställning. Metoden baserades på röntgenutsläckning för olika energinivåer.

(ii) Infiltration av organisk vätska i vattenmättade medier studerades för olika konfigurationer av geologisk heterogenitet. I experimentuppställningen packades olika sandmaterial noggrant för att konstruera en välkänd, stokastiskt heterogen struktur. Spridningsprocessen dokumenterades i tre detaljerade mätserier och heterogenitetens påverkan på flöde och kvarhållning av den organiska vätskan påvisades.

(iii) Experimenten simulerades med en numerisk modell. Olika modeller prövades för att beskriva de grundläggande relationerna mellan kapillärtryck (Pc) vätskehalt (S) och relativ permeabilitet (kr) för detta tvåfassystem av vatten och organisk vätska. En relation infördes för att beskriva partiell orörlighet hos den organiska vätskan i porer vars halsar tillfälligt blockeras av vatten då mediet avvattnas. Vikten av att i de grundläggande relationerna ta hänsyn till hysteresis och kvarhållning av organisk fas visades.

(iv) Olika Pc-S-kr relationer för trefassystem av vatten, organisk vätska och markluft testades mot befintliga experimentella data. En ny relation för hur slingrigheten (eng. tortuosity) beror av vätskehalten infördes i kr-S relationen och olika möjligheter för att skala Pc-S relationen analyserades.

(v) En modelleringsmetodik utvecklades för att studera spridningen av flerkomponentsföroreningar. Med metoden kunde spridningsbeteendet hos enskilda, särskilt skadliga komponenter som t.ex. bensen särskiljas då ett bensinutsläpp i samband med en transportolycka simulerades.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2006. 69 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 259
Hydrology, NAPL, Multi-phase flow, Modelling, Experiment design, Heterogeneity, Constitutive relations, Multi-constituent contaminants, Capillary pressure, Relative permeability, Hysteresis, Hydrologi
urn:nbn:se:uu:diva-7430 (URN)978-91-554-6768-5 (ISBN)
Public defence
2007-01-19, Hambergssalen, Geocentrum, Villavägen 16, Uppsala, 13:00 (English)
Available from: 2006-12-20 Created: 2006-12-20 Last updated: 2011-01-25Bibliographically approved

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