Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Flow and travel time statistics in highly heterogeneous porous media
KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
2009 (English)In: Water resources research, ISSN 0043-1397, E-ISSN 1944-7973, Vol. 45, no W07402Article in journal (Refereed) Published
Abstract [en]

In this paper we present flow and travel time ensemble statistics based on a new simulation methodology, the adaptive Fup Monte Carlo method (AFMCM). As a benchmark case, we considered two-dimensional steady flow in a rectangular domain characterized by multi-Gaussian heterogeneity structure with an isotropic exponential correlation and lnK variance sigma(2)(Y) up to 8. Advective transport is investigated using the travel time framework where Lagrangian variables (e. g., velocity, transverse displacement, or travel time) depend on space rather than on time. We find that Eulerian and Lagrangian velocity distributions diverge for increasing lnK variance due to enhanced channeling. Transverse displacement is a nonnormal for all sigma(2)(Y) and control planes close to the injection area, but after xI(Y) = 20 was found to be nearly normal even for high sigma(2)(Y). Travel time distribution deviates from the Fickian model for large lnK variance and exhibits increasing skewness and a power law tail for large lnK variance, the slope of which decreases for increasing distance from the source; no anomalous features are found. Second moment of advective transport is analyzed with respect to the covariance of two Lagrangian velocity variables: slowness and slope which are directly related to the travel time and transverse displacement variance, which are subsequently related to the longitudinal and transverse dispersion. We provide simple estimators for the Eulerian velocity variance, travel time variance, slowness, and longitudinal dispersivity as a practical contribution of this analysis. Both two-parameter models considered (the advection-dispersion equation and the lognormal model) provide relatively poor representations of the initial part of the travel time probability density function in highly heterogeneous porous media. We identify the need for further theoretical and experimental scrutiny of early arrival times, and the need for computing higher-order moments for a more accurate characterization of the travel time probability density function. A brief discussion is presented on the challenges and extensions for which AFMCM is suggested as a suitable approach.

Place, publisher, year, edition, pages
2009. Vol. 45, no W07402
Keyword [en]
HEAD SPATIAL VARIABILITY; SOLUTE FLUX APPROACH; MEAN UNIFORM-FLOW; STOCHASTIC-ANALYSIS; GROUNDWATER-FLOW; NUMERICAL SIMULATIONS; CONSERVATIVE SOLUTES; VELOCITY COVARIANCE; EVOLVING SCALES; CAPE-COD
National Category
Water Engineering
Identifiers
URN: urn:nbn:se:kth:diva-10650DOI: 10.1029/2008WR007168ISI: 000267648200001Scopus ID: 2-s2.0-69249101625OAI: oai:DiVA.org:kth-10650DiVA: diva2:222644
Note
QC 20100714Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2012-02-14Bibliographically approved
In thesis
1. A multi-resolution approach for modeling flow and solute transport in heterogeneous porous media
Open this publication in new window or tab >>A multi-resolution approach for modeling flow and solute transport in heterogeneous porous media
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Subsurface processes are usually characterized by rare field experiments, sparse measurements,multi-resolution interpretations, stochastic description, related uncertainties and computational complexity. Over the last few decades, different computational techniques and strategies have become indispensable tools for flow and solute transport prediction in heterogeneous porousmedia. This thesis develops a multi-resolution approach based on Fup basis functions with compactsupport, enabling the use of an efficient and adaptive procedure, closely related to currentunderstood physical interpretation. All flow and transport variables, as well as intrinsic heterogeneity,are described in a multi-resolution representation, in the form of a linear combination ofFup basis functions. Each variable is represented on a particular adaptive grid with a prescribedaccuracy. The methodology is applied to solving problems with sharp fronts, and to solving flowand advective transport in highly heterogeneous porous media, under mean uniform flow conditions.The adaptive Fup collocation method, through the well known method of lines, efficientlytracks solutions with sharp fronts, resolving locations and frequencies at all spatial and/or temporalscales. The methodology yields continuous velocity fields and fluxes, enabling accurate andreliable transport analysis. Analysis of the advective transport proves the robustness of the firstordertheory for low and mild heterogeneity. Moreover, due to the accuracy of the improved Monte-Carlo methodology, this thesis presents the effects of high heterogeneity on ensembleflow and travel time statistics. The difference between Eulerian and Lagrangian velocity statisticsand the importance of higher travel time moments are indicative of high heterogeneity. The thirdtravel time moment mostly describes a peak and late arrivals, while higher moments are requiredfor early arrivals which are linked with the largest uncertainty. A particular finding is the linearityof all travel time moments, which implies that in the limit an advective transport in multi-Gaussian field becomes Fickian. By comparison, the transverse displacement pdf converges to aGaussian distribution around 20 integral scales after injection, even for high heterogeneity. Thecapabilities of the presented multi-resolution approach, and the quality of the obtained results,open new areas for further research.

Abstract [sv]

Markprocesser karakteriseras ofta av fåtaliga fältexperiment, glesa mätningar, heterogenitet påolika skalor, slumpmässighet och relaterade osäkerheter, samt beräkningsmässiga svårigheter.Under de senaste årtiondena har olika beräkningstekniker och strategier blivit ovärderliga verktygför att förutspå vattenflöde och ämnestransport i heterogena porösa medier. Denna doktorsavhandling utvecklar ett angreppssätt med flerskaliga upplösningar baserat på Fup basis funktionermed kompakt stöd, som möjliggör en effektiv och anpassningsbar procedur, nära relaterad tillrådande fysiska tolkningar. Alla flödes- och transportvariabler, så väl som heterogeniteten, beskrivsav en flerskaligt upplöst representation, i form av linjära kombinationer av Fup basis funktioner.Varje variabel representeras på ett speciellt anpassningsbar gridnät med given noggrannhet.Metoden appliceras för att lösa problem med skarpa fronter, samt vattenflöde och advektivämnestransport i starkt heterogena porösa medier. Adaptive Fup collocation metoden tillsammansmed den välkända Method of lines, spårar effektivt lösningar med skarpa fronter och löserupp positioner och frekvenser på alla rums- och/eller tidsskalor. Metoden ger kontinuerliga hastighetsfältoch flöden, och möjliggör noggrann och tillförlitlig transportanalys. Analys av advektivtransport understöder stabiliteten i första-ordningens transport teori för låg och mild heterogenitet.Utöver detta, som resultat av noggrannheten i den förbättrade Monte-Carlo metodiken, visardenna avhandling effekten av hög heterogenitet på ensemble statistiken för flöden och transporttider.Skillnaden mellan Eulerisk och Lagrangian hastighetsstatistik och betydelsen av högrestatistiska moment för transporttider, indikerar hög heterogenitet. Det tredje transporttidsmomentetbeskriver huvudsakligen sannolikhetspiken och de långa transporttiderna, medan högremoment behövs för de korta transporttiderna, som har den största osäkerheten. En speciell upptäcktär linjäariteten i transporttidsmoment, som indikerar att advektiv transport i multi-Gaussiska fält blir Gaussisk i gränsen. Som jämförelse konvergerar sannolikhetsfunktioner förden transversella transportförflyttningen mot en Gaussisk fördelning vid runt 20 korrelationslängder efter injektion, även för hög heterogenitet. Förmågan i det presenterade angreppssättet med flerskalig upplösning, och resultatens noggrannhet, öppnar nya områden för fortsatt forskning.

Place, publisher, year, edition, pages
Stockholm: KTH, 2009. xiv, 51 p.
Series
Trita-LWR. PHD, ISSN 1650-8602 ; 1051
Keyword
Multi-resolution adaptive approach; Atomic and Fup basis functions; Monte- Carlo method; Heterogeneous porous media; Flow; Transport; Travel time
National Category
Water Engineering
Identifiers
urn:nbn:se:kth:diva-10655 (URN)978-91-7415-377-4 (ISBN)
Public defence
2009-06-18, M3, Entreplan, KTH, Brinellvägen 64, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20100714Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2011-08-30Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Gotovac, HrvojeCvetkovic, VladimirAndricevic, Roko
By organisation
Land and Water Resources Engineering
In the same journal
Water resources research
Water Engineering

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 1007 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf