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| Titel |
An Eulerian joint velocity-concentration PDF method for solute dispersion in highly heterogeneous porous media |
| VerfasserIn |
Daniel W. Meyer, Hamdi A. Tchelepi, Patrick Jenny |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250036590
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| Zusammenfassung |
| In risk analysis applications involving heterogeneous formations, the knowledge of the solute
concentration probability density function (PDF) at different spatial locations and times is
crucial. We propose a new joint velocity-concentration PDF method applicable for
highly heterogeneous porous media that accounts for advective transport, pore-scale
dispersion and molecular diffusion. Unlike in low order approximation (LOA) methods
that are valid for low conductivity variances ÏăY 2 and where the one-point velocity
PDF is typically assumed to be a Gaussian, the proposed joint PDF method honors
the increasingly non-Gaussian velocity one-point PDF and the long-term velocity
correlations that were reported in different Monte Carlo (MC) studies for ÏăY 2 > 0.5
[e.g., Salandin, P. and V. Fiorotto, WRR, 1998. 34(5) and Trefry, M.G., F.P. Ruan,
and D. McLaughlin, WRR, 2003. 39(3)]. Furthermore, the new joint PDF method
does not involve any a-priori assumption about the shape of the resulting marginal
concentration PDF. LOA methods that provide information on the concentration
mean and variance [Fiori, A. and G. Dagan, Journal of Contaminant Hydrology,
2000. 45(1-2)] on the other hand are typically complemented by assuming that the
concentration PDF has a β-PDF shape [Bellin, A. and D. Tonina, Journal of Contaminant
Hydrology, 2007. 94(1-2)]. The Eulerian joint velocity-concentration PDF transport
equation in our model is numerically solved with a computationally efficient particle
method. The suggested joint PDF method is validated by comparison with MC data
reported by Caroni and Fiorotto for Péclet numbers ranging from 10 to 104 and
ÏăY 2 = 1 and 2 [Caroni, E. and V. Fiorotto, Transport in Porous Media, 2005. 59(1)]. |
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