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| Titel |
Influence of viscous fingering on dynamic saturation-pressure curves in porous media |
| VerfasserIn |
G. Løvoll, R. Toussaint, K. J. Måløy, G. Schaefer, J. Schmittbuhl, M. Jankov, Y. Méheust |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250030084
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| Zusammenfassung |
| We study drainage-imbibition experiments on quasi-two-dimensional porous models. The
models are transparent, allowing the displacement process and structure to be monitored in
space and time. Results obtained in the case of quasi-static drainage cycles are compared to
standard water retention experiments.
We show that the so-called dynamic effects referred in the literature of experimentally
measured capillary pressure curves might be explained by the combined effect of capillary
pressure along the invasion front of the gaseous phase and pressure changes caused by
viscous effects.
A detailed study of the structure optically followed shows that the geometry of the invader
is self-similar with two different behaviors at small and large scales: the structure corresponds
to the ones of invasion percolation models at small scales (capillary fingering structures with
fractal dimension D=1.83), whereas at large scales, viscous pressure drops dominate over the
capillary threshold variations, and the structures are self-similar fingering structures with a
fractal dimension corresponding to Dielectric Breakdown Models (variants of the DLA
model), with D-1.5. The cross-over scale is set by the scale at which capillary fluctuations
are of the order of the viscous pressure drops. This leads physically to the fact that
cross-over scale between the two fingering dimensions, goes like the inverse of the
capillary number. This study utilizes these geometrical characteristics of the viscous
fingers forming in dynamic drainage, to obtain a meaningfull scaling law for the
saturation-pressure curve at finite speed, i.e. the so-called dynamic capillary pressure
relations. We thus show how the micromechanical interplay between viscous and
capillary forces leads to some pattern formation, which results in a general form of
dynamic capillary pressure relations. By combining these detailed informations
on the displacement structure with global measures of pressure, saturation and
controlling the capillary number Ca, a scaling relation relating pressure, saturation,
system size and capillary number is developed. By applying this scaling relation,
pressure-saturation curves for a wide range of capillary numbers can be collapsed. |
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