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| Titel |
Velocity dependence of biphasic flow structuration: steady-state and oscillating flow effects |
| VerfasserIn |
Ken Tore Tallakstad, Mihailo Jankov, Grunde Løvoll, Renaud Toussaint, Knut Jørgen Måløy, Eirik Grude Flekkøy, Jean Schmittbuhl, Gerhard Schäfer, Yves Meheust, Henning Arendt Knudsen |
| 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 |
250043915
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| Zusammenfassung |
| We study various types of biphasic flows in quasi-two-dimensional transparent porous
models. These flows imply a viscous wetting fluid, and a lowly viscous one. The models are
transparent, allowing the displacement process and structure to be monitored in space and
time. Three different aspects will be presented: 1. In stationary biphasic flows, we
study the relationship between the macroscopic pressure drop (related to relative
permeability) and the average flow rate, and how this arises from the cluster size
distribution of the lowly viscous fluid [1]. 2. In drainage situations, we study how
the geometry of the invader can be explained, and how it gives rise to apparent
dynamic capillary effects. We show how these can be explained by viscous effects on
evolving geometries of invading fluid [2]. 3. We study the impact of oscillating
pressure fields superimposed to a background flow over the flow regimes patterns
[3].
Steady-State Two-Phase Flow in Porous Media: Statistics and Transport Properties. First,
in stationary flow with a control of the flux of both fluids, we show how the pressure drop
depends on the flow rate. We will show that the dynamics is dominated by the interplay
between a viscous pressure field from the wetting fluid and bubble transport of a less viscous,
nonwetting phase. In contrast with more studied displacement front systems, steady-state
flow is in equilibrium, statistically speaking. The corresponding theoretical simplicity
allows us to explain a data collapse in the cluster size distribution of lowly viscous
fluid in the system, as well as the relation |-P|--Ca--. This allows to explain so
called relative permeability effects by the morphological changes of the cluster size
distribution.
Influence of viscous fingering on dynamic saturation-pressure curves in porous media.
Next, we study drainage in such models, and investigate the relationship between the pressure
field and the morphology of the invading fluid. This allows to model the impact of the
saturation changes in the system over the pressure difference between the wetting
and non wetting phase. We show that the so-called dynamic effects referred in the
hydrology 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.
Effects of pressure oscillations on drainage in an elastic porous medium: The effects of
seismic stimulation on the flow of two immiscible fluids in an elastic synthetic porous
medium is experimentally investigated. A wetting fluid is slowly evacuated from the medium,
while a pressure oscillation is applied on the injected non-wetting fluid. The amplitude and
frequency of the pressure oscillations as well as the evacuation speed are kept constant
throughout an experiment. The resulting morphology of the invading structure is found to be
strongly dependent on the interplay between the amplitude and the frequency of the
applied pressure oscillations and the elasticity of the porous medium. Different
combinations of these properties yield morphologically similar structures, allowing a
classification of structures that is found to depend on a proposed dimensionless
number.
[1] Tallakstad, K.T., H.A. Knudsen, T. Ramstad, G. Løvoll, K.J. Maløy, R. Toussaint and
E.G. Flekkøy , Steady-state two-phase flow in porous media: statistics and transport
properties, Phys. Rev. Lett. 102, 074502 (2009). doi:10.1103/PhysRevLett.102.074502 [2]
Løvoll, G., M. Jankov, K.J. Maløy, R. Toussaint, J. Schmittbuhl, G. Schaefer and Y. M´
eheust, Influence of viscous fingering on dynamic saturation-pressure curves in porous media,
submitted to Transport In Porous Media, (2010) [3] Jankov, M., G. Løvoll, H.A. Knudsen,
K.J. Maløy, R. Planet, R. Toussaint and E.G. Flekkøy; Effects of pressure oscillations on
drainage in an elastic porous medium, Transport In Porous Media, in press (2010). |
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