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| Titel |
Fluid Stretching in Heterogeneous Porous Media as a Lévy Process |
| VerfasserIn |
Marco Dentz, Daniel R. Lester, Tanguy Le Borgne, Felipe P. J. de Barros |
| Konferenz |
EGU General Assembly 2016
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 18 (2016) |
| Datensatznummer |
250126960
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| Publikation (Nr.) |
 EGU/EGU2016-6757.pdf |
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| Zusammenfassung |
| Stretching and compression of material fluid elements is key for the understanding and
quantification of the dispersion and mixing dynamics in heterogeneous porous media flows,
because they represent the support of a transported solute. The elongation and compression of
a material strip determine the mixing volume and mixing rate and thus the concentration
content of a heterogeneous mixture. While linear and exponential elongation dynamics
typical for shear and chaotic flows, respectively, are well understood, the mechanisms that
lead toobserved power-law elongation in heterogeneous porous media are in general
unknown. We cast the fluid deformation problem in streamline coordinates, which reveals
that the principal elongation mechanism for non-helical steady flows is due to shear
deformation and velocity fluctuations along the streamline. The impact of this coupling on the
elongation dynamics is quantified within a continuous time random walk (CTRW)
approach. The CTRW describes the movement of fluid particles in porous media flows
through a random in both space and time, in which the transition time τ over a
characteristic velocity length scale ℓc is coupled kinematically to streamline velocity vs
as τ = ℓc∕vc. In this framework, the elongation process isidentified as a coupled
CTRW in which the elongation increment is related to the transition time through the
velocity-shear coupling. For a broad distribution of transition, as found in strongly
heterogeneous porous media, the elongation is a Lévy process. These dynamics
describe a broad range of algebraic stretching behaviors with mean strip elongations
⟨ℓ(t)⟩∝ tν with 1∕2 ≤ ν < 2. These findings have broad implications for the
understanding and prediction of dilution and mixing in heterogeneous porous media flows. |
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