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| Titel |
From viscous fingers to wormholes - interactions between structures emerging in unstable growth |
| VerfasserIn |
Agnieszka Budek, Kamil Kwiatkowski, Piotr Szymczak |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250137870
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| Publikation (Nr.) |
 EGU/EGU2017-725.pdf |
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| Zusammenfassung |
| Dissolution of porous and fractured rock can lead to instabilities, where long finger-like
channels or „wormholes” are spontaneously formed, focusing the majority of the flow.
Formation of those structures leads to a significant increase in permeability of the
system, and is thus important in many engineering applications, e.g. in acidization
during oil and gas recovery stimulation. In this communication, we analyse this
process using two different numerical models (a network model and a Darcy scale
one). We show that wormhole patterns depend strongly on the amount of soluble
material in the system, as quantified by the permeability contrast κ between the
dissolved and undissolved medium. For small and intermediate values of κ, a large
number of relatively thin and strongly interacting channels are formed. The longer
channels attract shorter ones, with loops being formed as a result. However, for
large values of κ the pattern gets sparse with individual wormholes repelling each
other.
Interestingly, a similar succession of patterns can be observed in viscous fingering in a
rectangular network of channels. In such a system, anisotropy of the network promotes the
growth of long and thin fingers which behave similarly to wormholes. The attraction rate
between growing fingers depends strongly on the viscosity ratio, I. The latter plays a role
similar to that of permeability ratio for dissolution of porous material. To explain this
behaviour, we have created a simple analytical model of interacting fingers, allowing us to
quantify their mutual interaction as a function of finger lengths, distances between them and –
most importantly – relative permeabilities. The theoretical predictions are in a good
agreement with simulation data for both dissolution and viscous fingering processes. |
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