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| Titel |
Evolution of a gas bubble in porous matrix filled by methane hydrate |
| VerfasserIn |
Kirill Tsiberkin, Dmitry Lyubimov, Tatyana Lyubimova, Oleg Zikanov |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250081803
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| Zusammenfassung |
| Behavior of a small isolated hydrate-free inclusion (a bubble) within hydrate-bearing porous
matrix is studied analytically and numerically.
An infinite porous matrix of uniform properties with pores filled by methane
hydrates and either water (excessive water situation) or methane gas (excessive gas
situation) is considered. A small spherical hydrate-free bubble of radius R0 exists at
initial moment within the matrix due to overheating relative to the surrounding
medium.
There is no continuing heat supply within the bubble, so new hydrate forms on its
boundary, and its radius decreases with time. The process is analysed in the framework of the
model that takes into account the phase transition and accompanying heat and mass transport
processes and assumes spherical symmetry. It is shown that in the case of small
(~ 10-2-10-1 m) bubbles, convective fluxes are negligible and the process is fully described
by heat conduction and phase change equations.
A spherically symmetric Stefan problem for purely conduction-controlled evolution is
solved analytically for the case of equilibrium initial temperature and pressure within the
bubble. The self-similar solution is verified, with good results, in numerical simulations based
on the full filtration and heat transfer model and using the isotherm migration method.
Numerical simulations are also conducted for a wide range of cases not amenable to
analytical solution.
It is found that, except for initial development of an overheated bubble, its radius evolves
with time following the self-similar formula:
R(t) ( t)1-2
R0–= 1 - tm- ,
(1)
where tm is the life-time of bubble (time of its complete freezing). The analytical solution
shows that tm follows
2
tm ~ (R0-Î ) ,
(2)
where Î is a constant determined by the temperature difference ΔT between the bubble’s
interior and far field.
We consider implications for natural hydrate deposits. As an example, for a bubble with
R0 = 4 cm and ΔT = 0.001 K, we find tm ~ 5.7 -
106 s (2 months) in a water excess
system, and ~ 2.9 -
107 s (11 months) in a gas excess system.
Motion of the bubble is not considered in our study, but it can be estimated that at the
typical velocity of buoyancy-driven transport, a small bubble does not move a significant
distance over its life-time and, thus, cannot survive filtration through the hydrate stability
zone.
Work was financially supported by the Civilian Research and Development Foundation
(Grant RUP1-2945-PE-09) and the Russian Foundation for Basic Research (Grant
09-01-92505). |
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