Transcript МАКРОДИСПЕРСИЯ В ПОРИСТЫХ СРЕДАХ

Diffusive Evolution of Gaseous and
Hydrate Horizons of Methane in Seabed
Denis S. Goldobin (University of Leicester),
et al. (“Quaternary hydrate stability”)
MethaneNet Early Career Workshop ̶ Milton Keynes
29.04.2011
Evolution of Methane Horizons in Seabed
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Methane-bearing sediments
the Blake Ridge
crest
Florida
ODP Leg 164; Blake Ridge
Evolution of Methane Horizons in Seabed
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For our study:
- bubbles are immovably
trapped by porous matrix
Therefore,
- transport of methane mass
through aqueous solution;
- this transport is
the molecular diffusion
(not hydrodynamic dispersion)
+ advection
Mechanisms and origins of
bubble seepage do not break
our conclusions!
R.R. Haacke, G.K. Westbrook, M.S. Riley, J. Geophys. Res. 113, B05104 (2008)
Evolution of Methane Horizons in Seabed
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Molecular Diffusion & Thermodiffusion
Diffusive flux of molar fraction X:
thermodiffusion
r
r
éÑ X
ÑT
M 2g ù
ú
J = - DX ê
+a
êë X
T
RT ú
û
gravitational
stratification
a
CH4
?? 1.8 ??
CH3OH
1.5
C2H5OH
3.0
CO2
9.4 g/mol
C3H7OH (iso-)
4.5
CH4
-24.3 g/mol
CH3-CO-CH3
2.5
M2
Evolution of Methane Horizons in Seabed
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Diffusive solute fluxes:
r
r
éÑ X
ÑT
M 2g ù
ú
J = - DX ê
+a
êë X
T
RT ú
û
Evolution of Methane Horizons in Seabed
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Thermodiffusion to Form Bubbly Layers
G = 40
K
km
the Blake Ridge
crest
Florida
Evolution of Methane Horizons in Seabed
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Thermodiffusion to Form Bubbly Layers
G = 60
The Cascadia margin
K
km
Evolution of Methane Horizons in Seabed
Global Map of Stability of Free-Gas Zone
• no hydrate stability zone
• mass from free-gas zone diffuses into HSZ
• mass from free-gas zone diffuses deeper into sediments
a=1.0
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Evolution of Methane Horizons in Seabed
Global Map of Stability of Free-Gas Zone
• no hydrate stability zone
• mass from free-gas zone diffuses into HSZ
• mass from free-gas zone diffuses deeper into sediments
a=1.8
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Evolution of Methane Horizons in Seabed
Global Map of Stability of Free-Gas Zone
• no hydrate stability zone
• mass from free-gas zone diffuses into HSZ
• mass from free-gas zone diffuses deeper into sediments
a=2.5
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Presence of Methane Hydrate
Presence of Methane Hydrate
• Hydrate is more «preferable» than vapour phase.
In equilibrium, aqueous solubility of gas decreases.
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Evolution of Methane Horizons in Seabed
Conclusions
• Given the solubility depends on pressure and temperature,
thermodiffusion can lead to the formation of horizons of
non-dissolved substance (ex.: methane gas or hydrate).
• Concerning hydrates (methane, etc.),
– gaseous horizon can exist independently of the hydrate stability
zone (seismic prospecting detects gaseous horizons);
– mass can migrate from the hydrate horizon into the gaseous one;
– the gaseous horizon does not necessarily touch the HSZ.
D.S.G.&N.V.Brilliantov (2011) submitted [arXiv:1011.5140]
D.S.Goldobin et al. (2011) to be submitted [arXiv:1011.6345]
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Thank you!
Bubbles in a porous medium
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Bubbles in a porous medium
• Mass transport
Motion of a solitary bubble
― is always unstable to splitting
D.V. Lyubimov, et.al., Instability of a drop
moving in a brinkman porous medium,
Phys. Fluids 21, 014105 (2009)
P.G. Saffman & G. Taylor, The penetration of
a fluid into a porous medium or Hele-Shaw
cell containing a more viscous liquid,
Proc. Roy. Soc. Lond. A 245, 312 (1958)
Trapping the bubble in pores: r ~ l pore ~ 2.7mm
Bubbles in a porous medium
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When a bubble is solitary?
• Effective permeability of a porous medium for twocomponent mixture
«monodisperse» sand
(porosity 40%):
polydisperse sand
(porosity 33%):
Bubbles in a porous medium
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Diffusion of aqueous solution
• molecular diffusion
D » 10- 9 m 2/ s
• hydrodynamic dispersion (diffusion)
DP = V d 1 ,
D^ = V d2 .
Bubbles in a porous medium
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Hydrodynamic dispersion in
bubbly geological systems
lateral
hydrodynamic
Ground water flow
dispersion
• J.H. Donaldson, et.al., Dissolved gas transport in the presence of a
trapped gas phase: Experimental evaluation of a two-dimensional
kinetic model, Ground Water 36, 133 (1998)
Infiltration of pressure gradient related to global
ocean currents into seabed
D conv ~ V 2 t
corr
~ V ×l corr
V ~ 10- 9m/ s ( Ñ p ~ 10- 5 Pa/ m)
D mol » 10- 9 m 2/ s
Bubbles in a porous medium
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Solubility of a gas in a liquid
Concentration of gas molecules in a liquid is such that the
solution is in thermodynamic equilibrium with the vapour
phase: chemical potentials in two phases are equal
• Scaled particle theory for the solution
R. A. Pierotti, A scaled particle theory of aqueous and
nonaqueous solutions, Chemical Reviews 76, 717 (1976)
• Van der Waals equation for the vapour phase
Molar fraction of gas molecules in the solution:
X
(0)
(1 - Y )P v liq
é Gc + Gi
2an
1 ù
=
exp ê+
ú
êë
R T (1 - nb )
kT
kT
1 - nb ú
û
Bubbles in a porous medium
Solubility of a gas in a liquid
X
(0)
(1 - Y )P v liq
é Gc + Gi
2an
1 ù
=
exp ê+
ú
êë
R T (1 - nb )
kT
kT
1 - nb ú
û
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