Diffusive Evolution of Gaseous and Hydrate Horizons of Methane in Seabed Denis S. Goldobin...
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Transcript of Diffusive Evolution of Gaseous and Hydrate Horizons of Methane in Seabed Denis S. Goldobin...
Diffusive Evolution of Gaseous and Diffusive Evolution of Gaseous and Hydrate Horizons of Methane in SeabedHydrate Horizons of Methane in Seabed
Denis S. Goldobin (University of Leicester),Denis S. Goldobin (University of Leicester),et al.et al. (“Quaternary hydrate stability”) (“Quaternary hydrate stability”)
MethaneNet Early Career Workshop MethaneNet Early Career Workshop ̶̶ Milton KeynesMilton Keynes
2929..0404.20.201111
Evolution of Methane Horizons in Seabed 2
Methane-bearing sediments
ODP Leg 164; Blake Ridge
the Blake Ridgecrest
Florida
Evolution of Methane Horizons in Seabed 3
R.R. Haacke, G.K. Westbrook, M.S. Riley, J. Geophys. Res. 113, B05104 (2008)
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!
Evolution of Methane Horizons in Seabed 4
Molecular Diffusion & Thermodiffusion
2
rr X M gR
J DXX T
TT
a -é ùÑê ú=-ê úë û
Ñ+
Diffusive flux of molar fraction X: thermodiffusion
gravitationalstratification
M2
CO2 9.4 g/mol
CH4 -24.3 g/mol
CH4 ?? 1.8 ??
CH3OH 1.5
C2H5OH 3.0
C3H7OH (iso-) 4.5
CH3-CO-CH3 2.5
Evolution of Methane Horizons in Seabed 5
2
rr X M gR
J DXX T
TT
a -é ùÑê ú=-ê úë û
Ñ+
Diffusive solute fluxes:
Evolution of Methane Horizons in Seabed 6
Thermodiffusion to Form Bubbly Layers
the Blake Ridgecrest
Florida
K40
kmG =
Evolution of Methane Horizons in Seabed 7
Thermodiffusion to Form Bubbly LayersK
60km
G =
The Cascadia margin
Evolution of Methane Horizons in Seabed 8
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
=1.0
Evolution of Methane Horizons in Seabed 9
=1.8
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
Evolution of Methane Horizons in Seabed 10
=2.5
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
Presence of Methane Hydrate 11
Presence of Methane Hydrate
• Hydrate is more «preferable» than vapour phase.In equilibrium, aqueous solubility of gas decreases.
Evolution of Methane Horizons in Seabed 12
Conclusions
• Given the solubility depends on pressure and temperature, Given the solubility depends on pressure and temperature, thermodiffusion can lead to the formation of horizons of thermodiffusion can lead to the formation of horizons of non-dissolved substance (non-dissolved substance (ex.ex.: methane gas or hydrate): methane gas or hydrate)..
• Concerning hydratesConcerning hydrates ( (methane, methane, etc.etc.),),
– gaseous horizon can exist independently of the hydrate stability gaseous horizon can exist independently of the hydrate stability zonezone ( (seismic prospecting detects gaseous horizonsseismic prospecting detects gaseous horizons););
– mass can migrate from the hydrate horizon into the gaseous one;mass can migrate from the hydrate horizon into the gaseous one;
– the gaseous horizon does not necessarily touch the HSZ.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]
Thank you!
Bubbles in a porous medium 14
Bubbles in a porous medium
• Mass transportMotion 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: pore~ ~2.7mmr l
Bubbles in a porous medium 15
When a bubble is solitary?
• Effective permeability of a porous medium for two-component mixture
«monodisperse» sand polydisperse sand(porosity 40%): (porosity 33%):
Bubbles in a porous medium 16
Diffusion of aqueous solution
• molecular diffusion
• hydrodynamic dispersion (diffusion)
1 2, .PD Vd D Vd^= =
9 210 m/sD -»
Bubbles in a porous medium 17
Hydrodynamic dispersion inbubbly geological systems
Ground water flow
lateral hydrodynamic dispersion
2conv corr corr
9 5
9 2mol
~ ~
~10 m/s( ~10 Pa/m)
10 m/s
D V V l
V p
D
t- -
-
×
Ñ
»
• 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
Bubbles in a porous medium 18
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 solutionR. 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:( )
( )liq(0) 1 2 1exp
1 1c i
Y Pv G G anX
RT nb kT kT nb
- é ù+= - - +ê ú
ê ú- -ë û
Bubbles in a porous medium 19
Solubility of a gas in a liquid
( )( )
liq(0) 1 2 1exp
1 1c i
Y Pv G G anX
RT nb kT kT nb
- é ù+= - - +ê ú
ê ú- -ë û