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