Diffusive Evolution of Gaseous and Hydrate Horizons of Methane in Seabed

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1 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

2 Evolution of Methane Horizons in Seabed 2 Methane bearing sediments the Blake Ridge crest Florida ODP Leg 164; Blake Ridge

3 Evolution of Methane Horizons in Seabed 3 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)

4 Evolution of Methane Horizons in Seabed 4 Molecular Diffusion & Thermodiffusion Diffusive flux of molar fraction X: thermodiffusion X T Mg = + J DX 2 α X T R T α CH 4?? 1.8?? CH 3 OH 1.5 C 2 H 5 OH 3.0 C 3 H 7 OH (iso ) 4.5 CH 3 CO CH CO 2 CH 4 gravitational stratification M g/mol 24.3 g/mol

5 Evolution of Methane Horizons in Seabed 5 Diffusive solute fluxes: X T Mg = + J DX 2 α X T R T

6 Evolution of Methane Horizons in Seabed 6 Thermodiffusion to Form Bubbly Layers K G = 40 km the Blake Ridge crest Florida

7 Evolution of Methane Horizons in Seabed 7 Thermodiffusion to Form Bubbly Layers K G = 60 km The Cascadia margin

8 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 α=1.0

9 Evolution of Methane Horizons in Seabed 9 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 α=1.8

10 Evolution of Methane Horizons in Seabed 10 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 α=2.5

11 Presence of Methane Hydrate 11 Presence of Methane Hydrate Hydrate is more «preferable» than vapour phase. In equilibrium, aqueous solubility of gas decreases.

12 Evolution of Methane Horizons in Seabed 12 Conclusions Given the solubility depends on pressure and temperature, thermodiffusion can lead to the formation of horizons of non dissolved substance (ex.( 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: ] D.S.Goldobin et al. (2011) to be submitted [arxiv: ]

13 Thank you!

Fluids 21, 014105 (2009) P.G. Saffman & G.

14 Bubbles in a porous medium 14 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, (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

15 Bubbles in a porous medium 15 When a bubble is solitary? Effective permeability of a porous medium for twocomponent mixture «monodisperse» sand polydisperse sand (porosity 40%): (porosity 33%):

16 Bubbles in a porous medium 16 Diffusion of aqueous solution molecular diffusion D m /s hydrodynamic dispersion (diffusion) D = Vd, D = Vd. 1 2

Bubbles in a porous medium 17 Hydrodynamic dispersion in bubbly geological

17 Bubbles in a porous medium 17 Hydrodynamic dispersion in bubbly geological systems V Ground water flow D ~ V τ ~ V l 2 conv corr corr p 9 5 ~10 m/s ( ~10 Pa/m) lateral hydrodynamic 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 mol m /s

18 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 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: (0) ( 1 Y ) Pv liq c i 2 1 exp G + G an X = + RT ( 1 nb) kt kt 1 nb

19 Bubbles in a porous medium 19 Solubility of a gas in a liquid (0) ( 1 Y ) Pv liq c i 2 1 exp G + G an X = + RT ( 1 nb) kt kt 1 nb

Thermodynamics is the study of the relationship between heat and other forms of energy that are involved in a chemical reaction.

Ch 18 Thermodynamics and Equilibrium Thermodynamics is the study of the relationship between heat and other forms of energy that are involved in a chemical reaction. Internal Energy (U) Internal energy