Oct 2, 2009 - ... and Technology,. University of Bergen, Bergen, Norway ... Bunz et al., 2003), b) Seismic profile showing BSR characteristics on the western ...
Phase Field Theory modelling of methane fluxes from exposed natural gas hydrate reservoirs ICCMSE 2009, October 2, 2009 Hotel Rodos Palace, Rhodes, Greece Bjørn Kvamme, Pilvi-Helina Kivela, Khuram Baig, Mohammad Quasim Department of Physics and Technology, University of Bergen, Bergen, Norway
OUTLINE • A few words about hydrate and thermodynamic regions of stability • Global resources of hydrate and methane hydrate as threat to the environment • Theoretical modelling • Conclusions
What is natural gas hydrate? • Methane and other small no-polar (or slightly polar) molecules immersed in water will induce organisation of the water structure that maximizes the entropy. • Above certain pressures, and below certain temperatures , this results in a phase transition over to a solid like structure.
The glass to the right contains water at 0 C The pipe to the left contains hydrate at 5 C
Gas Hydrates: A Major Energy Resource:
http://geology.usgs.gov/
But also an environmental ”bomb” if released and entering the atmosphere. Methane is 25 times as aggressive as greenhouse gas compared to carbon dioxide
Pure methane and pure carbon dioxide form structure I hydrate with water
Hydrate Structures:
Ratio of 3:1 of large cavities to small cavities. Carbon dioxide can only fill large cavities
www.pet.hw.ac.uk/
Regions of pressure and temperature for stability of some hydrates Solid line is liquid/ice coexistence curve
120
Dashed line is for methane hydrate
100
Dash-dot is for 2 per cent ethane in methane + are hydrate formed from water and an ethane-rich mixture with methane (3 per cent)
P(bar)
80
60
40
20
0 250
260
270
280 T(K)
290
300
310
The motivation (and correspoding funding) for Norwegian hydrate research have earlier been related to either transport and processing issues or specific offshore installation concerns
Ormen Lange is an ordinary offshore oil and gas field. But the transport to shore passes regions of hydrate and the stability of these formations with respect to technical installations is a concern.
The tsunami following the first massive collapse due to rapidly dissociating hydrate in Storegga 7000 years ago drowned the lowlands of Skotland Extensive dissociation and hydrate, with corresponding limited collapses may have occured as late as 250 years ago
Remaining hydrate in Storegga is estimatet to about 4000 square kilometer with acerage thickness 40 – 50 m
Why? Hydrates in reservoirs are generally not stable and relate to trappings just like free hydrocarbons
a) BSR distribution on the south Vøring and Storegga Slide region (from Bunz et al., 2003), b) Seismic profile showing BSR characteristics on the western Svalbard margin (from Vanneste et al., submitted), c) Seismic and side scan sonar characteristics of a fluid migration pathway on the Mid-Norwegian (from Berndt et al., 2003)
Three component Phase Field Theory F
3 ε 2T ε 2T 2 2 i, j ci ∇c j − c j ∇ci ) + fbulk (ϕ , c1 , c2 , c3 , T ) ( ∫ d r 2 ( ∇ϕ ) + i∑ 4 , j =1 = fbulk wTg (ϕ ) + [1 − p(ϕ )] f S (c1 , c2 , c3 , T ) + p(ϕ ) f L (c1 , c2 , c3 , T )
δF + ζϕ δϕ
−M ϕ ϕ = 3
∑c i =1
i
=1
δF ∇M ci (c1 , c2 , c3 )∇ −ζi ci = δ ci
Parameters ε and w can be fixed from the interface thickness and interface free energy. ε ij set equal to ε
Interface density profiles for aqueous solution and hydrate
The sampled average interface thickness is applied (0.85 nm). Work is in progress on estimation of interface free energy but for the moment the Experimental value for ice/liquid water of 29 mJ/m2 (Hardy, 1956) is used
Interface thickness d and interface free energy fixes the two model parameters w and ε in the Phase FieldTheory. Evaluation of these parameters from model systems by Molecular Dynamics simulations of model systems Estimated to 8.5 Å – see previous overhead
d
1/ 2 0.95
ε T 2 2
γ ∞ = (ε T ) 2
∫ dξ {∆f [ξ , c(ξ )]}
−1/ 2
0.05
1
1/ 2
∫ dξ {∆f [ξ , c(ξ )]}
1/ 2
0 Phase Field Theory parameter ε Interface free energy ≈ 29 mJ/m2
Phase Field Theory parameter w is in the free energy f (see PFT slide)
where ∆f = f − f0, and
∂f L f 0 = f L (c ) + ( ) ceq (c − cLeq ) ∂c L ∂f = f S (cSeq ) + ( S ) ceq (c − cSeq ) ∂c S eq L
CO2 hydrate is more stable than methane hydrate The free energy profile is constructed from MD simulations (Kvamme & Tanaka,1995) and verified to reproduce experimental stability regions (Svandal et.al., 2006) Can it be experimentally verified that this will practically work in porous Medium?
Concentration of Methane inside the Hydrate at Different Regions 0.16
A B C D E
Concentration (Mole Fraction)
0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0
0.2
0.4
0.6
0.8
1
Time (sec)
1.2
1.4
1.6
1.8 -8 x 10
A,B,C,D & E are points away from the original interface
A=10 Å B=30 Å C=60Å D=80Å E=1000Å
Fluxes of Methane from Nyegga Site 2.5
x 10
5
10
8
5
10
Dissolution Rates (mmol/m s)
10
4
10
1.5 3
10
0
2
8
6
4
-9
x 10
1
0.5
10
10
4
-7.6
10
10
2
-7.7
10
-7.8
10
10
10
10
10
0 0
-7.4
10
-7.5
2
Dissolution Rate (mmol/m2s)
2
6
0 2
3
10
4
10
10
-2
-4
-6
-8
0.2
0.4
0.6
0.8
Time (Sec)
1
1.2
1.4
10 -25 10
1.6 x 10
-8
10
-20
10
-15
10
-10
10
-5
10
0
Time (years)
Dissolution rates and Extrapolation from 16.13 ns to 10000years. Applied PFT theory implicitly assumes that the kinetic rate of dilution of the released methane in the surrounding water is faster than the dissociation rate. Results are 2 – 4 orders of magnitudes higher than in situ observations
10
5
Further progress: Phase Field Theory with hydrodynamics (work in progress)
Conclusions • In situ observations of methane fluxes from exposed hydrate reservoirs are few and accuracy as well as relevance uncertain • Phase Field Theory without hydrodynamics underestimates methane fluxes from Nyegga by 2 – 4 orders of magnitude but then again these fluxes are characterized as pocmarks (visible bubbles) and could even be more or less open channels of fractures from direct methane souces
Conclusions continued • A method for extension of the Phase Field Theory with hydrodynamics is proposed and work is yet in progress on the implementation of this.
