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CO2-Hydrates
Andreas Jäger Václav Vinš
Roland Span Jan Hrubý
GERG ACADEMIC NETWORK EVENT - 2012
Brussels, June 15, 2012
2 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Introduction
• Relevance of gas hydrates to industry and science
Hydrates may form in gas pipelines
The pipelines might get blocked
due to hydrate formation
Prediction of hydrate formation is very
relevant to gas industry
1
http://www.planeterde.de/Members/holge
rkroker/1101/Gaspipeline-Sibirien-
WEG.jpg/image_preview
© Wirtschaftsverband Erdöl und
Erdgasgewinnung e.V.
3 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Introduction
• Relevance of gas hydrates to industry and science
Hydrates may form in gas pipelines
The pipelines might get blocked
due to hydrate formation
Prediction of hydrate formation is very
relevant to gas industry
Models for hydrate formation are available (e.g.,
Ballard and Sloan (2002))
None of the existing models might be used with highly
accurate EoS (like the GERG EoS)
1
http://www.planeterde.de/Members/holge
rkroker/1101/Gaspipeline-Sibirien-
WEG.jpg/image_preview
© Wirtschaftsverband Erdöl und
Erdgasgewinnung e.V.
4 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Introduction
• Relevance of gas hydrates to industry and science
Hydrates may form in gas pipelines
The pipelines might get blocked
due to hydrate formation
Prediction of hydrate formation is very
relevant to gas industry
Models for hydrate formation are available (e.g.,
Ballard and Sloan (2002))
None of the existing models might be used with highly
accurate EoS (like the GERG EoS)
1
http://www.planeterde.de/Members/holge
rkroker/1101/Gaspipeline-Sibirien-
WEG.jpg/image_preview
© Wirtschaftsverband Erdöl und
Erdgasgewinnung e.V.
5 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Introduction
• Hydrates also relevant to
CCS-Technology (CO2 hydrate + mixtures)
Separated CO2 from power plants will always contain
water
The tolerable amount of water has to be determined
Models for the prediction of hydrates in the complex
system CO2 / water required
2
6 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Introduction
• Hydrates also relevant to
CCS-Technology (CO2 hydrate + mixtures)
Separated CO2 from power plants will always contain
water
The tolerable amount of water has to be determined
Models for the prediction of hydrates in the complex
system CO2 / water required
First step: Focus on CO2 hydrates
2
7 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Introduction
• Gas hydrates
Are solid mixtures of water with other substances
The water forms metastable cages that are stabilized
by a so called guest molecule
Dependent on the guest the structures SI (8:46), SII
(24:136) and SH (6:34) might be formed
Different types of cages exist and not every cage has to
be filled in order to form thermodynamically stable
hydrate
The composition of hydrates may vary
3
8 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
CO2 hydrates
• Cooperation with the Academy of Sciences
in Prague (Václav Vinš, Jan Hrubý)
• CO2 hydrates – literature review:
Structure SI, six large,
two small cages
Composition is not fixed!
46 molecules of H2O
1 to 8 molecules of CO2
E.D. Sloan and C.A. Koh:
Clathrate hydrates of
natural gases, 3rd ed.,
Taylor & Francis group (2008)
2
2
min
CO
max
CO
1/ 47 0,021
8 / 54 0,148
x
x
Lenny Martinez,
Los Alamos National Laboratory (2009)
4
9 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
CO2 hydrates
• Data
Thermal expansion
Compressibility (few data, no direct measurements)
Phase equilibrium data
5
10 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
CO2 hydrates
• Data
Thermal expansion
Compressibility (few data, no direct measurements)
Phase equilibrium data
• Existing models for hydrates
Ballard and Sloan (2002): fugacity / activity model for
fluid phases
Klauda and Sandler(2000): UNIFAC for fluid phases
Yoon et al. (2004): PSRK for fluid phases
No hydrate model for highly accurate EoS available
5
11 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
The system H2O - CO2
6
• pTx diagram for the system H2O - CO2
Diamond (2001) demonstrated the complexity of this
system:
12 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
The system H2O - CO2
6
• pTx diagram for the system H2O - CO2
Diamond (2001) demonstrated the complexity of this
system:
Fluid region:
H2O: IAPWS
Wagner, W.; Pruss, A. (2002)
CO2: Span, R.; Wagner, W. (1996)
Mixing rules:
Gernert, J.; Span, R. (2010)
AND: GERG 2004 EoS
The focus of this equation is not
on this system!
13 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
The system H2O - CO2
6
• pTx diagram for the system H2O - CO2
Diamond (2001) demonstrated the complexity of this
system:
Solid H2O:
Feistel, R.; Wagner, W. (2006)
14 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
The system H2O - CO2
6
• pTx diagram for the system H2O - CO2
Diamond (2001) demonstrated the complexity of this
system:
Solid CO2:
Jäger, A.; Span, R. (2012)
15 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
EoS for solid CO2
7
• Explicit in the Gibbs energy g(T,p)
• EoS for CO2 by Span and Wagner (1996) & EoS for solid CO2
allows for accurate calculation of sublimation and melting
pressures
-500
-250
0
250
500
80 100 120 140 160 180 200 220
Δp
sub
[Pa
]
T [K]
Uncertainty Calculated
Fernandez-F. and del Rio (1984) Ambrose (1955)
Bedford (1984) Bilkadi (1974)
Bryson (1974) Giauque and Egan (1937)
-2
-1
0
1
2
210 220 230 240 250 260 270
100 Δ
pm
elt/p
mel
t, c
orr
. eq
.
T [K]
Uncertainty Calculated Michels (1942) Clusius (1960)
Sublimation pressure
Melting pressure
16 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
The system H2O - CO2
8
• pTx diagram for the system H2O - CO2
Diamond (2001) demonstrated the complexity of this
system:
Hydrates:
Modified model of Ballard
and Sloan (2002)
17 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Model for CO2 hydrates
9
• The model of Ballard und Sloan (2002) was chosen and
slightly modified:
,, , , ln 1 ,H
w J w i i J J
i J
T p f g T p RT v C T p f
18 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Model for CO2 hydrates
9
• The model of Ballard und Sloan (2002) was chosen and
slightly modified:
,, , , ln 1 ,H
w J w i i J J
i J
T p f g T p RT v C T p f
0 0
,0
2
0
, ,d d
pT
w w ww
T p
g T p h T v T pgT p
RT RT RT RT
19 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Model for CO2 hydrates
9
• The model of Ballard und Sloan (2002) was chosen and
slightly modified:
,, , , ln 1 ,H
w J w i i J J
i J
T p f g T p RT v C T p f
0 0
,0
2
0
, ,d d
pT
w w ww
T p
g T p h T v T pgT p
RT RT RT RT
0
,0 d
T
w w pw
T
h T h c T T
-1 -1J mol K
0.12814 K 2.74566
I
pw pwc T c T
T
… Ice Ih ~ cubic ice
20 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Model for CO2 hydrates
9
• The model of Ballard und Sloan (2002) was chosen and
slightly modified:
,, , , ln 1 ,H
w J w i i J J
i J
T p f g T p RT v C T p f
0 0
,0
2
0
, ,d d
pT
w w ww
T p
g T p h T v T pgT p
RT RT RT RT
3AV
3 2 3AV0 1 0 2 0 3 0 0
, ,
exp 3 3 3 3
w w
w
w
Nv T p a T p
N
Na T T T T T T p p
N
21 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Model for CO2 hydrates
9
• The model of Ballard und Sloan (2002) was chosen and
slightly modified:
,, , , ln 1 ,H
w J w i i J J
i J
T p f g T p RT v C T p f
0 0
,0
2
0
, ,d d
pT
w w ww
T p
g T p h T v T pgT p
RT RT RT RT
3AV
3 2 3AV0 1 0 2 0 3 0 0
, ,
exp 3 3 3 3
w w
w
w
Nv T p a T p
N
Na T T T T T T p p
N
3
3 2 3 1 0AV0 1 0 2 0 3 0
2 0
exp 3 3 3 11
a
a a a
w a
p pNa T T T T T T
N p p
22 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Model for CO2 hydrates
9
• The model of Ballard und Sloan (2002) was chosen and
slightly modified:
• Adjustable parameters of the model:
,, , , ln 1 ,H
w J w i i J J
i J
T p f g T p RT v C T p f
Langmuirconstant: s and e are
adjustable parameters
1 2, ,0 ,0,w wg h ,s e
Reference state Pressure dependence
of the molar volume
Potential-
parameters
23 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Available phase equilibrium data
10
24 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Fitting procedure
• Calculate the respective two phase equilibrium at hydrate
formation conditions, i.e. T and p, (LwLc, VLw, VIw, VLc)
Get the chemical potential of water in hydrate
and the fugacity of the guest
Fit the parameters of
the hydrate model
H
w
2COf
, ,H
w JT p f
11
25 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Three phase equilibria with hydrates
12
26 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
VHIw
VLwH
Three phase equilibria with hydrates
13
27 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
VLcH
LwLcH
14
Three phase equilibria with hydrates
28 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Summary
15
• Established modified hydrate model of Ballard and Sloan
(2002) for pure CO2 hydrate
• Fitted to data on
Thermal expansion
Compressibility
Phase equilibria
• Accurate prediction of hydrate formation using the hydrate
model and either the reference equations or the GERG
2004 equations
29 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Outlook
16
• Collecting data and fitting the hydrate model for CH4
hydrates GERG 2004 results interesting!!
E.D. Sloan and C.A. Koh:
Clathrate hydrates of
natural gases, 3rd ed.,
Taylor & Francis group (2008)
30 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Outlook
16
• Collecting data and fitting the hydrate model for CH4
hydrates GERG 2004 results interesting!!
• Hydrate formation in multicomponent mixtures
More difficult since the structure of the hydrate is also
unknown
31 Andreas Jäger, Václav Vinš, Roland Span, Jan Hrubý June 15, 2012
Thank you!
Questions?