co2-hydrates andreas jäger václav vinš roland span · pdf file-hydrates...

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.


Introduction







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







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


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


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


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


CO2 hydrates

• Data

Thermal expansion

Compressibility (few data, no direct measurements)

Phase equilibrium data

5


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


The system H2O - CO2

6

• pTx diagram for the system H2O - CO2

Diamond (2001) demonstrated the complexity of this

system:



6



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!



6



system:

Solid H2O:

Feistel, R.; Wagner, W. (2006)



6



system:

Solid CO2:

Jäger, A.; Span, R. (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



8



system:

Hydrates:

Modified model of Ballard

and Sloan (2002)


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



9


slightly modified:

,, , , ln 1 ,H

w J w i i J J

i J


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



9


slightly modified:

,, , , ln 1 ,H

w J w i i J J

i J


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



9


slightly modified:

,, , , ln 1 ,H

w J w i i J J

i J


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



9


slightly modified:

,, , , ln 1 ,H

w J w i i J J

i J


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



9


slightly modified:

• Adjustable parameters of the model:

,, , , ln 1 ,H

w J w i i J J

i J


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


Available phase equilibrium data

10


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


Three phase equilibria with hydrates

12


VHIw

VLwH


13


VLcH

LwLcH

14



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


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)


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


Thank you!

Questions?

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