CO 2 -Hydrates GERG ACADEMIC NETWORK EVENT Brussels, June 15, 2012

Transcription

1 CO 2 -Hydrates Andreas Jäger Roland Span Václav Vinš Jan Hrubý GERG ACADEMIC NETWORK EVENT Brussels, June 15, 2012

2 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 rkroker/1101/gaspipeline-sibirien- WEG.jpg/image_preview Wirtschaftsverband Erdöl und Erdgasgewinnung e.v. 12

3 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)) rkroker/1101/gaspipeline-sibirien- WEG.jpg/image_preview Wirtschaftsverband Erdöl und Erdgasgewinnung e.v. None of the existing models might be used with highly accurate EoS (like the GERG EoS) 13

4 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)) rkroker/1101/gaspipeline-sibirien- WEG.jpg/image_preview Wirtschaftsverband Erdöl und Erdgasgewinnung e.v. None of the existing models might be used with highly accurate EoS (like the GERG EoS) 14

5 Introduction Hydrates also relevant to CCS-Technology (CO 2 hydrate + mixtures) Separated CO 2 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 CO 2 / water required 25

6 Introduction Hydrates also relevant to CCS-Technology (CO 2 hydrate + mixtures) Separated CO 2 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 CO 2 / water required First step: Focus on CO 2 hydrates 26

7 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 37

8 CO 2 hydrates Cooperation with the Academy of Sciences in Prague (Václav Vinš, Jan Hrubý) CO 2 hydrates literature review: Structure SI, six large, two small cages Composition is not fixed! 46 molecules of H 2 O Lenny Martinez, Los Alamos National Laboratory (2009) 1 to 8 molecules of CO 2 x x min CO 2 max CO 2 1/ 47 0,021 8 / 54 0,148 E.D. Sloan and C.A. Koh: Clathrate hydrates of natural gases, 3rd ed., Taylor & Francis group (2008) 48

9 CO 2 hydrates Data Thermal expansion Compressibility (few data, no direct measurements) Phase equilibrium data 59

10 CO 2 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 10

11 The system H 2 O - CO 2 ptx diagram for the system H 2 O - CO 2 Diamond (2001) demonstrated the complexity of this system: 6 11

12 The system H 2 O - CO 2 ptx diagram for the system H 2 O - CO 2 Diamond (2001) demonstrated the complexity of this system: Fluid region: H 2 O: IAPWS Wagner, W.; Pruss, A. (2002) CO 2 : 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 12

13 The system H 2 O - CO 2 ptx diagram for the system H 2 O - CO 2 Diamond (2001) demonstrated the complexity of this system: Solid H 2 O: Feistel, R.; Wagner, W. (2006) 6 13

14 The system H 2 O - CO 2 ptx diagram for the system H 2 O - CO 2 Diamond (2001) demonstrated the complexity of this system: Solid CO 2 : Jäger, A.; Span, R. (2012) 6 14

15 Δp sub [Pa] EoS for solid CO 2 Explicit in the Gibbs energy g(t,p) EoS for CO 2 by Span and Wagner (1996) & EoS for solid CO 2 allows for accurate calculation of sublimation and melting pressures Melting pressure T [K] Uncertainty Calculated Fernandez-F. and del Rio (1984) Ambrose (1955) Bedford (1984) Bilkadi (1974) Bryson (1974) Giauque and Egan (1937) Sublimation pressure 100 Δp melt /p melt, corr. eq T [K] Uncertainty Calculated Michels (1942) Clusius (1960) 7 15

16 The system H 2 O - CO 2 ptx diagram for the system H 2 O - CO 2 Diamond (2001) demonstrated the complexity of this system: Hydrates: Modified model of Ballard and Sloan (2002) 8 16

17 Model for CO 2 hydrates The model of Ballard und Sloan (2002) was chosen and slightly modified: T p f g T p RTv C T p f,,, ln 1, H w J w i i, J J i J 9 17

18 Model for CO 2 hydrates The model of Ballard und Sloan (2002) was chosen and slightly modified: T p f g T p RTv C T p f,,, ln 1, H w J w i i, J J i J,0 T p, g, g T p h T v T p w w w w dt 2 0 T p RT RT RT RT 0 0 dp 9 18

19 Model for CO 2 hydrates The model of Ballard und Sloan (2002) was chosen and slightly modified: T p f g T p RTv C T p f,,, ln 1, H w J w i i, J J i J,0 T p, g, g T p h T v T p w w w w dt 2 0 T p RT RT RT RT,0 h T h c T dt w w pw T I pw T c T c T T -1-1 pw J mol K K Ice Ih ~ cubic ice dp 9 19

20 Model for CO 2 hydrates The model of Ballard und Sloan (2002) was chosen and slightly modified: T p f g T p RTv C T p f,,, ln 1, H w J w i i, J J i J,0 T p, g, g T p h T v T p w w w w dt 2 0 T p RT RT RT RT N vw T p aw T p N AV,, N w dp a exp 3 T T 3 T T 3 T T 3 p p AV N w 9 20

21 Model for CO 2 hydrates The model of Ballard und Sloan (2002) was chosen and slightly modified: T p f g T p RTv C T p f,,, ln 1, H w J w i i, J J i J,0 T p, g, g T p h T v T p w w w w dt 2 0 T p RT RT RT RT N vw T p aw T p N AV,, N w dp a exp 3 T T 3 T T 3 T T 3 p p AV N w N a T T T T T T AV a 0 exp 3 1 0a 3 2 0a 3 3 0a 1 N w 1 2 p p0a p p

22 Model for CO 2 hydrates The model of Ballard und Sloan (2002) was chosen and slightly modified: T p f g T p RTv C T p f,,, ln 1, H w J w i i, J J i J Langmuirconstant: s and e are adjustable parameters Adjustable parameters of the model: se, Potentialparameters,0,0 g, h 1, 2 Pressure dependence of the molar volume w w Reference state 9 22

23 Available phase equilibrium data 10 23

24 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 f CO2 H w H w T, p, f J 11 24

25 Three phase equilibria with hydrates 12 25

26 Three phase equilibria with hydrates VLwH VHIw 13 26

27 Three phase equilibria with hydrates LwLcH VLcH 14 27

28 Summary Established modified hydrate model of Ballard and Sloan (2002) for pure CO 2 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 15 28

29 Outlook Collecting data and fitting the hydrate model for CH 4 hydrates GERG 2004 results interesting!! E.D. Sloan and C.A. Koh: Clathrate hydrates of natural gases, 3rd ed., Taylor & Francis group (2008) 16 29

30 Outlook Collecting data and fitting the hydrate model for CH 4 hydrates GERG 2004 results interesting!! Hydrate formation in multicomponent mixtures More difficult since the structure of the hydrate is also unknown 16 30

31 Thank you! Questions? 31