1、Gas Processors Association - _ - - GPA TP-17 8 U 3824677 0013640 080 E4 Technical Publication TP-19 Vapor-Solid Equilibrium Ratios for Structure I and li Natural Gas Hydrates Susan L. Mann Mobil Oil Corp. Louise M. McClure Columbus Energy Corp. E. Dendy Sloan Fred H. Poettmann Colorado School of Min
2、es December 1988 6526 East 60th St. Tulsa, Okla. 74145 Phone: 918/493-3872 TECHNI CAL PUBLICATION TP-19 VAPOR-SOLID EQUILIBRIUM RATIOS FOR STRUCTURE I and II NATURAL GAS HYDRATES Susan L. Mann - Mobil Oil Co. Louise M. McClure - Columbus Energy Corp. E. Dendy Sloan - Colorado School of Mines Fred H.
3、 Poettmann - Colorado School of Mines FOREWORD Natural gas hydrates are a continuing operating problem in the petroleum and natural gas industries. Pre conversely for components with Kv-s less than unity the hydrate phase is preferred to the vapor phase. 2. The primary requirement for the stabilizat
4、ion of each hydrate cavity is the ratio of the diameter of the guest molecule to that of the cavity. Since the diameters of the hydrate cavities are fixed, there are guest molecules which have more optimum diameters than others. The first principle above is self-evident from the definition of Kvs (=
5、 yi/Xis) and follows the same guidelines of vapor-liquid equilibria KVL values. The second principle should be briefly explained, however. In order to provide a quantitative explanation, consider the ratios for natural gas hydrate formers, mentioned in the second principle. These ratios .are given i
6、n Table 15, ordered in increasing size of molecule. In Table 15 the single guest hydrates, called “simple hydratestt are shown to form the cavities marked with an crystal structures of simple hydrates have been determined through X-ray diffraction (see Davidson et al. (26). molecules add the most st
7、ability to the cavity for which their size ratio R approximates a value of 0.92. preferentially stabilizes the large cavity of structure I (RIL = 0.955) but it is too large to fit into the small cavities of structure I or structure II (RIS = 1.118, RIIS = 1.122) and ethane is too small to stabilize
8、the large cavity of structure II The Guest For example, ethane ia (RIIL = 0.851). fit only into the large cavity of structure II because of their large sizes. Normal butane is too large to fit into any cavity as a pure component (minimum ratio RIIL = 1.098) but, in the cis configuration of the molec
9、ule, it can squeeze into the large cavity of structure II when another guest molecule (such as methane) stabilizes the small cavity of structure II. Similarly, propane and isobutane are shown to For the smaller natural gas molecules Table 15 shows the optimal cavities to be the small cavity of struc
10、ture I for methane, carbon dioxide, and hydrogen sulfide, but the small Cavity of structure II for nitrogen. principally the small cavities of their respective structure and, because no other hydrate former is present for simple hydrates, they enter the large cavities, but they do not add substantia
11、l stability to the large cavities. For that reason, the four smaller molecules may be shown with a large cavity marked values appreciably less than 0.92. These molecules stabilize for For mixtures of natural gas components there is competition between molecules for the available cavities of the crys
12、tal structure. Just as for simple hydrate formers, the occupation of each cavity is principally determined by the component with size ratio fraction closest to 0.92. methane, ethane, and hydrogen sulfide would form structure I because all of the simple hydrates of these components form that structur
13、e. The large cavities structure I would be principally occupied by ethane (RIL = 0.955) with only a small percentage For example a mixture of 19 occupied by methane (RIL = 0.757) or hydrogen sulfide (RIL = 0.795). exclude ethane (RIS = 1.118) and so contain methane (RIS = 0.886 or, preferentially hy
14、drogen sulfide (RIS = 0.931). The small cavities of structure I are of a size to The effect of competition for structure I cavities is demonstrated in the Kvs values of the example problem in Table 3. According to the first principle stated above those molecules with the lowest Kv, values prefer the
15、 hydrate phase. the lowest K values are for ethane (due to its optimal size ratio in the small cavity). Nitrogen and methane have the largest K values due to their relatively low size ratios. effect of competition for structure II cavities is illustrated in the Kvs values of the example problems of
16、Tables 11 and 12. Table 11 shows propane and isobutane with the lowest Kvs values In Table 3 The due to their optimal size ratios in the large cavity (RIIL = 0.971 and 1.005, respectively). Ethane, on the other hand has a higher Kvs value than in the structure I problem of Table 3 because it cannot
17、enter the small cavity of structure II and must compete for the large cavity with more optimally sized molecules, such as propane and isobutane. This competition for the large cavity forces more ethane into the vapor, resulting in a larger Kvs value than that for methane, in contrast to their relati
18、ve Kvs values for structure I. In structure II, normal butane is also.tlforced out“ of the large cavity by the optimally sized molecules of propane and isobutane. In Table 11, of the molecules which fit the small cavity, methane has the lowest Kvs 20 value, which is 1.4, indicating that it does not
19、add appreciable stability to the hydrate structure. The example problem of Table 12 shows the Kvs effect of the addition of a small amount of hydrogen sulfide to the natural gas. high stability of the small cavity. cavity so well that it forces methane from the cavity into the vapor phase, as indica
20、ted by a higher Kvs value (1.6) than the example of Table 11 with no H2S in the gas. The hydrogen sulfide Kvs value is very low, indicating a In fact, H2S stabilizes the The size ratios of Table 15 may provide the user with similar concepts for reckoning the relative values of Kvs for various natura
21、l gas components. COMPARIS ON OF P REDICTI NC WITH ACTUAL DA TA Hydrate forming temperature and pressure predictions using the equilibrium ratio correlations should, as expected, agree with the computer generated predictions. However, the computer generated predictions may or may not agree with the
22、experimental measurements. Thus the equilibrium ratio predictions of temperature and pressure will be no better than the computer program. Comparisons were also made with a computer program written by B. K. Berge (1986) (30). equilibrium ratio method using the K-charts taken from the API data.book.
23、temperature range of the Katzs charts. for temperatures below 32“ F. Berges program is based on the The comparisons of necessity were limited to the No comparisons were made 21 For structure I hydrates the average deviation of predicted pressures using the new equilibrium ratio charts was 8.3% (usin
24、g 98 points) whereas using Katzs charts the average deviation was 14.4% (using 86 points, Katz had no nitrogen K-values). If the Deaton and Frost data, which Katz used to develop his correlations were excluded, the average deviation for this work is 13.1% while that of Katzs charts the average devia
25、tion was 19.9%. For structure II hydrates, out of twenty-eight gas systems (136 points) the average absolute error of predicting the experimental dissociation pressure by the equations developed in this work 17.0%, and by Katzs 14.8%. However, of the twenty- eight gases, only fifteen met the criteri
26、a of a natural gas. Of the gases for which these comparisons were made only one system contained hydrogen sulfide. sulfide the Katz Kvs-values would predict dissociation pressures with considerable error. Katzs K-values are constant whereas the actual K-values are a function of the hydrogen sulfide
27、concentration in the natural gas system as well as the gas gravity. For systems containing hydrogen The charts for structure II hydrates from this work predict the composition of the hydrate phase more accurately than the . tentative charts developed by Katz. temperature Katzs charts have only one v
28、alue. The K-values for structure II are gravity dependent and hydrogen sulfide concen- tration dependent, thus at a given temperature and pressure the At a given pressure and 22 K-value varies as the gas gravity changes and as the composition of the hydrogen sulfide in the gas changes. predict the h
29、ydrate structure whereas the Katz charts do not predict structure. Also, the charts To show the difference between the K-values predicted by Katzs method and this work, Gas A of Deaton and Frost was used(8) dissociation pressure and the pressures predicted bj the three methods. reasonably well, but
30、the K-values from this study and the Katz Kvs values are significantly different. the K-values predicted by each method. the methane K-values for each method versus the experimental temperature. agree closely with those predicted by the CSM hydrate program. Katzs, though, predict higher values for t
31、he methane K-values, indicating less methane in the hydrate phase. graphically the difference in the K-value predicted for each component by each method for Gas A at 44F and 183 psia. components the equations from this work essentially predict the same K-value as the hydrate program, and thus the sa
32、me hydrate composition. anywhere from half to double those predicted by the program depending upon the component. between Katzs Kvs values and the program Kvs is that Katzs Kvs values predict that no normal butane enters the hydrate Figure 10 shows the comparison of the experimental Both methods pre
33、dict the dissociation pressure Table 14 is a summary of Figure 11 is a plot of As anticipated the K-values predicted by this work Figure 12 shows For all . The K-values predicted by Katzs charts are Another significant difference 23 structure for Gas A system at any temperature or pressure. this tim
34、e experimental data of the composition of the hydrate phase is not available for natural gas mixtures. comparisons of the degree of accuracy of the K-values predicted, experimental data is necessary. At To make further CONCLUSIONS Charts and equations of vapor-solid equilibrium ratios have been deve
35、loped for the prediction of structure I and II natural gas hydrates. statistical thermodynamic model of van der Waals and Platteeuw and Parrish and Prausnitz. The results calculated using the K- value charts are consistent with those calculated by the CSM hydrate prediction program. The charts cover
36、 a wide range of temperature both above and below 32 OF. The charts supersede those of Katz et al. which are not a function of structure or composition, and are limited to a range of temperature above 32F only. These charts are consistent with the current Polynomial regression analysis was used to c
37、urve fit the computer generated K-values. The equations have been programmed and used to predict the hydrate forming conditions of pressure and temperature as well as the structure and composition of the hydrate phase. 24 Kvs Yi Xi C y2 P T MFH SG = vapor-solid equilibrium ratio - dimensionless = mo
38、le fraction of component in the gas phase on a water free basis mole fraction of component in the hydrate phase on water free basis = = correction factor (Kvs corrected/Kvs from chart) = mole fraction ethane in vapor phase - pressure, psia = temperature, R = mole fraction hydrogen sulfide = normal.i
39、zed gravity of the hydrate formers, for Structure II equations ACKNOWLEDGEMENT This paper is a summary of two theses submitted to the Colorado School of Mines in partial fulfillment for the requirements of the degree of Master of Science in Petroleum Engineering by Louise M. McClure (Zimmerman) and
40、Susan L. Mann. Copies of the thesis are available from the Colorado School of Mines Library. 25 LITERATURE CITED 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Carson, D.B. and Katz, D.L.: “Natural Gas Hydrates, It Trans. AIME , 146, 150 (1942) Van der Waals, J.H. and Platteeuw, J.C.: “Clathrate Solutions,t
41、t Adv. Chem. Phvs., Vol II, 1 (1959) Parrish, W.R. and Prausnitz, J.M.: lDissociation of Gas Hydrates Formed by Gas Mixtures,“ Ind. Ena. Chem. Process Des . DeveloD., Vol II No. 1, 26 (1972) Sloan, E.D.: “The CSM Hydrate Program,It presented at 64th Annual GPA Convention, March 18-20, 1985, Houston,
42、 Texas Jeffrey, G.A.: “Hydrate Inclusion Compounds,t8 Chapter 5 Inclusion Comx)ounds, Vol. 1, J.L. Atwood, J.E.D. Davis, D-D. MacNichols, Ed., Academic Press (1984) Davy, H.: Phil. Tr ans. Rov. Soc. London, 101, 1 (1811) Hammerschmidt, E.G.: tlFormation of Gas Hydrates in Natural Gas Transmission Li
43、nes,t8 Jnd. Ena. Chem., 26, 851, (1934) Deaton, W.M. and Frost, E.M.: “Gas Hydrates and Their Relation to the Operation of Natural-Gas Pipe Lines,# U.S.B.M. MonouraDh 8 (1946) Unruh, C.H. and Katz, D.L.: “Hydrates of Carbon Dioxide-Methane Mixtures.tf Trans. AIMX, 186, 83 (1949) Noaker, L.J. and Kat
44、z, D.L.: “Gas Hydrates of 201, 237 (1951) Hydrogen Sulfide-Methane Mixtures,t1 Trans AIME, Robinson, D.B. and Ng, H.J.: IImprove Hydrate Predictions,Il Hydrocarbon Processinq, 95 (Dec. 1975) Jhaveri, J. and Robinson, D.B.: “Hydrates in the 43, 75 (1965) Methane-Nitrogen Systern,lf Canadian J. Chem.
45、Ena *I 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. GPA TP-39 88 E3 3824699 0033668 3bT Ng, H.J. and Robinson, D.B.: Hydrate Formation,“ AIChE Journal 1977, Vol. 22 #4, 656 “The Role of N Butane in McLeod, H.O. and Campbell, J.M.: *Natural Gas Hydrates at Pressures to 10,000 psiat* Trans. AIM
46、E, 222, 590 (1961) Poettmann, F.H. : IIHerels Butane Hydrate Equilibriat1, Hydrocarbon Processinq, 111 (June 1984) GPSA Enaineerina D ata Book, Vol. II, 10th Edition (1987) Technical Data Book, American Petroleum Institute, New York, New York, (1983) Hammerschmidt, E.G.: Comment in addendum to artic
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48、d Robinson D.B.: IlThe Measurement and Prediction of Hydrate Formation in Liquid Hydrocarbon-Water Systems,I* Ind. Eng. Chem. Fund. Vol. 15 #4 (1976) Holder, G.D., et al.: tlThermodynamics and Molecular Properties of Gas Hydrates From Mixtures Containing Methane, Argon and Krypton,lI Ind. and Eng. C
49、hem. Fund. 19, 282 (1980) Sloan, E.D.; IlThe CSM Hydrate Program,lI Proceedings of the 64th Annual GPA Convention, March 18-20, 1985, Houston, Texas Wagner, .J., Erbar, R.C. and Majeed, A.I.: IIAQUA*SIM, Phase Equilibria, Hydrate Inhibition,lI pg. 129, Proceedings of 64th GPA Annual Convention, March 18-20, 1985, Houston, Texas Holder, G.D. and Grigoriaon, G.C.: “Hydrate Dissociation Pressures of Methane Plus Ethane Plus Water-Existance of a Lotus of Minimum Pressures,“ J. Chem. Therm. 150, pg. 1093 (1980) 27 26. 27. 28. 29. 30. 31. 32. 33. Thakore, J.L. and Hol
