- Email: [email protected]
Enthalpies of dissociation of clathrate hydrates of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + tetrahydrofuran)
J. Chem. Thermodynamics 2001, 33, 513–521 doi:10.1006/jcht.2000.0765 Available online at http://www.idealibrary.com on
Enthalpies of dissociation of clathrate hydrates of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + tetrahydrofuran) S.-P. Kang, H. Lee,a Department of Chemical Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, Korea
and B.-J. Ryu Petroleum & Marine Resources Division, Korea Institute of Geology, Mining & Materials, 30 Kajung-dong, Yusong-gu, Taejon 305-701, Korea
A calorimetric technique is described for measuring the enthalpy of dissociation liberated from solid hydrates. In this study, the enthalpies of dissociation were determined at T = 273.65 K and p = 0.1 MPa for simple and mixed hydrates of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + tetrahydrofuran) using an isothermal microcalorimeter. The addition of tetrahydrofuran (THF) promoted hydrate stability and increased the number of guest molecules encaged in the small and large cavities of the hydrate lattice, resulting in lower enthalpy of dissociation, compared with structure II hydrate. The composition ratio of guest molecules did not affect the enthalpy of dissociation, which was found to be nearly constant for the same mixture. c 2001 Academic Press
KEYWORDS: calorimeter; hydrate; enthalpy of dissociation; carbon dioxide; nitrogen; tetrahydrofuran
1. Introduction Clathrate hydrates are non-stoichiometric solid compounds formed by cavities of the “host” water molecules, strongly hydrogen bonded under certain conditions of pressure and temperature, which enclose low molar mass “guest” species of suitable size and shape. While the guest molecule is enclosed within the cavity, there is no chemical union between the guest and host molecules. The guest molecules interact with the host molecules through van der Waals forces. a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/01/050513 + 09
$35.00/0
c 2001 Academic Press
514
S.-P. Kang, H. Lee, and B.-J. Ryu
Investigations of thermophysical properties of clathrate hydrates have concentrated mainly on the determination of the ( p, T ) conditions of formation/dissociation or crystal structures. Most of these studies were motivated by applications in natural gas industries and other related technologies. Only a few studies on time-independent thermal properties have been reported. (1–5) The experimental difficulties in measuring thermal properties lie mainly in the analysis procedure of the hydrate composition. At hydrate-forming temperatures above the ice point, high-pressure conditions are required to prevent the hydrate from dissociating into water and gaseous guest molecules. Furthermore, water occlusion causes extreme difficulty in completely converting water to hydrate. However, to avoid these problems, cyclic ethers such as epoxyethane and tetrahydrofuran have been used as hydrate stabilizers, which are known to be completely miscible with liquid water. It might be interesting to note that they form hydrates with water at atmospheric pressure condition. Their hydration numbers have been already known from structure information. The enthalpy of dissociation may be determined from the univariant slope of the phase equilibrium line (ln p/Pa against 1/T ) using the Clausius–Clapeyron equation: d ln p/d(1/T ) = −1H/Z R,
(1)
where p is the pressure, T is the temperature, 1H is the enthalpy of dissociation, Z is the compression factor, and R is the universal gas constant. If the compression factor does not change rapidly, this equation can be used to calculate the enthalpy of dissociation from commonly available ( p, T ) data. However, this equation is hard to apply to mixed guests of more than two components. Sloan and Fleyfel (6) constructed a number of plots for some common pure hydrate formers and gas mixtures. Even though their results were challenged by Skovborg and Rasmussen, (7) the relation showed good agreement with Handa’s experimental results. At this point, it must be recognized that the above approach can only be recommended as an alternative method, but actual calorimetric measurements are required. In this work, we have measured the enthalpies of dissociation of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + THF) hydrates using an isothermal microcalorimeter (i.m.c.). The present calorimetric technique was verified by comparing the measured enthalpies of dissociation of methane hydrates with the reported literature values.
2. Experimental In this study, the isothermal operation method was used to measure the enthalpy of dissociation of hydrates of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + THF). The isothermal microcalorimeter (Calorimetric Science Corporation, UT, model 4400 IMC) was modified to accommodate samples under high pressure. A diagram of the i.m.c. is shown schematically in figure 1. The measuring unit of the calorimeter is a large aluminium heat sink incorporating two test wells. The measurement principle is quite simple: heat produced or absorbed by any process occurring in a test well is completely exchanged with a heat sink kept at constant temperature. A heat change occurring in a sample creates a temperature difference between the sample and the
Enthalpies of dissociation of clathrate hydrates
515
7 1
7 P 4 2
6
3
10
8
5
9
12
13
14 15 11
FIGURE 1. Schematic diagram of the calorimeter for measuring the enthalpy of dissociation: 1, valve 1; 2, valve 2; 3, valve 3; 4, valve 4; 5, valve 5; 6, gas cylinder; 7, pressure gauge; 8, gas reservoir; 9, thermal shunt; 10, access tube; 11, thermoelectric sensors; 12, sample cell; 13, reference cell; 14, heat sink; 15, water bath.
heat sink. Thermoelectric sensors located between the sample and the aluminium block generate a voltage proportional to the temperature gradient across the sensors and the temperature gradient is directly dependent on the heat flux. A reference cell is used to correct for any heat flux due to temperature fluctuations in the heat sink. The differential signal from the twin calorimeter test wells (sample and reference) corresponds to the rate of heat production from the sample itself. The differential heat conduction design makes it possible to measure a heat value as low as 1 · 10−7 J · s−1 . Logged data in a connected PC are analyzed with a supplied software program. Originally, the sample cell was designed for flow/perfusion adsorption experiments at normal pressure, but was modified to measure enthalpies of dissociation of clathrate hydrates under high-pressure conditions. Figure 2 illustrates the modified sample cell. A stirring motor was installed to agitate the contents of the sample cell and the heat-conducting liquid in the outer container. An inlet flow thermal equilibration part helped the gas phase to minimize the temperature difference between outer room and calorimeter jacket temperature. All attached parts outside the calorimeter outer jacket were kept at room temperature, which was measured by a thermometer. The
516
S.-P. Kang, H. Lee, and B.-J. Ryu 1 outlet inlet 2
3
43 cm 4
5 6
7
3.8 cm
FIGURE 2. Cell accessories for an isothermal microcalorimeter: 1, stirring motor; 2, top access cover; 3, inlet flow thermal equilibrator; 4, thermal shunt; 5, stirrer; 6, heat conduction liquid; 7, hydrate sample.
reference cell was filled with N2 gas to a pressure of 0.1 MPa at room temperature and was permanently maintained in the calorimeter. About 0.85 g of water were weighed and loaded into the sample cell. The sample cell was then placed in the calorimeter, which was previously cooled to T = 278.15 K. The system was flushed with the test gas to exclude air. After flushing at least three times, the system was pressurized with the test gas. The system was kept above the equilibrium dissociation pressure because clathrate hydrates are stable only under the pressure of a hydrate-forming gas. The calorimeter was then cooled to T = 248 K at the rate of 1 K · h−1 . A stirring motor provided sufficient agitation to promote the hydrate formation reaction between water and the guest gas. The reaction was continued for 7 days so as to ensure complete enclathration. The calorimeter was then heated to T = 273.65 K at the same rate as in the cooling stage. To initiate hydrate dissociation, valves 3 and 4 were opened to connect the gas reservoir to
Enthalpies of dissociation of clathrate hydrates
517
the sample cell. The cell pressure was measured with a Heise bourdon gauge (0 to 20) MPa. The temperature of the reservoir was measured with a thermometer. The large reservoir volume (380.7 cm3 ) ensured a low enough pressure to continue the smooth dissociation of the sample. The pressure was usually between (0.1 and 0.3) MPa after the completion of the dissociation. The volumes of the parts of the system were determined by expansion of high-purity nitrogen (mole fraction = 0.999995). The volume calibrations were performed by using ( p, V, T ) data from the literature. (8) The volume V1 between valves 3 and 5 was 426.4 cm3 and the volume V2 between valves 1 and 2 was 57.12 cm3 . The volumes V3 between valve 2 and the top of the cell and V4 between valve 3 and the top of the cell were 8.75 cm3 and 6.58 cm3 , respectively. The volume Vs of the sample cell was found to be 10.17 cm3 by calibration with double distilled and deionized water. Carbon dioxide and nitrogen with stated mole fraction purities of 0.9999 and 0.999995 were purchased from World Gas Co. (Korea). Mixtures thereof were supplied by Duk-Yang Gas Co. (Korea). Their composition was confirmed by analysis with gas chromatography. The stated mole fraction purity of (carbon dioxide + nitrogen) was >0.9995. H.p.l.c.-grade THF was obtained from Sigma-Aldrich Chemical Co.
3. Results and discussion The amount of gas liberated from hydrates had to be accurately measured in order to determine the enthalpy of dissociation. In this work, the total amount of gas released from simple hydrates of carbon dioxide or nitrogen n g was calculated from the ( p, V, T ) results of each run and thermodynamic information. The following calculation procedure suggested by Handa (2) was used n g = {( pf − pi − pw )(Vt − Vw )}/{RTg + B( pf − pi − pw )},
(2)
where pf and pi are the pressures at the end of a run and the beginning of hydrate dissociation, respectively, pw is the saturated vapor pressure of water at the cell temperature Tc at the end of a run, by Vt is the total volume of the system, Vw is the volume of liquid water in the sample cell measured by weighing at the end of a run, B is the second virial coefficient of the gas, and Tg the volume-fraction weighted temperature of the gas phase obtained from: Tg = {(V1 + V2 )Tr + 0.5(V3 + V4 )(Tc + Tr ) + (Vs − Vw )Tc }/(Vt − Vw ),
(3)
where Tr is room temperature. The solubility of the gas in water was calculated using the Soave–Redlich–Kwong equation of state. The volume of the gas reservoir had to be large enough to minimize any possible temperature fluctuation. The second virial coefficients of the pure gases were obtained from the literature. (9) The amount of water in the gas phase n w,g was calculated from pw at the end of a run and the amount of water n w present in the hydrate phase was obtained by subtracting n w,g from the amount of initially loaded water. The hydrate composition is described by G · nH2 O where n = n w /n g and G is the guest molecule. However, the possible existence of water in the form of ice must be considered because complete conversion of water into hydrate might not occur. Consequently, if a small amount of ice is present, the enthalpy of fusion of ice needs to be
518
S.-P. Kang, H. Lee, and B.-J. Ryu TABLE 1. Comparison of the enthalpies of dissociation 1H for methane hydrate Reference
1H/(kJ · mol−1 )
This work
56.84
Handa (3)
54.19
Rueff et al. (4)
53.79
Lievois et al. (5)
54.77
Deaton and Frost (13)a
55.12
Kuustraa and Hammerschaimb (14)a
52.00
de Roo et al. (10)a
67.85
a Calculated values based on the Clausius–Clapeyron equation.
taken into account. To avoid ice formation in the hydrate phase, the equilibrium cell was kept for a long time at a sufficiently lower temperature condition than the corresponding three-phase (hydrate + water-rich liquid + vapor) equilibrium temperature of hydrates. To verify the present experimental procedure, the enthalpy of dissociation for methane hydrate was measured and compared with the literature data of Handa. (3) In his work the composition of methane hydrate was determined to be CH4 · 6.00H2 O, while, in the current work, the hydration number was 6.38. The measured enthalpy of dissociation of pure methane hydrate was 56.84 kJ · mol−1 at T = 274.15 K and is compared with several reported experimental results listed in table 1. In this table, the comparison of the calculated and measured dissociation enthalpies is based on a reference temperature of 273.15 K. All the results except that of de Roo et al. (10) agree within the experimental uncertainty. The enthalpies of dissociation of simple and mixed hydrates were measured three times at a same condition and their average values are listed in table 2. The enthalpy of dissociation of simple carbon dioxide and nitrogen hydrates were measured and found to be (65.22 and 65.81) kJ · mol−1 and their corresponding hydration numbers were 7.23 and 5.94, respectively. Figure 3 shows an endothermic dissociation process for simple methane and carbon dioxide hydrates. The total amount of absorbed heat during hydrate dissociation was obtained by integrating the heat flux q between the sample and reference cells over the duration of the dissociation process. All runs of simple and mixed hydrates gave a similar dissociation pattern to that of figure 3. Unlike simple hydrates of pure guest molecules, the hydration numbers of mixed guest molecules encaged in small and large cavities of a hydrate lattice are difficult to determine. To overcome this difficulty, an indirect approach was adopted using the equilibrium model calculation. The equilibrium conditions and compositions of mixed hydrates consisting of carbon dioxide and nitrogen can be readily determined by using a thermodynamic model based on van der Waals theory. However, the phase equilibria of mixed hydrates containing a hydrate promoter should take into account the large shift of pressure and temperature due to the addition of a small amount of promoter.
Enthalpies of dissociation of clathrate hydrates
519
TABLE 2. Measured values of the enthalpies of dissociation 1H for simple and mixed hydrates at T = 273.65 K 1H/(kJ · mol−1 )
Hydrate composition
CH4
56.84 ± 0.89
n = 6.38a
CO2
65.22 ± 1.03
n = 7.23a
N2
65.81 ± 1.04
n = 5.94a
(0.17CO2 + 0.83N2 )
64.59 ± 1.02
x = 5.43, y = 1.89b
Guest(s)
(0.70CO2 + 0.30N2 )
63.41 ± 1.00
x = 7.08, y = 0.25b
(0.17CO2 + 0.83N2 ) with (0.01C4 H8 O + 0.99H2 O)
109.01 ± 1.72
x = 2.96, y = 9.47, z = 11.39c
(0.17CO2 + 0.83N2 ) with (0.03C4 H8 O + 0.97H2 O)
118.94 ± 1.87
x = 2.35, y = 7.42, z = 12.53c
(0.70CO2 + 0.30N2 ) with (0.01C4 H8 O + 0.99H2 O)
107.18 ± 1.69
x = 9.97, y = 2.58, z = 10.94c
(0.70CO2 + 0.30N2 ) with (0.03C4 H8 O + 0.97H2 O)
113.66 ± 1.79
x = 8.11, y = 2.19, z = 13.16c
a (G · nH O); n is the number of water molecules in the unit structure and G is the pure guest species. 2 b (xCO · yN · 46H O); x and y are the numbers of carbon dioxide and nitrogen molecules, respectively, 2 2 2 in structure I. c (xCO2 · yN2 · zC4 H8 O · 136H2 O); x, y, and z are the numbers of carbon dioxide, nitrogen, and THF molecules, respectively, in structure II; C4 H8 O is THF.
0.1 0.0 – 0. 1
q/(J . s – 1)
– 0. 2 – 0. 3 – 0 .4 – 0 .5 – 0 .6 – 0 .7
0
2000
4000
6000 8000 10000 12000 14000 16000 18000 20000 t/s
FIGURE 3. Plot of heat flux q against time t for the endothermic process of hydrate dissociation of simple CH4 and CO2 hydrates. —, CH4 ; – –, CO2 .
Jager et al. (11) suggested a thermodynamic model for predicting equilibrium conditions of methane hydrate with 1,4-dioxane as promoter. They assumed that the mixed hydrate of methane and 1,4-dioxane formed structure II, which would be general for other mixed hydrates having different promoters. We used a similar calculation method to determine
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S.-P. Kang, H. Lee, and B.-J. Ryu
the composition of mixed hydrates. It was found that the model calculation results were in good agreement with experimental data. The required Kihara potential parameters for THF were directly obtained from experimental equilibrium dissociation pressures. The hydration number can be determined from both the equilibrium hydrate compositions and cage occupancy by guest molecules. The resulting experimental enthalpies of dissociation for several simple and mixed hydrates consisting of carbon dioxide, nitrogen, and THF are listed in table 2. As discussed by Sloan and Fleyfel, (6) the enthalpies of dissociation appear to be relatively constant over a wide range of composition for (carbon dioxide + nitrogen). The guest (0.17CO2 + 0.83N2 ) was particularly chosen because of our interest in carbon dioxide recovery from power-plant flue gas. Mixed hydrates of (carbon dioxide + nitrogen) form either structure I or II, depending on the composition of the guest species. Above a mole fraction content of 0.15 of carbon dioxide structure I hydrates form, but below this composition structure II hydrates form. (12) Thus, both (0.17CO2 + 0.83N2 ) and (0.70CO2 + 0.30N2 ) form structure I hydrates, resulting in almost the same values for the dissociation enthalpy. For mixed hydrates of (carbon dioxide + nitrogen + THF), the enthalpies of dissociation were higher than those of structure II hydrates, but smaller than those of the structure II hydrates of propane or isobutane. (3) The mixed hydrates containing THF of table 2 refer to a THF mole fraction of 0.01 to 0.03 in the water. Although the enthalpies of dissociation of the mixed hydrates containing THF appear to be similar, they do depend on the THF content. The addition of THF to (carbon dioxide + nitrogen) changed the hydrate structure I to II and increased the total amount of entrapped guest species, thus leading to enhanced hydrate stability. For structures I and II, the enthalpy of dissociation becomes a function of the number of crystal hydrogen bonds and about 80 per cent of the total enthalpy of dissociation comes from the strength of water hydrogen bonds. (7) It can therefore be expected that an increase in guest molecules in the cavities renders the hydrate structure loose and decreases the enthalpy of dissociation. In addition, THF greatly enhances hydrate stability and leads to increasing equilibrium temperature and decreasing corresponding equilibrium pressure of hydrate-contained mixture. This enhanced hydrate stability indicates that guest molecules occupy readily the cavities, resulting in a smaller enthalpy of dissociation than is the case for other structure II hydrates. Using an indirect approach, Skovborg and Rasmussen (7) calculated the enthalpy of dissociation using the Clausius–Clapeyron equation. The resulting values for the simple carbon dioxide and nitrogen hydrates were found to be (68.71 and 66.74) kJ · mol−1 , respectively and are in agreement with the experimental values. The results of this study are useful for separating carbon dioxide, methane, nitrogen, and many other guest molecules from multi-component gas mixtures. This work was supported by grant No. 98-0502-04-01-3 from the Basic Research program of the KOSEF and also partially by the Brain Korea 21 Project. REFERENCES 1. Handa, Y. P.; Hawkins, R. E.; Murray, J. J. J. Chem. Thermodynamics 1984, 16, 623–632. 2. Handa, Y. P. J. Chem. Thermodynamics 1986, 18, 891–902. 3. Handa, Y. P. J. Chem. Thermodynamics 1986, 18, 915–921.
Enthalpies of dissociation of clathrate hydrates 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
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Rueff, R. M.; Sloan, E. D.; Yesavaga, V. F. AIChE J. 1988, 34, 1468–1476. Lievois, J. S.; Perkins, R.; Martin, R. J.; Kobayashi, R. Fluid Phase Equilib. 1990, 59, 73–97. Sloan, E. D.; Fleyfel, F. Fluid Phase Equilib. 1992, 76, 123–140. Skovborg, P.; Rasmussen, P. Fluid phase Equilib. 1994, 96, 223–231. Vargaftik, N. B. Tables on the Thermophysical Properties of Liquids and Gases. John Wiley & Sons, Inc.: New York. 1975. Lide, D. R. CRC Handbook of Chemistry and Physics. CRC Press: Boca Raton. 1994. de Roo, J. L.; Peters, C. J.; Lichitenthaler, R. N.; Diepen, G. A. M. AIChE J. 1983, 29, 651–657. Jager, M. D.; de Deugd, R. M.; Peters, C. J.; de Swaan Arons, J.; Sloan, E. D. Fluid Phase Equilib. 1999, 165, 209–223. Diamond, L. W. Geochim. Cosmochim. Acta 1994, 58, 19–41. Deaton, W. M.; Frost, E. M. U.S. Bureau of Mines Monograph 1946, 8, 101. Kuustraa, V. A.; Hammerschaimb, E. C. Handbook of Gas Hydrate Properties and Occurrence, DOE/MC/19239, National Technical Information Service, U.S. Department of Commerce, 1983. (Received 6 April 2000; in final form 7 August 2000)
WA 00/020
Enthalpies of dissociation of clathrate hydrates of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + tetrahydrofuran) S.-P. Kang, H. Lee,a Department of Chemical Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon 305-701, Korea
and B.-J. Ryu Petroleum & Marine Resources Division, Korea Institute of Geology, Mining & Materials, 30 Kajung-dong, Yusong-gu, Taejon 305-701, Korea
A calorimetric technique is described for measuring the enthalpy of dissociation liberated from solid hydrates. In this study, the enthalpies of dissociation were determined at T = 273.65 K and p = 0.1 MPa for simple and mixed hydrates of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + tetrahydrofuran) using an isothermal microcalorimeter. The addition of tetrahydrofuran (THF) promoted hydrate stability and increased the number of guest molecules encaged in the small and large cavities of the hydrate lattice, resulting in lower enthalpy of dissociation, compared with structure II hydrate. The composition ratio of guest molecules did not affect the enthalpy of dissociation, which was found to be nearly constant for the same mixture. c 2001 Academic Press
KEYWORDS: calorimeter; hydrate; enthalpy of dissociation; carbon dioxide; nitrogen; tetrahydrofuran
1. Introduction Clathrate hydrates are non-stoichiometric solid compounds formed by cavities of the “host” water molecules, strongly hydrogen bonded under certain conditions of pressure and temperature, which enclose low molar mass “guest” species of suitable size and shape. While the guest molecule is enclosed within the cavity, there is no chemical union between the guest and host molecules. The guest molecules interact with the host molecules through van der Waals forces. a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/01/050513 + 09
$35.00/0
c 2001 Academic Press
514
S.-P. Kang, H. Lee, and B.-J. Ryu
Investigations of thermophysical properties of clathrate hydrates have concentrated mainly on the determination of the ( p, T ) conditions of formation/dissociation or crystal structures. Most of these studies were motivated by applications in natural gas industries and other related technologies. Only a few studies on time-independent thermal properties have been reported. (1–5) The experimental difficulties in measuring thermal properties lie mainly in the analysis procedure of the hydrate composition. At hydrate-forming temperatures above the ice point, high-pressure conditions are required to prevent the hydrate from dissociating into water and gaseous guest molecules. Furthermore, water occlusion causes extreme difficulty in completely converting water to hydrate. However, to avoid these problems, cyclic ethers such as epoxyethane and tetrahydrofuran have been used as hydrate stabilizers, which are known to be completely miscible with liquid water. It might be interesting to note that they form hydrates with water at atmospheric pressure condition. Their hydration numbers have been already known from structure information. The enthalpy of dissociation may be determined from the univariant slope of the phase equilibrium line (ln p/Pa against 1/T ) using the Clausius–Clapeyron equation: d ln p/d(1/T ) = −1H/Z R,
(1)
where p is the pressure, T is the temperature, 1H is the enthalpy of dissociation, Z is the compression factor, and R is the universal gas constant. If the compression factor does not change rapidly, this equation can be used to calculate the enthalpy of dissociation from commonly available ( p, T ) data. However, this equation is hard to apply to mixed guests of more than two components. Sloan and Fleyfel (6) constructed a number of plots for some common pure hydrate formers and gas mixtures. Even though their results were challenged by Skovborg and Rasmussen, (7) the relation showed good agreement with Handa’s experimental results. At this point, it must be recognized that the above approach can only be recommended as an alternative method, but actual calorimetric measurements are required. In this work, we have measured the enthalpies of dissociation of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + THF) hydrates using an isothermal microcalorimeter (i.m.c.). The present calorimetric technique was verified by comparing the measured enthalpies of dissociation of methane hydrates with the reported literature values.
2. Experimental In this study, the isothermal operation method was used to measure the enthalpy of dissociation of hydrates of carbon dioxide, nitrogen, (carbon dioxide + nitrogen), and (carbon dioxide + nitrogen + THF). The isothermal microcalorimeter (Calorimetric Science Corporation, UT, model 4400 IMC) was modified to accommodate samples under high pressure. A diagram of the i.m.c. is shown schematically in figure 1. The measuring unit of the calorimeter is a large aluminium heat sink incorporating two test wells. The measurement principle is quite simple: heat produced or absorbed by any process occurring in a test well is completely exchanged with a heat sink kept at constant temperature. A heat change occurring in a sample creates a temperature difference between the sample and the
Enthalpies of dissociation of clathrate hydrates
515
7 1
7 P 4 2
6
3
10
8
5
9
12
13
14 15 11
FIGURE 1. Schematic diagram of the calorimeter for measuring the enthalpy of dissociation: 1, valve 1; 2, valve 2; 3, valve 3; 4, valve 4; 5, valve 5; 6, gas cylinder; 7, pressure gauge; 8, gas reservoir; 9, thermal shunt; 10, access tube; 11, thermoelectric sensors; 12, sample cell; 13, reference cell; 14, heat sink; 15, water bath.
heat sink. Thermoelectric sensors located between the sample and the aluminium block generate a voltage proportional to the temperature gradient across the sensors and the temperature gradient is directly dependent on the heat flux. A reference cell is used to correct for any heat flux due to temperature fluctuations in the heat sink. The differential signal from the twin calorimeter test wells (sample and reference) corresponds to the rate of heat production from the sample itself. The differential heat conduction design makes it possible to measure a heat value as low as 1 · 10−7 J · s−1 . Logged data in a connected PC are analyzed with a supplied software program. Originally, the sample cell was designed for flow/perfusion adsorption experiments at normal pressure, but was modified to measure enthalpies of dissociation of clathrate hydrates under high-pressure conditions. Figure 2 illustrates the modified sample cell. A stirring motor was installed to agitate the contents of the sample cell and the heat-conducting liquid in the outer container. An inlet flow thermal equilibration part helped the gas phase to minimize the temperature difference between outer room and calorimeter jacket temperature. All attached parts outside the calorimeter outer jacket were kept at room temperature, which was measured by a thermometer. The
516
S.-P. Kang, H. Lee, and B.-J. Ryu 1 outlet inlet 2
3
43 cm 4
5 6
7
3.8 cm
FIGURE 2. Cell accessories for an isothermal microcalorimeter: 1, stirring motor; 2, top access cover; 3, inlet flow thermal equilibrator; 4, thermal shunt; 5, stirrer; 6, heat conduction liquid; 7, hydrate sample.
reference cell was filled with N2 gas to a pressure of 0.1 MPa at room temperature and was permanently maintained in the calorimeter. About 0.85 g of water were weighed and loaded into the sample cell. The sample cell was then placed in the calorimeter, which was previously cooled to T = 278.15 K. The system was flushed with the test gas to exclude air. After flushing at least three times, the system was pressurized with the test gas. The system was kept above the equilibrium dissociation pressure because clathrate hydrates are stable only under the pressure of a hydrate-forming gas. The calorimeter was then cooled to T = 248 K at the rate of 1 K · h−1 . A stirring motor provided sufficient agitation to promote the hydrate formation reaction between water and the guest gas. The reaction was continued for 7 days so as to ensure complete enclathration. The calorimeter was then heated to T = 273.65 K at the same rate as in the cooling stage. To initiate hydrate dissociation, valves 3 and 4 were opened to connect the gas reservoir to
Enthalpies of dissociation of clathrate hydrates
517
the sample cell. The cell pressure was measured with a Heise bourdon gauge (0 to 20) MPa. The temperature of the reservoir was measured with a thermometer. The large reservoir volume (380.7 cm3 ) ensured a low enough pressure to continue the smooth dissociation of the sample. The pressure was usually between (0.1 and 0.3) MPa after the completion of the dissociation. The volumes of the parts of the system were determined by expansion of high-purity nitrogen (mole fraction = 0.999995). The volume calibrations were performed by using ( p, V, T ) data from the literature. (8) The volume V1 between valves 3 and 5 was 426.4 cm3 and the volume V2 between valves 1 and 2 was 57.12 cm3 . The volumes V3 between valve 2 and the top of the cell and V4 between valve 3 and the top of the cell were 8.75 cm3 and 6.58 cm3 , respectively. The volume Vs of the sample cell was found to be 10.17 cm3 by calibration with double distilled and deionized water. Carbon dioxide and nitrogen with stated mole fraction purities of 0.9999 and 0.999995 were purchased from World Gas Co. (Korea). Mixtures thereof were supplied by Duk-Yang Gas Co. (Korea). Their composition was confirmed by analysis with gas chromatography. The stated mole fraction purity of (carbon dioxide + nitrogen) was >0.9995. H.p.l.c.-grade THF was obtained from Sigma-Aldrich Chemical Co.
3. Results and discussion The amount of gas liberated from hydrates had to be accurately measured in order to determine the enthalpy of dissociation. In this work, the total amount of gas released from simple hydrates of carbon dioxide or nitrogen n g was calculated from the ( p, V, T ) results of each run and thermodynamic information. The following calculation procedure suggested by Handa (2) was used n g = {( pf − pi − pw )(Vt − Vw )}/{RTg + B( pf − pi − pw )},
(2)
where pf and pi are the pressures at the end of a run and the beginning of hydrate dissociation, respectively, pw is the saturated vapor pressure of water at the cell temperature Tc at the end of a run, by Vt is the total volume of the system, Vw is the volume of liquid water in the sample cell measured by weighing at the end of a run, B is the second virial coefficient of the gas, and Tg the volume-fraction weighted temperature of the gas phase obtained from: Tg = {(V1 + V2 )Tr + 0.5(V3 + V4 )(Tc + Tr ) + (Vs − Vw )Tc }/(Vt − Vw ),
(3)
where Tr is room temperature. The solubility of the gas in water was calculated using the Soave–Redlich–Kwong equation of state. The volume of the gas reservoir had to be large enough to minimize any possible temperature fluctuation. The second virial coefficients of the pure gases were obtained from the literature. (9) The amount of water in the gas phase n w,g was calculated from pw at the end of a run and the amount of water n w present in the hydrate phase was obtained by subtracting n w,g from the amount of initially loaded water. The hydrate composition is described by G · nH2 O where n = n w /n g and G is the guest molecule. However, the possible existence of water in the form of ice must be considered because complete conversion of water into hydrate might not occur. Consequently, if a small amount of ice is present, the enthalpy of fusion of ice needs to be
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S.-P. Kang, H. Lee, and B.-J. Ryu TABLE 1. Comparison of the enthalpies of dissociation 1H for methane hydrate Reference
1H/(kJ · mol−1 )
This work
56.84
Handa (3)
54.19
Rueff et al. (4)
53.79
Lievois et al. (5)
54.77
Deaton and Frost (13)a
55.12
Kuustraa and Hammerschaimb (14)a
52.00
de Roo et al. (10)a
67.85
a Calculated values based on the Clausius–Clapeyron equation.
taken into account. To avoid ice formation in the hydrate phase, the equilibrium cell was kept for a long time at a sufficiently lower temperature condition than the corresponding three-phase (hydrate + water-rich liquid + vapor) equilibrium temperature of hydrates. To verify the present experimental procedure, the enthalpy of dissociation for methane hydrate was measured and compared with the literature data of Handa. (3) In his work the composition of methane hydrate was determined to be CH4 · 6.00H2 O, while, in the current work, the hydration number was 6.38. The measured enthalpy of dissociation of pure methane hydrate was 56.84 kJ · mol−1 at T = 274.15 K and is compared with several reported experimental results listed in table 1. In this table, the comparison of the calculated and measured dissociation enthalpies is based on a reference temperature of 273.15 K. All the results except that of de Roo et al. (10) agree within the experimental uncertainty. The enthalpies of dissociation of simple and mixed hydrates were measured three times at a same condition and their average values are listed in table 2. The enthalpy of dissociation of simple carbon dioxide and nitrogen hydrates were measured and found to be (65.22 and 65.81) kJ · mol−1 and their corresponding hydration numbers were 7.23 and 5.94, respectively. Figure 3 shows an endothermic dissociation process for simple methane and carbon dioxide hydrates. The total amount of absorbed heat during hydrate dissociation was obtained by integrating the heat flux q between the sample and reference cells over the duration of the dissociation process. All runs of simple and mixed hydrates gave a similar dissociation pattern to that of figure 3. Unlike simple hydrates of pure guest molecules, the hydration numbers of mixed guest molecules encaged in small and large cavities of a hydrate lattice are difficult to determine. To overcome this difficulty, an indirect approach was adopted using the equilibrium model calculation. The equilibrium conditions and compositions of mixed hydrates consisting of carbon dioxide and nitrogen can be readily determined by using a thermodynamic model based on van der Waals theory. However, the phase equilibria of mixed hydrates containing a hydrate promoter should take into account the large shift of pressure and temperature due to the addition of a small amount of promoter.
Enthalpies of dissociation of clathrate hydrates
519
TABLE 2. Measured values of the enthalpies of dissociation 1H for simple and mixed hydrates at T = 273.65 K 1H/(kJ · mol−1 )
Hydrate composition
CH4
56.84 ± 0.89
n = 6.38a
CO2
65.22 ± 1.03
n = 7.23a
N2
65.81 ± 1.04
n = 5.94a
(0.17CO2 + 0.83N2 )
64.59 ± 1.02
x = 5.43, y = 1.89b
Guest(s)
(0.70CO2 + 0.30N2 )
63.41 ± 1.00
x = 7.08, y = 0.25b
(0.17CO2 + 0.83N2 ) with (0.01C4 H8 O + 0.99H2 O)
109.01 ± 1.72
x = 2.96, y = 9.47, z = 11.39c
(0.17CO2 + 0.83N2 ) with (0.03C4 H8 O + 0.97H2 O)
118.94 ± 1.87
x = 2.35, y = 7.42, z = 12.53c
(0.70CO2 + 0.30N2 ) with (0.01C4 H8 O + 0.99H2 O)
107.18 ± 1.69
x = 9.97, y = 2.58, z = 10.94c
(0.70CO2 + 0.30N2 ) with (0.03C4 H8 O + 0.97H2 O)
113.66 ± 1.79
x = 8.11, y = 2.19, z = 13.16c
a (G · nH O); n is the number of water molecules in the unit structure and G is the pure guest species. 2 b (xCO · yN · 46H O); x and y are the numbers of carbon dioxide and nitrogen molecules, respectively, 2 2 2 in structure I. c (xCO2 · yN2 · zC4 H8 O · 136H2 O); x, y, and z are the numbers of carbon dioxide, nitrogen, and THF molecules, respectively, in structure II; C4 H8 O is THF.
0.1 0.0 – 0. 1
q/(J . s – 1)
– 0. 2 – 0. 3 – 0 .4 – 0 .5 – 0 .6 – 0 .7
0
2000
4000
6000 8000 10000 12000 14000 16000 18000 20000 t/s
FIGURE 3. Plot of heat flux q against time t for the endothermic process of hydrate dissociation of simple CH4 and CO2 hydrates. —, CH4 ; – –, CO2 .
Jager et al. (11) suggested a thermodynamic model for predicting equilibrium conditions of methane hydrate with 1,4-dioxane as promoter. They assumed that the mixed hydrate of methane and 1,4-dioxane formed structure II, which would be general for other mixed hydrates having different promoters. We used a similar calculation method to determine
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the composition of mixed hydrates. It was found that the model calculation results were in good agreement with experimental data. The required Kihara potential parameters for THF were directly obtained from experimental equilibrium dissociation pressures. The hydration number can be determined from both the equilibrium hydrate compositions and cage occupancy by guest molecules. The resulting experimental enthalpies of dissociation for several simple and mixed hydrates consisting of carbon dioxide, nitrogen, and THF are listed in table 2. As discussed by Sloan and Fleyfel, (6) the enthalpies of dissociation appear to be relatively constant over a wide range of composition for (carbon dioxide + nitrogen). The guest (0.17CO2 + 0.83N2 ) was particularly chosen because of our interest in carbon dioxide recovery from power-plant flue gas. Mixed hydrates of (carbon dioxide + nitrogen) form either structure I or II, depending on the composition of the guest species. Above a mole fraction content of 0.15 of carbon dioxide structure I hydrates form, but below this composition structure II hydrates form. (12) Thus, both (0.17CO2 + 0.83N2 ) and (0.70CO2 + 0.30N2 ) form structure I hydrates, resulting in almost the same values for the dissociation enthalpy. For mixed hydrates of (carbon dioxide + nitrogen + THF), the enthalpies of dissociation were higher than those of structure II hydrates, but smaller than those of the structure II hydrates of propane or isobutane. (3) The mixed hydrates containing THF of table 2 refer to a THF mole fraction of 0.01 to 0.03 in the water. Although the enthalpies of dissociation of the mixed hydrates containing THF appear to be similar, they do depend on the THF content. The addition of THF to (carbon dioxide + nitrogen) changed the hydrate structure I to II and increased the total amount of entrapped guest species, thus leading to enhanced hydrate stability. For structures I and II, the enthalpy of dissociation becomes a function of the number of crystal hydrogen bonds and about 80 per cent of the total enthalpy of dissociation comes from the strength of water hydrogen bonds. (7) It can therefore be expected that an increase in guest molecules in the cavities renders the hydrate structure loose and decreases the enthalpy of dissociation. In addition, THF greatly enhances hydrate stability and leads to increasing equilibrium temperature and decreasing corresponding equilibrium pressure of hydrate-contained mixture. This enhanced hydrate stability indicates that guest molecules occupy readily the cavities, resulting in a smaller enthalpy of dissociation than is the case for other structure II hydrates. Using an indirect approach, Skovborg and Rasmussen (7) calculated the enthalpy of dissociation using the Clausius–Clapeyron equation. The resulting values for the simple carbon dioxide and nitrogen hydrates were found to be (68.71 and 66.74) kJ · mol−1 , respectively and are in agreement with the experimental values. The results of this study are useful for separating carbon dioxide, methane, nitrogen, and many other guest molecules from multi-component gas mixtures. This work was supported by grant No. 98-0502-04-01-3 from the Basic Research program of the KOSEF and also partially by the Brain Korea 21 Project. REFERENCES 1. Handa, Y. P.; Hawkins, R. E.; Murray, J. J. J. Chem. Thermodynamics 1984, 16, 623–632. 2. Handa, Y. P. J. Chem. Thermodynamics 1986, 18, 891–902. 3. Handa, Y. P. J. Chem. Thermodynamics 1986, 18, 915–921.
Enthalpies of dissociation of clathrate hydrates 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
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Rueff, R. M.; Sloan, E. D.; Yesavaga, V. F. AIChE J. 1988, 34, 1468–1476. Lievois, J. S.; Perkins, R.; Martin, R. J.; Kobayashi, R. Fluid Phase Equilib. 1990, 59, 73–97. Sloan, E. D.; Fleyfel, F. Fluid Phase Equilib. 1992, 76, 123–140. Skovborg, P.; Rasmussen, P. Fluid phase Equilib. 1994, 96, 223–231. Vargaftik, N. B. Tables on the Thermophysical Properties of Liquids and Gases. John Wiley & Sons, Inc.: New York. 1975. Lide, D. R. CRC Handbook of Chemistry and Physics. CRC Press: Boca Raton. 1994. de Roo, J. L.; Peters, C. J.; Lichitenthaler, R. N.; Diepen, G. A. M. AIChE J. 1983, 29, 651–657. Jager, M. D.; de Deugd, R. M.; Peters, C. J.; de Swaan Arons, J.; Sloan, E. D. Fluid Phase Equilib. 1999, 165, 209–223. Diamond, L. W. Geochim. Cosmochim. Acta 1994, 58, 19–41. Deaton, W. M.; Frost, E. M. U.S. Bureau of Mines Monograph 1946, 8, 101. Kuustraa, V. A.; Hammerschaimb, E. C. Handbook of Gas Hydrate Properties and Occurrence, DOE/MC/19239, National Technical Information Service, U.S. Department of Commerce, 1983. (Received 6 April 2000; in final form 7 August 2000)
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