Article pubs.acs.org/jced
Equilibrium of Ethane Hydrate Formation in Carbon Pores Hongrui Pan,† Yaping Zhou,† Yan Sun,† Wei Su,‡ and Li Zhou‡,* ‡
High Pressure Adsorption Laboratory, School of Chemical Engineering and Technology, and †Department of Chemistry, School of Science, Tianjin University, Tianjin 300072, China ABSTRACT: The formation of hydrates in carbon pores was utilized to store natural gas, and ethane is the second major component of natural gas; therefore, ethane hydrate formation in carbon pores is studied in comparison with that of methane. Ethane is a major raw material of ethylene in the petrochemical industry; therefore, its mixture with ethylene is of importance and the formation condition of ethane hydrates was compared also with that of ethylene. The equilibrium isotherms of ethane on wet carbons with different water contents as well as the isotherms for different temperatures were collected, from which the formation pressures of ethane hydrates as well as the enthalpy change of ethane hydrate formation were determined. It was shown that the largest volumetric capacity for ethane storage is observed at the water load that just about fully fills pore spaces. Ethane hydrates were formed in wet activated carbons at about same pressures as in water media and the formation pressure is much lower than that required for methane hydrates formation.
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INTRODUCTION The storage of natural gas in terms of wet activated carbon is recently well studied,1 and the same V/V (volumetric ratio of the stored gas at standard state to cylinder) was reached at half storage pressure in comparison with CNG (compressed natural gas).2 The storage mechanism on wet carbons is hydrate formation in carbon pores. Although quite a few studies have been reported for methane, one cannot find a work regarding the formation of ethane hydrates in carbon pores, though ethane is the second major component of natural gas and accounts for (5 to10) % of the total. In the petrochemical industry, ethane is used to produce ethylene, and both ethane and ethylene are important gases of the industry. Gas hydrate is a high-density form of gas with relatively high stability; therefore, it attracts extensive research interest.3 The supercritical temperature of methane is 190.6 K, and that of ethylene and ethane is 282.4 and 305.4 K, respectively; therefore, methane forms hydrates always at supercritical temperatures, and ethane forms hydrates at subcritical temperatures while ethylene forms hydrates at both sides of the critical temperature, and big difference was shown between them.4 Although ethane hydrate formation is well studied,5,6 the formation pressures of ethane hydrates reported in literature were for water media and for temperatures (283 to 323) K.7−9 It has been known that the temperature of hydrate formation applicable for natural gas storage is below 283 K since the formation pressure of methane hydrates becomes too high to be applied in practice. In addition, the formation of ethane hydrates in carbon pores has not been reported; therefore, it is of interest to carry out the present study.
Table 1. Purity of Gases Used in Experiments purity 0.9999 0.9999 0.995
Figure 1. Adsorption isotherm of N2 on a carbon sample at 77 K (n, adsorbed amount, mmol·g−1; p and ps, adsorption and saturated pressure of nitrogen, MPa).
formation equilibrium of methane hydrates, the details of which were previously described.1 As was previously indicated,4 the measurement precision was determined by errors embedded in the values of temperature, pressure, and compressibility factor.
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EXPERIMENTAL SECTION The equilibrium of ethane hydrate formation in wet activated carbon was measured on a volumetric setup, the same as that used for the measurement of adsorption equilibrium and for the © XXXX American Chemical Society
gases helium nitrogen ethane
Received: February 12, 2013 Accepted: May 1, 2013
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dx.doi.org/10.1021/je400145z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 2. The Adsorption Data of N2 on Carbon Sample at 77 K n
n
n
p/ps
mmol·g−1
p/ps
mmol·g−1
p/ps
mmol·g−1
1.02·10−07 1.52·10−07 2.50·10−07 4.08·10−07 6.40·10−07 9.61·10−07 1.38·10−06 1.93·10−06 2.61·10−06 3.46·10−06 4.48·10−06 5.67·10−06 7.18·10−06 8.84·10−06 1.07·10−05 1.28·10−05 1.52·10−05 1.78·10−05 2.07·10−05 2.39·10−05 2.74·10−05 3.12·10−05 3.54·10−05 3.99·10−05 4.49·10−05 5.03·10−05 5.62·10−05 6.26·10−05 6.95·10−05 7.70·10−05 8.51·10−05
0.23 0.46 0.69 0.92 1.15 1.38 1.61 1.84 2.06 2.29 2.52 2.75 2.98 3.21 3.44 3.67 3.90 4.13 4.36 4.58 4.81 5.04 5.27 5.50 5.73 5.96 6.19 6.42 6.65 6.88 7.10
9.38·10−05 1.03·10−04 1.14·10−04 1.25·10−04 1.38·10−04 1.50·10−04 1.64·10−04 1.79·10−04 1.96·10−04 2.13·10−04 2.32·10−04 2.53·10−04 2.75·10−04 3.00·10−04 3.26·10−04 3.55·10−04 3.86·10−04 4.20·10−04 4.57·10−04 4.97·10−04 5.47·10−04 6.09·10−04 6.69·10−04 7.33·10−04 7.92·10−04 8.49·10−04 8.49·10−04 9.29·10−04 1.02·10−03 1.13·10−02 2.91·10−02
7.33 7.56 7.79 8.02 8.25 8.47 8.70 8.93 9.16 9.38 9.61 9.84 10.06 10.29 10.52 10.74 10.97 11.19 11.42 11.64 11.86 12.08 12.31 12.53 12.75 12.97 13.21 13.43 13.65 18.47 20.66
6.35·10−02 7.71·10−02 9.99·10−02 1.20·10−01 1.40·10−01 1.61·10−01 1.81·10−01 2.02·10−01 2.50·10−01 3.07·10−01 3.60·10−01 3.99·10−01 4.50·10−01 4.99·10−01 5.50·10−01 6.00·10−01 6.67·10−01 7.17·10−01 7.67·10−01 8.16·10−01 8.36·10−01 8.66·10−01 8.91·10−01 9.16·10−01 9.41·10−01 9.65·10−01 9.75·10−01 9.80·10−01 9.90·10−01 9.95·10−01
23.53 24.52 26.02 27.23 28.33 29.34 30.26 31.08 32.66 34.00 34.83 35.27 35.69 35.99 36.22 36.39 36.57 36.67 36.78 36.88 36.94 37.00 37.06 37.12 37.19 37.28 37.34 37.38 37.52 37.70
Table 3. The Pore Size Distribution Data of Carbon Sample
Figure 2. Pore size distribution of carbon sample (dp, pore size, nm; Vp, pore volume with size dp, cm3·g−1).
A pressure transmitter, model PAA-23/8465.1-200 manufactured by Keller Druckmesstechnik of Switzerland, was used to measure pressure, and the deviation from linearity for the whole range of 20 MPa is less than 0.05 %. The volume of the reference cell was determined by the volume of liquid filling in the cell, and that of the sorption cell was determined by helium expansion. The amplitude of temperature fluctuation is less than ± 0.1 K. The compressibility factor was evaluated by a virial equation of state. The relative error of the measurement varies in (2 to 3) %
dp/nm
Vp/cm3·g−1
dp/nm
Vp/cm3·g−1
0.39 0.43 0.46 0.50 0.54 0.59 0.64 0.68 0.73 0.80 0.86 0.93 1.00 1.09 1.18 1.27 1.36 1.48
0.000 0.000 0.000 0.000 0.096 0.020 0.000 0.012 0.021 0.044 0.014 0.000 0.000 0.049 0.007 0.118 0.044 0.031
1.59 1.72 1.86 2.00 2.16 2.34 2.52 2.73 2.95 3.18 3.43 3.70 4.00 4.32 4.66 5.04 5.43
0.037 0.030 0.050 0.066 0.087 0.081 0.077 0.077 0.049 0.033 0.026 0.013 0.008 0.005 0.003 0.002 0.000
depending on equilibrium temperature as was previously discussed.10 The purity of ethane and other gases used in experiments is shown in Table 1. The activated carbon used in the experiments was manufactured from carbonized corncobs using KOH as the B
dx.doi.org/10.1021/je400145z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 4. Isotherm and its derivative over sorption pressure with Rw = 1.2 (n, adsorbed amount, mmol·g−1; p, adsorption pressure, MPa).
Figure 3. Ethane isotherms on wet carbon with different water contents at 277 K (n, adsorbed amount, ·mol.g−1; p, adsorption pressure, MPa; Rw, water load). 0, Rw = 0; 1, Rw = 0.70; 2, Rw = 1.00; 3, Rw = 1.50; 4, Rw = 2.00; 5, Rw = 2.50.
Pore size distribution of the carbon was determined by the NLDFT (nonlocal density function theory) method12 and is shown in Figure 2 (also in Table 3). A set of ethane isotherms above the wet activated carbons with different water loads was collected at 277 K, and then the experiment switched to the measurement of equilibrium at different temperatures targeting at the evaluation of hydrate formation pressures and hydrate formation enthalpy.
activation agent. The pulverized dry corncobs of size 0.4−0.9 mm were initially carbonized at 400 °C in nitrogen atmosphere for 0.5 h. The corncob charcoal was uniformly mixed with KOH according to the weight ratio of 2 (KOH):1 (charcoal), and the mixture was heated in nitrogen atmosphere at 850 °C for 1.5 h. The carbon sample was first washed with 0.1 M HCl solution and then with distilled water after cooling to room temperature. Then the carbon sample was dried at 120 °C for 12 h, at which time Cl− ions were not detected in the washing water. The activation procedure was repeated for two more times to obtain the final sample. To characterize the final carbon sample, the adsorption isotherm of N2 on the sample was collected with a Micromeritics ASAP 2020 instrument at 77 K and the result is shown in Figure 1 (also in Table 2), based on which the BET (Brunauer, Emmett, and Teller)11 surface area was evaluated as 2552 m2·g−1. The pore volume was estimated based on the adsorbed amount of N2 at relative pressure of 0.98, and the result was 1.30 cm3·g−1.
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RESULTS AND DISCUSSION The Isotherms of Ethane on Wet Carbons with Different Water Loads. A set of ethane isotherms on wet carbons is shown in Figure 3 (also in Table 4) for different water contents. The water content is expressed as Rw, the weight ratio of loaded water to dry carbon. The no. 0 isotherm is the one on dry carbon. It shows a typical unimodal feature of a Type I adsorption isotherm. However, the other isotherms numbered from 1 to 5 are the ones on wet carbons with different water contents. As the isotherms of methane and ethylene are above wet carbon, an inflection point is shown on the isotherms
Table 4. The Amount of Ethane Fixed on Wet Carbons with Different Water Contents at 277 K Rw = 0
Rw = 0.70
Rw = 1.00
Rw = 1.50
Rw = 2.00
Rw = 2.50
p
n
p
n
p
n
p
n
p
n
p
n
MPa
mmol·g−1
MPa
mmol·g−1
MPa
mmol·g−1
MPa
mmol·g−1
MPa
mmol·g−1
MPa
mmol·g−1
0.00 0.02 0.08 0.24 0.52 0.84 1.14 1.43 1.70 1.91 2.07 2.18 2.27 2.33 2.40 2.48 2.56 2.63
0.00 1.82 5.00 8.49 11.08 12.78 13.91 14.58 14.90 15.02 15.02 14.97 14.95 14.95 15.11 14.97 15.02 15.05
0.00 0.12 0.31 0.52 0.65 0.79 0.87 1.02 1.22 1.46 1.69 1.87 1.99 2.31 2.52
0.00 2.01 3.41 4.59 6.30 8.20 11.34 14.23 16.36 17.23 17.37 17.43 17.44 17.53 17.61
0.00 0.16 0.36 0.57 0.73 0.88 0.95 1.08 1.31 1.55 1.76 1.95 2.10 2.30 2.46 2.61
0.00 0.91 1.60 2.67 4.99 7.88 12.27 15.99 18.28 19.42 20.01 20.15 20.31 20.42 20.45 20.51
0.00 0.21 0.37 0.50 0.61 0.73 0.85 0.85 0.91 1.03 1.20 1.40 1.61 1.80 1.97 2.15 2.32 2.48 2.60
0.00 0.24 0.74 1.73 3.22 4.83 6.87 11.09 14.31 16.75 18.82 20.25 21.00 21.18 21.34 21.54 21.53 21.65 21.68
0.00 0.19 0.35 0.48 0.60 0.71 0.82 0.83 0.85 0.98 1.18 1.42 1.66 1.85 2.04 2.19 2.34 2.49 2.60
0.00 0.26 0.75 1.57 2.84 4.51 6.75 11.09 15.14 18.80 21.23 22.71 23.29 23.52 23.50 23.57 23.56 23.48 23.62
0.00 0.20 0.39 0.54 0.67 0.78 0.83 0.85 1.05 1.30 1.55 1.77 1.95 2.11 2.28 2.44 2.58
0.00 0.16 0.91 2.03 3.70 5.92 10.46 17.21 21.80 24.38 25.39 26.06 26.25 26.27 26.23 26.19 26.26
C
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Table 5. The Isotherm and Its Derivative over Sorption Pressure (Rw = 1.2) p
n
dn/dp −1
MPa
mmol·g
0.00 0.17 0.36 0.51 0.65 0.78 0.81 0.88 1.02 1.18 1.38 1.58 1.78 1.98 2.18 2.39
0.00 0.52 1.69 3.18 4.97 7.19 10.70 14.60 17.15 19.00 20.03 20.75 21.17 21.42 21.41 21.30
mmol·g−1·MPa−1 3.06 4.61 7.96 11.32 15.21 67.44 87.73 37.81 14.39 8.33 4.48 2.84 1.65 0.58 −0.31 −0.56
Figure 6. Ethane isotherms on wet carbon with Rw = 1.2 at several temperatures (n, adsorbed amount, mmol·g−1; p, adsorption pressure, MPa). 1, 273 K; 2, 277 K; 3, 281 K; 4, 285 K.
Figure 7. Plot of ln f vs 1/T for the formation of ethane hydrate in carbon pores ( f, fugacity, MPa; T, temperature, K).
Figure 5. Effect of water load on storage capacity (Rw, water load; V/V, volumetric quantity of stored gas per unit volume of container; TVC, theoretical volumetric capacity).
stored gas per 100 g of dry carbon), which is close to that for ethylene (100 w = 84)4 and much larger than for methane (100 w = 65)2. Too much water content led to a decrease of isotherms for methane,2 but this phenomenon was not shown for ethane. Effect of Water Content on Storage. Although the quantity of fixed ethane increases with increasing water content of carbon, there still is an optimal water content for the maximization of storage capacity if hydrate formation is applied for storage and/or transportation of ethane. A theoretical volumetric capacity (TVC) was previously defined1 in order to discuss the upper limit of gas storage, and the effect of water content on TVC is shown in Figure 5 (also in Table 6) for ethane and the tested carbon. Apparently, the maximal storage capacity would occur around Rw = 1.3, which is equivalent to fully filled pore spaces with water. Thermal Effect of Hydrate Formation. The enthalpy change of hydrate formation can be evaluated from another set of formation isotherms at different temperatures, and such a set of data is shown in Figure 6 (also in Table 7), from which the formation pressures are obtained for different temperatures. The enthalpy change of hydrate formation in carbon pores is determined based on the Clausius−Clapeyron equation:13
Table 6. Effect of Water Load on Storage Capacity. Rw
V/V
0 0.70 1.00 1.20 1.50 2.00 2.50
198 230 267 282 245 215 199
indicating the formation of hydrates, and the equilibrium pressure at the inflection point is regarded as the formation pressure of hydrates in carbon pores. Because the isotherm shows the maximum slope at the inflection point as shown in Figure 4 (also in Table 5), the formation pressure of hydrates is determined by differentiating isotherms. The formation pressure of ethane hydrates is rather low, about 0.8 MPa at 277 K compared to about 5.5 and 0.9 MPa, respectively, for methane and ethylene. The highest gravimetric storage capacity corresponding to no. 5 isotherm is about 100 w = 79 (g of D
dx.doi.org/10.1021/je400145z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 7. The Ethane Isotherms on Wet Carbon (Rw = 1.2) at Several Temperatures T = 273 K
T = 277 K
p
n
T = 281 K
p
MPa
mmol·g
0.00 0.15 0.34 0.47 0.50 0.58 0.68 0.85 1.07 1.27 1.52 1.87 2.29
0.00 0.61 1.97 3.47 6.95 10.47 14.23 17.36 19.47 20.96 21.27 21.65 21.68
−1
n
MPa
mmol·g
0.00 0.17 0.36 0.51 0.65 0.78 0.81 0.88 1.02 1.18 1.38 1.58 1.78 1.98 2.18 2.39
0.00 0.52 1.69 3.18 4.97 7.19 10.70 14.60 17.15 19.00 20.03 20.75 21.17 21.42 21.41 21.30
p −1
T = 285 K n
MPa
mmol·g
0.00 0.16 0.37 0.59 0.81 1.01 1.21 1.27 1.40 1.54 1.73 2.03 2.36
0.00 0.37 1.48 3.43 6.23 8.99 11.10 15.11 17.84 19.63 20.29 20.81 21.02
−1
p
n
MPa
mmol·g−1
0.00 0.18 0.38 0.57 0.78 1.00 1.23 1.47 1.72 1.92 2.06 2.17 2.17 2.30 2.47
0.00 0.68 1.51 2.87 4.99 7.21 9.43 10.87 11.22 11.38 11.38 11.46 14.07 14.08 14.16
Table 8. Data for Clausius−Clapeyron Plot T/K
P/MPa
285.0 281.0 277.0 273.0
2.17 1.25 0.80 0.49
f/MPa −02
3.996·10 1.411·10−02 4.963·10−03 1.796·10−03
(1/T)/K−1
ln( f)
0.003507 0.003557 0.003608 0.003661
−3.220 −4.261 −5.306 −6.322
Table 9. Comparison of Formation Pressures with Literature in pure water6
in carbon pore
T/K
p/MPa
T/K
p/MPa
273.70 274.30 274.80 275.70 275.90 277.60 277.95 278.70 278.80 279.30 279.80 280.20 280.40 280.53 280.90 281.10 281.27 281.50 282.00 282.10 282.60 282.98 283.20
0.51 0.55 0.58 0.65 0.66 0.81 0.86 0.93 0.95 1.01 1.08 1.14 1.17 1.19 1.26 1.28 1.32 1.35 1.45 1.45 1.56 1.64 1.69
273 277 281 285
0.50 0.81 1.27 2.17
⎡ d ln f ⎤ −ΔH = −R ⎢ ⎥ ⎣ d(1/T ) ⎦n
Figure 8. Comparison of hydrate formation pressures in carbon pore (present work, red dots) and in water media (curve) (p, formation pressure; MPa; T, temperature, K).
temperature (K); R is gas constant (8.314 J·mol−1 K−1). Therefore, the formation enthalpy change is determined from the slope of the plot ln f vs 1/T shown in Figure 7 (also in Table 8), and the result was −167.5 kJ·mol−1. The thermal effect of forming ethane hydrates is 2.8 times larger than that of methane hydrate formation (about −60 kJ·mol−1),9 and 3.3 times larger than ethylene hydrate formation (−50.3 kJ·mol−1).4 The large thermal effect of ethane hydrate formation may account for the fact that too much water content did not lead to a decrease of the fixed ethane because hydrate may form even outside pore spaces. A comparison is made for formation pressures of ethane hydrates in carbon pores and in water media (Table 9).6 As is shown in Figure 8, almost no difference was observed between them.
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CONCLUSION Ethane hydrates were formed in wet activated carbons at about the same pressures as in water media. The formation pressure (0.8 MPa) is lower than required for ethylene hydrates (0.9 MPa) and much lower than for methane hydrates (5.5 MPa). The largest volumetric storage capacity for ethane is observed at the water load that just about fully fills pore spaces. The enthalpy
(1)
where ΔH is the enthalpy change (kJ·mol−1); f is the fugacity (MPa) corresponding to the hydrate formation pressure; T is E
dx.doi.org/10.1021/je400145z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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change of ethane hydrate formation is 2.8 times larger than that of methane hydrate formation and 3.3 times larger than that of ethylene hydrate formation. Therefore, ethane hydrates are much easier to form than ethylene and methane at comparable conditions.
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AUTHOR INFORMATION
Corresponding Author
*Tel./Fax: +86 22 8789 1466. E-mail:
[email protected]. Funding
Financial support of the National Natural Science Foundation of China (No. 21076142 and No. 21206108) is sincerely acknowledged. Notes
The authors declare no competing financial interest.
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REFERENCES
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