Article pubs.acs.org/jced
Phase Equilibria of Clathrate Hydrates of Ethane + Ethene Kaniki Tumba,† Paramespri Naidoo,† Amir H. Mohammadi,*,†,‡ Dominique Richon,†,§ and Deresh Ramjugernath*,† †
Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban, 4041, South Africa ‡ Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France § Department of Biotechnology and Chemical Technology, School of Science and Technology, Aalto University, P.O. Box 16100, 00076 Aalto, Finland ABSTRACT: Dissociation conditions for simple and mixed hydrates of ethane and ethene (ethylene) have been measured using the isochoric pressure-search technique. Simple hydrate dissociation data for ethane and ethene measured in this work are compared to existing literature data. The agreement between the measured ethane hydrate dissociation data with the literature data is acceptable while some deviations between the measured ethene hydrate dissociation data and those reported in the literature are observed. All new data for simple and mixed hydrates of ethene and ethane are well-correlated using an empirical correlation proposed by Adisasmito and coworkers. However, agreement between the experimental data with the predictions of the CSMGem model is found to be unsatisfactory. A gas chromatography technique combined with the isochoric-pressure search method is used to measure composition of the vapor phase in equilibrium with the hydrate and aqueous phases inside the hydrate stability region. The feed compositions investigated were 0.174, 0.420, and 0.810 mole fractions of ethane. In addition, dissociation points were found to be in the vicinity of the ethane hydrate dissociation conditions regardless of the initial content of ethane in the feed. It was also found that temperature does not have a considerable effect on ethane content of the vapor phase in equilibrium with hydrate and aqueous phases inside the hydrate stability region at given pressures.
1. INTRODUCTION The term “gas hydrate or clathrate hydrate” refers to a class of icelike compounds consisting of appropriately sized small molecules (guests, typically gases and small volatile liquids) encapsulated into cage-like structures made of water molecules (host), due to van der Waals forces.1,2 The guest occupancy of the cavities formed by water molecules as well as the composition of the entrapped guests within the lattice can vary. For this reason, gas hydrates are nonstoichiometric compounds. Gas hydrates were documented for the first time by Humphrey Davy in a lecture hosted by the Royal Society in 1810.3 They attracted the attention of the engineering community when Hammerschmidt4 revealed that the blockage of crude oil and gas pipelines was due to their formation during flow assurance processes. However, it has been found recently that the formation of gas hydrates could be advantageously exploited in a number of industrial processes. The most studied and most promising potential applications of gas hydrates include carbon dioxide capture and sequestration;5,6 water treatment and desalination;7 gas storage and transportation;8−11 separation processes;12 refrigeration;13,14 fire extinction;15 natural gas recovery from natural formations,16−18 and so forth. Phase equilibrium data are required to design and optimize the aforementioned processes. Moreover, they can be used to test © 2013 American Chemical Society
existing thermodynamic models for prediction of the phase behavior of hydrate forming systems. To simulate, design, or optimize any of these processes, the knowledge of equilibrium data under hydrate forming conditions is essential. Such data, when experimentally generated, can be helpful in testing existing thermodynamic models or tuning new thermodynamic models for phase behavior under hydrate forming conditions. The present work is aimed at investigating the equilibrium dissociation conditions of simple and mixed hydrates of ethane and ethene at different gas feed compositions. It is worth noting that several data sets are available for the water + ethane system as summarized in Table 1. In most cases, good agreement is observed between the various literature sources. However, literature hydrate dissociation data for the water + ethene system are scarce and exhibit some discrepancies from one laboratory to another. The literature data are listed in Table 2. Furthermore, there are no experimental data for the dissociation conditions of the (ethane + ethene) mixed-gas hydrate in the open literature. One remarkable reference to this system is found in a thermodynamic modeling-based study undertaken by Ballard Received: September 25, 2012 Accepted: January 3, 2013 Published: March 27, 2013 896
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measurement uncertainty, which is estimated to be ± 0.1 K. The calibrations of the thermometers were performed against a reference platinum resistance thermometer (WIKA digital thermometer calibration standard, model no. CTH 6500). The pressure in the vessel is measured with a WIKA pressure transducer rated for pressures up to 20 MPa. The combined expanded uncertainty on pressure measurement is estimated to be ± 0.007 MPa. The transducer was calibrated against a pressure calibration standard (WIKA 6000). The equilibrium cell is connected to a ROLSI autosampler and a SHIMADZU 2010 gas chromatograph (GC) equipped with a thermal conductivity detector (TCD) and fitted with a PORAPAK-Q packed column. Table 4 summarizes the
Table 1. Literature Data for Ethane Hydrate Dissociation Conditions. Trange, Prange, and N, Respectively, Refer to the Temperature Range, Pressure Range, and Number of Data Points author(s)
Trange/K
Prange/MPa
N
Avlonitis24 (1988) Clarke and Bishnoi25 (2000) Deaton and Frost26 (1946) Englezos and Bishnoi27 (1991) Galloway et al.28 (1970) Long et al.29 (2010) Maekawa30 (2012) Mohammadi et al.31 (2008) Nixdorf and Oellrich32 (1997) Reamer et al.33 (1952) Roberts et al.34(1940)
277.8 to 287.2 274.2 to 280.7 273.7 to 286.5 274.3 to 283.0 277.6 to 282.5 280.1 to 285.6 276.6 to 287.5 275.2 to 282.1 273.7 to 287.6 279.9 to 287.4 273.4 to 287.0
0.848 to 3.082 0.487 to 1.087 0.510 to 2.730 0.548 to 1.637 0.814 to 1.551 1.110 to 2.320 0.730 to 3.220 0.600 to 1.400 0.499 to 3.244 0.972 to 3.299 0.545 to 3.054
10 3 17 6 3 5 9 3 15 4 11
Table 4. GC Specification and Set-up, Including the Detector Temperature (Td), the Carrier Gas Flow Rate (Ucg), the Injection Port Temperature (Tinj), the Column Temperature (Tcol), and the Column Inner (ID) and Outer (OD) Diameters
Table 2. Literature Data for Ethene Hydrate Dissociation Conditions. Trange, Prange, and N, Respectively, Refer to the Temperature Range, Pressure Range, and Number of Data Points author(s)
Trange/K
Prange/MPa
N
Sugahara et al.35 (2000) Reamer et al.33(1952) Ma et al.36 (2001) Snell et al.37 (1961)
279.5 to 328.0 272.0 to 285.8 273.7 to 287.2 278.1 to 286.3
1.170 to 465.0 0.567 to 3.035 0.665 to 3.210 1.000 to 2.800
46 11 10 4
data acquisition software detector type Td/K carrier gas Ucg/m3·s−1 Tinj/K column type ID/m OD/m L/m Tcol/K
and Sloan.19 They assessed hydrate-based technology as separation process for gas mixtures, including ethane−ethene system. The latter process was found to be potentially effective and potentially more economic than the currently used cryogenic distillation process to separate ethane−ethene mixtures. However, these authors underlined the importance of experimental data to confirm their findings. The present work aims at providing the necessary hydrate equilibrium data for the ethane + ethene + water system for vapor feed compositions of 0.174, 0.420, and 0.810 mole fractions of ethane. The experimental data are well-correlated using the Adisasmito and co-workers correlation. The predictions of the CSMGem model are found to be unsatisfactory with the experimental data.
conditions under which GC analyses were conducted. The TCD was calibrated for ethane and ethene using helium as carrier gas. The obtained calibration data were fitted to a linear equation which was then used to relate the two peak areas of the unknown sample to the quantitative vapor phase composition at a given equilibrium condition. The combined expanded uncertainty in determining molar compositions was estimated to be ± 0.005 mole fraction. 2.2. Experimental Procedure. 2.2.1. Simple Hydrate Dissociation Conditions. The hydrate dissociation conditions were measured using the well-established isochoric pressure search method as used by other researchers.20−23 The reliability of this method using the aforementioned apparatus has been examined successfully and reported in ref 20. Prior to any component loading, the cell was immersed into the temperaturecontrolled ethanol bath and evacuated down to 0.8 kPa for approximately two hours. Approximately 40 % of the total volume of the cell was loaded before supplying the gas from its cylinder through a pressure-regulating valve. The impeller was started to allow proper mixing of the components. After obtaining temperature and pressure stability (far enough from the hydrate formation region), the temperature of the system under investigation was slowly decreased to form the hydrate. Hydrate formation in the vessel was detected by a notable pressure drop. The temperature was then increased by steps of 0.1 K. At every temperature step, the temperature was kept constant for a sufficient time to achieve an equilibrium state in the vessel. In this way, a pressure−temperature diagram was obtained for each experimental run, from which the hydrate dissociation point was determined. If the temperature is increased in the hydrate-forming region, hydrate crystals partially
2. EXPERIMENTAL SECTION 2.1. Materials and Apparatus. Table 3 provides details about the purities and suppliers of chemical components, namely, water, ethane, and ethene, used in this study. Table 3. Purities and Suppliers of the Materialsa
a
gas
origin
mole fraction purity
ethane ethene
Afrox Afrox
0.9999 0.9999
GC solution TCD 523.15 helium 3.33·10−7 523.15 packed column Poropak Q 2.2·10−3 3.2·10−3 2.5 323.15
Ultrapure Millipore Q water was used in all experiments.
The experimental setup was described in detail previously.20 Its main part is a stainless steel cylindrical cell, which can withstand pressures up to 20 MPa. The volume of the cell is approximately 60 cm3. It is immersed in a temperature-controlled ethanol bath. A magnetically coupled stirrer, incorporating rare earth magnets, was installed in the vessel. Two platinum resistance thermometers (Pt100) are used to measure temperatures and check for agreement within the temperature 897
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Table 5. Experimental (Pexp) and Predicted (Ppred) Dissociation Pressures for Simple and Mixed Hydrates of Ethene and Ethane. yo,ethane Represents Ethane Mole Fraction in the Feed, on a Water-Free Basisa yo,ethane
T/K
Pexp/MPa
Ppred d/MPa
RDb,d/%
Dc,d/MPa
Pcal /MPa
RDb,e/%
Dc,e/MPa
0
273.3 275.6 276.5 278.5 281.3 282.8 285.1 286.7 288.0 288.9 289.6 284.8 285.7 286.4 276.2 278.8 282.3 285.3 286.2 288.3 273.8 277.4 283.4
0.609 0.798 0.891 1.164 1.634 1.998 2.715 3.405 4.265 4.853 5.559 2.039 2.300 2.478 0.676 0.929 1.444 2.201 2.430 3.191 0.451 0.732 1.648
0.567 0.745 0.829 1.052 1.473 1.770 2.366 2.924 3.509 4.017 4.501 2.253 2.537 2.790 0.754 1.037 1.597 2.301 2.627 3.745 0.508 0.794 1.735
6.9 6.6 7.0 9.6 9.9 11 13 14 18 17 19 −11 −10 −13 −12 −12 −11 −4.5 −8.1 −17 −13 −8.5 −5.3
0.042 0.053 0.062 0.112 0.161 0.228 0.349 0.481 0.756 0.836 1.058 −0.214 −0.237 −0.312 −0.078 −0.108 −0.153 −0.100 −0.197 −0.554 −0.057 −0.062 −0.087
0.609 0.798 0.890 1.140 1.634 1.994 2.726 3.405 4.092 4.655 5.150 2.305 2.612 2.882 0.654 0.909 1.444 2.081 2.367 3.214 0.465 0.732 1.647
0.0 0.0 0.1 2.1 0.0 0.2 −0.4 0.0 4.1 4.1 7.4 −13 −14 −16 3.3 2.2 0.0 5.5 2.6 −0.7 3.1 0.0 0.1
0.000 0.000 0.001 0.024 0.000 0.004 −0.011 0.000 0.173 0.198 0.409 −0.266 −0.312 −0.404 0.022 0.020 0.000 0.120 0.063 −0.023 −0.014 0.000 0.001
0.174
0.428
0.810
1
Combined expanded uncertainties Uc are Uc(T) = ± 0.1 K, Uc(Pexp) = ± 0.007 MPa, Uc(yo,ethane) = ± 0.005. The reported uncertainties are based on combined standard uncertainties multiplied by a coverage factor k = 2, providing a level of confidence of approximately 95 %. bRD = ((Pexp −Pcal/pred)/Pexp)·100. cD = Pexp −Pcal/pred. dCSMGem Software, used for prediction. eEquation 2, used for calculation. a
pressure. To measure the equilibrium condition at a higher pressure, the cell was further pressurized by successively adding water to the equilibrium cell until the desired pressure was attained. In this manner, different temperature, pressure and compositional data at equilibrium were measured for each feed gas mixture in the hydrate-forming region. The point at which all hydrate crystals dissociated was identified in the same manner as for simple hydrates.
dissociate, thereby substantially increasing the pressure. If the temperature is increased outside the hydrate region, only a smaller increase in the pressure is observed as a result of the temperature change of the fluids in the vessel. Consequently, the point at which the slope of pressure−temperature data plot changes sharply is considered to be the point at which all hydrate crystals have dissociated, and hence this is reported as the dissociation point. 2.2.1. Mixed Hydrate Equilibrium Data. The vessel was cleaned and evacuated (down to 0.8 kPa). Ethane and ethene mixtures at different compositions were prepared in the cell by loading pure ethane and pure ethene from corresponding cylinders fitted with pressure regulating valves. Meanwhile, the content of the cell was agitated to allow proper mixing of the components. After pressure and temperature stabilized far enough from the hydrate forming, the feed gas was sampled by means of ROLSI sampler and analyzed using the GC. Sampling and analysis were repeated five times to ensure reproducibility. After determining the feed gas composition, a well-known amount of water was added to the cell using a calibrated injector. The amounts of all the three components supplied to the cell were quantified. The isochoric pressure search method, as described in the previous section, was later followed. However, after hydrate formation, during the heating stage inside the hydrate stability region, at each temperature step, the temperature was kept constant for four to five hours to allow the system to reach equilibrium. Once this was achieved as observed by no change in system pressure, the compositions of the vapor phase were analyzed about every hour until successive composition values would agree with each other within 0.001 mole fraction. Average concentrations were registered as the composition of the vapor phase at the corresponding equilibrium temperature and
3. RESULTS AND DISCUSSION Newly obtained dissociation conditions of simple and mixed hydrates of ethane and ethene are presented in Table 5, while equilibrium conditions inside the hydrate stability region are reported in Table 6. Dissociation conditions for simple ethane and ethene hydrates provided a good check of the validity of the experimental procedure. As shown in Figures 1 and 2, the hydrate dissociation data obtained in this work are generally in satisfactory agreement with those of other authors.24−36 To show clearly discrepancies between various sources of data, fractional experimental pressure differences (ΔP/P) with respect to CSMGem software predictions are used in both Figures 1 and 2. For a given temperature, fractional pressure difference from CSMGem is calculated as: ⎛ ΔP ⎞ P exp − P pred ⎜ ⎟ = ⎝ P ⎠ P pred
(1)
Superscripts exp and pred stand for experimental and predicted data, respectively. A notable discrepancy is observed for temperatures greater than 280 K between the new data and those available in the literature.33,35−37 In fact, all literature data for ethene hydrate dissociation conditions agree with each other 898
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in the temperature range from 273 K to approximately 280 K. The reason remains unclear. Dissociation conditions for simple and mixed hydrates of ethane and ethene were fitted to the following equation, proposed by Adisasmito and co-workers originally for hydrate dissociation conditions of carbon dioxide + methane38 (hereafter, it is referred to as the Adisasmito−Frank−Sloan equation):
Table 6. Equilibrium Temperatures (T), Pressures (P), and Vapor Phase Compositions Obtained in the Hydrate Stability Region with Various Feed Compositions. yo,ethane Refers to pred Ethane Mole Fraction in the Feeda. yexp ethane and yethane Are Respectively the Experimental Vapor-Phase Mole Fraction of Ethane and That Predicted Using the CSMGem Software at Equilibrium. All Compositions Are Given on Water-Free Basisa gaseous feed
ln(P cal /MPa) = A + B(T /K)−1 + Cy + D(T /K)−2
liquid (water)−hydrate−gas equilibrium
yo,ethane
T/K
P/MPa
yexp ethane
ypred ethane
0.703 0.428 0.704 0.428 0.428 0.174 0.428 0.428 0.174 0.174 0.428 0.174 0.174 0.174 0.174 0.174 0.174 0.810 0.810 0.810 0.810 0.810 0.609 0.609 0.609 0.201 0.201 0.201
273.7 274.1 274.1 274.2 274.6 275.2 275.7 276.4 280.1 280.1 281.1 282.1 282.1 282.2 282.2 282.2 284.1 284.1 284.1 284.2 285.1 285.2 286.1 287.1 287.9 288.1 288.2 289.2
0.522 0.547 0.508 0.542 0.560 0.579 0.653 0.715 1.170 1.141 1.283 1.610 1.482 1.442 1.487 1.473 1.896 1.895 1.862 1.892 2.012 1.893 2.244 2.833 3.097 3.097 3.191 3.643
0.711 0.298 0.703 0.432 0.299 0.296 0.434 0.457 0.274 0.430 0.481 0.163 0.256 0.479 0.273 0.282 0.277 0.727 0.715 0.814 0.794 0.804 0.794 0.603 0.794 0.395 0.206 0.204
0.720 0.418 0.720 0.417 0.426 0.173 0.437 0.438 0.172 0.174 0.450 no convergence 0.174 0.173 0.174 0.174 0.173 0.807 0.804 0.807 0.811 0.811 0.609 0.609 0.618 0.203 0.203 0.204
+ Ey(T /K)−1 + Fy 2
(2)
where Ppred and T are the predicted equilibrium pressure and temperature, respectively; y is ethane mole fraction in the feed on a water-free basis. The coefficients were optimized as A = 146.514, B = −71767.6 K, C = 0.765, D = 8633499 K2, E = −452.5 K, F = 0.560. Calculations and predictions using the Adisasmito−Frank−Sloan equation38 as well as the CSMGem model1 are compared to experimental dissociation data in Table 5. The average absolute relative deviations (AARD-P) of the calculated/predicted pressures were found to be 3.4 % and 11.1 % for Adisasmito−Frank−Sloan equation38 and the CSMGem software,1 respectively. AARD-P is defined as follows: %AARD − P =
100 Ndata
∑ i
Pipred/cal − Piexp Piexp
(3)
In the above equation, N represents the number of data points. Superscript cal refers to calculated values. The plots shown in Figure 3 allow a better analysis of mixed hydrate dissociation data. It emerges that all of the measured mixed hydrate dissociation points are, close to the ethane hydrate phase boundary. This implies that addition of ethene has little effect on the ethane hydrate dissociation conditions whereas a small amount of ethane leads to a very large decrease of ethene hydrate dissociation pressures over the temperature and pressure ranges studied in this work. It is worth to note that the effect of ethene content on ethane hydrate dissociation conditions is not negligible. Finally, Figure 4 shows compositional data for the vapor phase in equilibrium with the hydrate and aqueous phases at various temperatures and pressures for the ethane + ethene + water system. It is clear that temperature has a little effect on the ethane content of the vapor phase at given pressures inside the hydrate stability region. This effect is noticeable at high ethane content of the gaseous feed.
a Combined expanded uncertainties Uc are Uc(T) = ± 0.1 K, Uc(P) = ± 0.007 MPa,Uc(yo,ethane) = Uc(yexp ethane) = ± 0.005. The reported uncertainties are based on combined standard uncertainties multiplied by a coverage factor k = 2, providing a level of confidence of approximately 95 %.
Figure 1. Comparison of the experimental dissociation pressures measured in this work for ethane simple hydrates with literature data in terms of fractional differences (ΔP/P) from CSMGem software predictions: ■, this work; ◇, ref 24; ◆, ref 25; , ref 26; ●, ref 27; □, ref 29; ▲, ref 30; ○, ref 31; ×, ref 32; ∗, ref 33; +, ref 34. 899
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Figure 2. Comparison of the experimental dissociation pressures measured in this work for ethene simple hydrates with literature data in terms of fractional differences (ΔP/P) from CSMGem software predictions: □, this work; ●, ref 33; △, ref 35; ○, ref 36.
dissociation data of simple ethane hydrates and the literature data was found. However, the latter agreement for ethene simple hydrates was found unsatisfactory. The CSMGem model1 predictions were found to be in unsatisfactory agreement with experimental ethane and ethene mixed hydrate dissociation data. It was shown that the empirical correlation38 employed in the present work correlates the hydrate dissociation conditions of ethane + ethene well. The study also reported compositional data for the vapor phase in equilibrium with hydrate and aqueous phases for the ethane + ethene + water system. It was interpreted that a small amount of ethane results in a large decrease of ethene hydrate dissociation pressures over the temperature ranges studied in this work. It was finally shown that ethane content of the vapor phase inside the hydrate stability region is negligibly affected by temperature change at given pressures. However, a noticeable effect at high ethane content of the gaseous feed is observed.
Figure 3. Experimental hydrate dissociation conditions for ethane + ethene + water system at various ethane mole fractions in the gas feed. Symbols represent experimental data: ◆, 0; △, 0.174; □, 0.428; ○, 0.810; ●, 1.000. To eliminate any confusion, the predictions of the CSMGem software1 have not been shown in this figure.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (D. Ramjugernath); a.h.m@ irgcp.fr (A.H.M.). Funding
This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation. The authors would also like to thank the National Research Foundation of South Africa (NRF) for financial assistance for this work. Notes
The authors declare no competing financial interest. This manuscript was presented at the South African Institution of Chemical Engineers Conference 2012.
■
Figure 4. Equilibrium conditions for ethane + ethene + water system at ◇, 274 K; ○, 282 K; △, 284 K. Symbols represent experimental data. To eliminate any confusion, the predictions of the CSMGem software1 have not been shown in this figure. yethane denotes ethane mole fraction in the vapor phase in equilibrium with hydrate and aqueous phases. Equilibrium pressures for simple hydrates were determined using eq 2.
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4. CONCLUSION Ethane and ethene simple and mixed hydrate dissociation data were measured and compared to the literature data, the results of an empirical correlation38 as well as the predictions of the CSMGem model.1 A good agreement between the new 900
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dx.doi.org/10.1021/je301051c | J. Chem. Eng. Data 2013, 58, 896−901
