Article pubs.acs.org/jced
Phase Equilibria of Clathrate Hydrates of Ethyne + Propene Kaniki Tumba,†,‡ Hamed Hashemi,† Paramespri Naidoo,† Amir H. Mohammadi,*,†,§ and Deresh Ramjugernath*,† †
Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban, 4041, South Africa ‡ Department of Chemical Engineering, Mangosuthu University of Technology, Umlazi, Durban 4031, South Africa § Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France ABSTRACT: In the present study, experimental incipient dissociation data obtained by the isochoric pressure search method for mixed ethyne and propene (0.189, 0.544 and 0.846 mol fraction of ethyne) hydrates are reported in the temperature and pressure ranges of (275.9 to 283.4) K and (0.651 to 1.827) MPa, respectively. Additionally, three-phase equilibrium conditions inside the hydrate stability region were measured in the temperature and pressure ranges of (273.4 to 282.6) K and (0.441 to 1.709) MPa, with compositional analysis. Experimental ethyne mole fractions at equilibrium on a water-free basis ranged from 0.080 to 0.856. The van der Waals and Platteeuw solid solution theory, with the Valderama− Patel−Teja equation of state and nondensity dependent mixing rules were used to model the hydrate dissociation conditions of the ethyne + propane + water system. Good agreement was found between experimental data and predicted values.
1. INTRODUCTION Clathrate hydrates, or gas hydrates, are inclusion compounds in which appropriately sized small molecules (guests, typically gases and small volatile liquids) are encapsulated in cage-like structures made of hydrogen-bonded water molecules (hosts).1,2 Three typical hydrate crystalline structures are structure I (sI), structure II (sII) and structure H (sH) in which the size and the number of cavities are different.1,2 The hydrate structure is stabilized by van der Waals forces between the guest and the host molecules. A comprehensive account of the properties, the importance, and applications of gas hydrates is given by Sloan and Koh.2 Ethyne3,4 and propene5,6 are well-known hydrate formers. Propene hydrate dissociation data sets which are available in the literature were listed and compared in a recent article.4 Regarding ethyne hydrate, two phase equilibrium data sets are available to date in the open literature.3,4 To the best of our knowledge, no phase equilibrium data are available in the literature for the ethylene + propene + water system under hydrate forming conditions. Clathrate hydrate equilibrium data sets are important as they are required for the simulation and design of potential hydrate-based processes such as carbon dioxide capture and sequestration, separation processes, gas storage and transportation, water treatment and desalination, fire extinction, natural gas recovery from natural hydrate formations, refrigeration, etc.2 In the present study, experimental measurements of phase equilibrium data are reported in terms of mixed ethyne and propene hydrate dissociation pressures and temperatures on © 2014 American Chemical Society
one hand and HLV (hydrate−liquid−vapor) equilibrium pressures, temperatures, and compositions on the other hand. Hydrate dissociation data for mixed propene and ethyne hydrates were measured using the isochoric pressure search method at different feed compositions, 0.189, 0.544 and 0.846 mol fractions of ethyne on a water-free basis. Dissociation data were measured in the temperature and pressure ranges from (275.9 to 283.4) K and (0.651 to 1.827) MPa, respectively. For compositional data in the hydrate forming region, these ranges were (273.4 to 282.6) K and (0.441 to 1.709) MPa. Ethyne mole fractions on a free-water basis were experimentally determined by gas chromatography. They ranged from 0.080 to 0.856. It is worth mentioning that the ethyne−propene system on which the present study is centered appears in hydrocarbon cracking streams7−9 and as a polyethylene pyrolysis product.10 Polyethylene pyrolysis is an interesting process in the context of solid waste management as it is associated with plastic conversion into valuable chemicals. Gas hydrate formation is likely to be used to recover either ethyne or propene from mixtures emanating from the two aforementioned processes. The hydrate dissociation data measured in this study was modeled with an approach combining the solid solution theory Special Issue: In Honor of E. Dendy Sloan on the Occasion of His 70th Birthday Received: January 10, 2014 Accepted: February 18, 2014 Published: March 7, 2014 217
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of van der Waals and Platteeuw,11 with the Valderrama−Patel− Teja equation of state12 (VPT EoS) and nondensity dependent (NDD) mixing rules.13 The performance of the model used is discussed in terms of deviations between its predictions and the reported experimental data.
The composition of the mixture was prepared in the cell by loading the two gases from the corresponding cylinders via pressure regulating valves. The stirrer was started to allow proper mixing of the two gases. A few minutes later, a sample was withdrawn from the cell using a ROLSI sampler15,18,19 and conveyed to a Shimadzu 2010 gas chromatograph (GC) for compositional analysis. This was repeated five times to ensure reproducibility. In this way, the composition of the gaseous feed was determined. Water was added to the cell by means of a calibrated injector. After obtaining temperature and pressure stability (far enough from the hydrate formation region), the isochoric pressure search method, as described in literature2,4,5,14−17,19,20 was then followed. The system temperature was slowly decreased to form the hydrate, and the hydrate formation in the vessel was detected by a pressure drop. After hydrate formation, the system temperature was slowly increased in steps. At each step, temperature was maintained constant for a suitable time to reach equilibrium. When there was no change in system pressure (within the uncertainty in pressure measurement), equilibrium was considered to be achieved. Samples of the vapor phase were analyzed every 30 min until successive composition values were in agreement with each other to within 0.001 mole fraction. The average concentration was recorded as the composition of the vapor phase at the corresponding equilibrium pressure and temperature. If the temperature is increased in the hydrate-forming region, hydrate crystals partially 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.2,4,5,14−17,19,20 Consequently, the point at which the slope of the pressure−temperature data plots changes sharply is considered to be the point at which all hydrate crystals have dissociated and hence this is reported as the dissociation point.2,4,5,14−17,19,20 To ensure accuracy, a stepwise increase of 0.1 K was adopted in the vicinity of the dissociation point. To move on to a higher equilibrium pressure, the cell was pressurized by adding water to the equilibrium cell until the desired starting pressure was reached. In this way, various temperature, pressure, and compositional data at equilibrium were measured for each feed gas mixture in the hydrate forming region.15,18,19
2. EXPERIMENTAL SECTION 2.1. Materials and Experimental Setup. Information related to the origin and the purity of the materials used in this study is provided in Table 1. The experimental setup consisted Table 1. Purities and Suppliers of the Materialsa
a
gas
origin
mole fraction purity
ethyne propene
Afrox Afrox
0.999 0.995
Ultrapure Millipore Q water was used in all experiments.
of a cylindrical equilibrium cell (approximately 60 cm3) which contained two viewing windows. The cell was immersed in a thermostatted ethylene glycol bath. It was designed to withstand pressures up to 20 MPa. Agitation of the cell contents was achieved by a magnetic stirrer bar installed in the cell, coupled to a motor-driven rare earth magnet that was placed underneath the bath. Two platinum resistance thermometers (Pt100) were used to measure temperatures; at the top and the bottom of the cell. These thermometers were calibrated against a reference platinum resistance thermometer (WIKA CTH 6500 digital thermometer calibration standard (uncertainty: ± 0.03 %)). The pressure in the vessel was measured using a 20 MPa WIKA pressure transducer which was calibrated using a WIKA pressure standard. Taking into account all sources of uncertainty, the expanded uncertainties in temperature and pressure measurements are estimated as ± 0.1 K and ± 0.007 MPa, respectively. Greater detail on the apparatus used in this study has been provided in previous studies.14 The vapor phase composition was measured on a water-free basis with a Shimadzu 2010 gas chromatograph (GC) equipped with a thermal conductivity detector (TCD) under the operating conditions given in Table 2. Table 2. GC Specification and Setup, 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 detector type Td/K carrier gas Ucg/m3·s−1 Tinj/K column type ID/m OD/m L/m Tcol/K
3. THERMODYNAMIC MODEL The equality of fugacity in coexisting phases has been used in this study as the equilibrium criterion. 3.1. Hydrate Phase. The solid solution theory of van der Waals and Platteeuw was used for the calculation of fugacity of water in the hydrate phase, f Hw , as follows:2,4,5,11,14,21,22
TCD 523.15 helium 8.33·10−7 523.15 packed column Poropak Q 22·10−3 3.2·10−3 2.5 463.15
⎛ −Δμ β− H ⎞ w ⎟⎟ f wH = f wβ exp⎜⎜ RT ⎝ ⎠
(1)
where ⎛ −Δμ β− L ⎞ w ⎟⎟ f wβ = f wL exp⎜⎜ RT ⎝ ⎠
(2)
In eq 2, f βw denotes the fugacity of water in the empty hydrate lattice, f Lw indicates the fugacity of pure water in the liquid phase, R stands for the universal gas constant, and T is the temperature. The difference between the chemical potential of water in the empty hydrate lattice and the hydrate phase, 22 Δμβ−H w , is given by
2.2. Experimental Procedure. The isochoric pressure search method2,4,5,14−17 was employed to determine the dissociation conditions for mixed ethyne + propene hydrates. The cell was first washed with deionized water, dried, and immersed in the temperature-controlled ethylene glycol bath before being evacuated down to 0.8 kPa for approximately 2 h. 218
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Journal of Chemical & Engineering Data Δμwβ − H = μwβ − μwH = RT ∑ vm̅ ln(1 +
Article
∑ Cjmf j )
m
Table 3. Experimental Dissociation Pressures (P) and Temperatures (Texp) for Simple and Mixed Hydrates of Propene and Ethynea,b
(3)
j
where vm̅ is the number of cavities of type m per water molecule in the unit hydrate cell, f j is the fugacity of the hydrate former j. Cjm is the Langmuir constant, which represents the interaction between the hydrate former and water molecules in the hydrate cavity and can be evaluated using the Kihara potential function.23,24 The following equation has been used to calculate Δμβ−L which is the difference between the chemical potential w of water in the empty hydrate lattice and that in the liquid phase:22,24 Δμwβ − L RT
=
Δμwβ (T , P)
=
Δμw0
RT RT
−
∫T
−
273.5 273.6 273.7 273.8 274.1 274.2 274.4
μwL (T , P) RT
T Δh β − L w
0
Texp/K
zo,water
RT
dT +
∫p
P Δv β − L w
0
RT
dP
0.920 0.968 0.979 0.986
275.9 276.2 276.5 276.6
0.913 0.946 0.972 0.984
278.5 278.8 279.1 279.6
0.825 0.940 0.943 0.972
282.3 282.7 283.1 283.4
(4)
μβw
μLw
In eq 4, and are the chemical potential of the empty hydrate lattice and that of pure water in the liquid (L) state respectively. P denotes the equilibrium pressure and T0 stands for the absolute temperature at ice point. Δμ0w is the reference chemical potential difference between water in the empty hydrate lattice and pure water in the ice phase at 273.15 K.2,22,24 Δhβ−L w and Δvβ−L w are molar enthalpy and volume differences between an empty hydrate lattice and ice or liquid water which were taken from the literature along with values used for the phase transition parameters from water to sI and sII clathrate hydrates. More details for modeling the hydrate phase are given in reference 24. 3.2. Fluid Phase. In this study, the fugacities of water and hydrate formers in liquid and vapor phases have been calculated using the Valderrama−Patel−Teja equation of state12,24 which is described by the following equations: P=
RT a − 2 v−b v + (b + c)v − bc
273.2 275.5 277.6 279.5 281.7 283.6 284.5 285.5
(5)
ΩaR2Tc2 Pc
(7)
b=
Ω bRTc Pc
(8)
c=
ΩcRTc Pc
(9)
Ωa = 0.66121 − 0.76105Zc 2
(10)
Ω b = 0.02207 + 0.20868Zc
(11)
Ωc = 0.57765 − 1.87080Zc
(12)
α(Tr) = [1 + F(1 −
a = ac + a A
0.3 0.1 0.2 0.5 0.0 0.0 0.2 0.3 0.3 0.3 0.2 0.1 0.1 0.1 0.3 0.2
(16)
where
where F = 0.46286 + 3.58230(ωZc) + 8.19417(ωZc)
0.2 0.2 0.4 0.5
For water, F and Ψ are constants equal to 0.72318 and 0.52084, respectively. In the above equations v and Z represent the molar volume and the compressibility factor, respectively and ω is the acenteric factor. The nondensity dependent mixing rules developed by Avlonitis et al.13 has been used to take into account the polar-nonpolar interaction in the attraction parameter of the equation of state (a), for water + ethyne and water + propene systems. In NDD mixing rules, the attraction parameter (a) is split into two parts:13
(13)
2
0 0 0 0 0 0 0
(15)
Ψ = 0.52084
where subscripts r and c denote the reduced and critical properties, respectively. The alpha function in eq 6 is defined as follows: TrΨ)]2
zo,eth = 0c,d 0.492 273.5 0.505 273.6 0.521 273.7 0.530 273.8 0.565 274.1 0.588 274.2 0.613 274.4 zo,eth = 0.189d 0.651 276.1 0.694 276.4 0.754 276.9 0.782 277.1 zo,eth = 0.544d 0.909 278.8 0.934 278.7 0.986 279.3 1.100 280.1 zo,eth = 0.846d 1.652 282.3 1.718 282.7 1.774 282.9 1.827 283.1 zo,eth = 1c,d 0.614 272.9 0.780 275.2 0.986 277.4 1.224 279.4 1.554 281.6 1.968 283.7 2.223 284.8 2.467 285.7
AD/Ke
Combined expanded uncertainties UC are UC (Texp) = ± 0.1 K, UC (P) = ± 0.007 MPa, UC (z0,eth) = ± 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 %. b z0,eth and z0,water represent ethyne and water mole fractions in the feed, respectively. Tcal denotes calculated value of temperature. cData for pure guests were taken from a previous work.4 dMolar fraction on water-free basis. eAverage deviation: AD = |Texp − Tcal|.
(6)
ac =
Tcal/K
a
where
a = acα(Tr)
P/MPa
ac = (14)
∑ ∑ xixj(aiaj)0.5 (1 − kij) i
219
j
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reported data for simple hydrates4 are also provided in Figure 1. Care was taken to generate data that are confined to the region where both components are enclathrated. This led to the small temperature ranges for the present data. In fact, propene forms hydrates under HLV equilibrium conditions over narrow temperature and pressure ranges. As mentioned in the previous section, the solid solution theory of van der Waals and Platteeuw2,4,5,11,14,21,22,24 combined to the VPT equation of state,12,24 incorporating nondensity dependent mixing rules13,24 was used to model the hydrate dissociation conditions of the ethyne + propene + water system. Table 5 shows the transition parameters from hydrate to water as found in the literature.24 Binary interaction parameters and Kihara potential function parameters used in this study have been taken from our previous work.4 They are provided in Tables 6 and 7, respectively. The acentric factors and critical properties (Pc, Tc, Zc) of water and hydrate formers25,26 are reported in Table 8.
Figure 1. Clathrate hydrate dissociation conditions of propene + ethyne: ○, pure ethyne; ▲, 0.189 ethyne mole fraction; ■, 0.544 ethyne mole fraction; ◇, 0.846 ethyne mole fraction; +, pure propene; , model predictions.
aA =
∑ xp2 ∑ xiapilpi
(18)
Table 5. Phase Transition Parameters24 from Water to Hydrate Used in This Studya
In the two previous equations, x stands for the mole fraction of the species, kij is the classical binary interaction parameter, p denotes the polar component. The binary interaction parameter, lpi, between the polar component and the other components, has been obtained using the following temperature-dependent equation:13,24 lpi = lp0i − lp1i(T − T0)
structure
Δμ0w/J mol−1
Δh0w/J mol−1
Δv0w/cm3·mol−1
I II
1297 937
−4620.5 −5201
4.6 5.0
a Parameters: Δμ0w, chemical potential difference between empty hydrate lattice and pure water; Δh0w, molar enthalpy difference between empty hydrate lattice and ice at the ice point and zero pressure; Δv0w; volume difference between empty hydrate lattice and pure water.
(19)
4. RESULTS AND DISCUSSION Experimental dissociation data for mixed ethyne and propene hydrates are presented in Table 3 and Figure 1. HLV equilibrium temperatures, pressures, and vapor phase compositions obtained in the hydrate stability region with various feed compositions are reported in Table 4. To visualize the effect of each component on the clathrate phase behavior, previously
Table 6. Binary Interaction Parameters Values4 between Water (i) and Hydrocarbon (j) for the VPT-EoS12 and NDD Mixing Rules13 system
kij
lij0
lij1
source
ethyne (j) propene (j)
0.2260 0.233
0.9373 0.9758
0.0019 0.0030
4 4
Table 4. HLV Equilibrium Temperatures (T), Pressures (P), and Vapor Phase Compositions Obtained in the Hydrate Stability Region with Various Feed Compositions for the Ethyne + Propene + Water Systema,b zo,eth = 0.189c
zo,eth = 0.544c
zo,water
T/K
P/MPa
yethc
0.919 0.919 0.919 0.968 0.919 0.979 0.968 0.919 0.968 0.987 0.919 0.979 0.968 0.968 0.987 0.987
273.4 273.7 274.1 274.1 274.4 274.5 274.6 274.7 275.1 275.1 275.3 275.5 275.6 276 276.1 276.4
0.441 0.465 0.494 0.492 0.523 0.543 0.544 0.555 0.592 0.628 0.607 0.625 0.643 0.687 0.754 0.777
0.149 0.157 0.143 0.098 0.147 0.101 0.159 0.146 0.166 0.113 0.15 0.151 0.141 0.123 0.08 0.097
zo,water
T/K
0.913 0.946 0.913 0.972 0.913 0.913 0.946 0.984 0.946 0.972 0.984 0.946 0.984 0.913 0.984 0.984
274.1 274.1 274.6 275.1 275.7 276 276.1 276.1 277.1 277.1 277.1 278.1 278.1 278.2 279.1 279.3
zo,eth = 0.846c
P/MPa
yethc
zo,water
T/K
P/MPa
yethc
0.613 0.604 0.618 0.609 0.643 0.667 0.649 0.704 0.771 0.776 0.804 0.873 0.918 0.879 1.053 1.083
0.465 0.464 0.474 0.516 0.481 0.501 0.481 0.399 0.490 0.443 0.388 0.437 0.361 0.518 0.365 0.366
0.8247 0.9625 0.8247 0.9401 0.9625 0.8247 0.9401 0.9625 0.9401 0.9625 0.972 0.963
279.1 280.0 281.1 281.1 281.1 282.1 282.1 282.1 282.3 282.3 282.6 282.6
1.430 1.324 1.541 1.497 1.459 1.608 1.643 1.609 1.652 1.655 1.687 1.709
0.845 0.843 0.856 0.835 0.812 0.844 0.809 0.784 0.806 0.774 0.741 0.765
Combined expanded uncertainties UC are UC (Texp) = ± 0.1 K, UC (P) = ± 0.007 MPa, UC (z0,eth) = UC (z0,water) = UC (yeth) = ± 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%. bz0,eth and z0,water represent ethyne and water mole fractions in the feed, respectively. yeth is the experimental vapor phase mole fraction of ethyne at equilibrium. cMolar fraction on a water-free basis. a
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Table 7. Kihara Potential Function Parametersa,23,24 Used in This Study4 compound
α/Å
σ/Å
(ε/k)/K
ethyne propene
0.3630 0.7100
3.255 3.230
171.94 203.60
(5) Chapoy, A.; Alsiyabi, I.; Gholinezhad, J.; Burgass, R.; Tohidi, B. Clathrate hydrate equilibria in light olefins and mixed methane−olefins systems. Fluid Phase Equilib. 2013, 337, 150−155. (6) Clarke, E. C.; Ford, R. W.; Glew, D. N. Propylene gas hydrate stability. Can. J. Chem. 1964, 42 (8), 2027−2029. (7) Froment, G. P.; Van de Steene, B. O.; Van Damme, P. S.; Narayanan, S.; Goossens, A. G. Thermal cracking of ethane and ethane-propane mixtures. Ind. Eng. Chem. Process Des. Dev. 1976, 15 (4), 495−504. (8) Gál, T.; Lakatos, B. G. Re-pyrolysis of recycled hydrocarbon gasmixtures: A simulation study. Chem. Eng. Process.: Process Intensif. 2008, 47 (4), 603−612. (9) Godínez, C.; Cabanes, A. L.; Víllora, G. Experimental study of the tail end selective hydrogenation of steam cracking C2-C3 mixture. Can. J. Chem. Eng. 1996, 74 (1), 84−93. (10) Conesa, J. A.; Font, R.; Marcilla, A.; Garcia, A. N. Pyrolysis of polyethylene in a fluidized bed reactor. Energy Fuels 1994, 8 (6), 1238−1246. (11) Van der Waals, J.; Platteeuw, J. Clathrate solutions. Adv. Chem. Phys. 1959, 2 (1), 1−57. (12) Valderrama, J. O. A generalized Patel-Teja equation of state for polar and nonpolar fluids and their mixtures. J. Chem. Eng. Japan 1990, 23 (1), 87−91. (13) Avlonitis, D.; Danesh, A.; Todd, A. Prediction of VL and VLL equilibria of mixtures containing petroleum reservoir fluids and methanol with a cubic EoS. Fluid Phase Equilib. 1994, 94, 181−216. (14) Tumba, K.; Reddy, P.; Naidoo, P.; Ramjugernath, D.; Eslamimanesh, A.; Mohammadi, A. H.; Richon, D. Phase equilibria of methane and carbon dioxide clathrate hydrates in the presence of aqueous solutions of tributylmethylphosphonium methylsulfate ionic liquid. J. Chem. Eng. Data 2011, 56 (9), 3620−3629. (15) Belandria, V.; Eslamimanesh, A.; Mohammadi, A. H.; Théveneau, P.; Legendre, H.; Richon, D. Compositional analysis and hydrate dissociation conditions measurements for carbon dioxide+ methane+ water system. Ind. Eng. Chem. Res. 2011, 50 (9), 5783−5794. (16) Afzal, W.; Mohammadi, A. H.; Richon, D. Experimental measurements and predictions of dissociation conditions for carbon dioxide and methane hydrates in the presence of triethylene glycol aqueous solutions. J. Chem. Eng. Data 2007, 52 (5), 2053−2055. (17) Tohidi, B.; Burgass, R.; Danesh, A.; Østergaard, K.; Todd, A. Improving the accuracy of gas hydrate dissociation point measurements. Ann. N.Y. Acad. Sci. 2000, 912 (1), 924−931. (18) Belandria, V.; Eslamimanesh, A.; Mohammadi, A. H.; Richon, D. Gas hydrate formation in carbon dioxide+ nitrogen+ water system: Compositional analysis of equilibrium phases. Ind. Eng. Chem. Res. 2011, 50 (8), 4722−4730. (19) Tumba, K.; Naidoo, P.; Mohammadi, A. H.; Richon, D.; Ramjugernath, D. Phase equilibria of clathrate hydrates of ethane + ethene. J. Chem. Eng. Data 2013, 58 (4), 896−901. (20) Mohammadi, A. H.; Afzal, W.; Richon, D. Experimental data and predictions of dissociation conditions for ethane and propane simple hydrates in the presence of distilled water and methane, ethane, propane, and carbon dioxide simple hydrates in the presence of ethanol aqueous solutions. J. Chem. Eng. Data 2007, 53 (1), 73−76. (21) Anderson, F.; Prausnitz, J. Inhibition of gas hydrates by methanol. AIChE J. 1986, 32 (8), 1321−1333. (22) Holder, G.; Corbin, G.; Papadopoulos, K. Thermodynamic and molecular properties of gas hydrates from mixtures containing methane, argon, and krypton. Ind. Eng. Chem. Fundam. 1980, 19 (3), 282−286. (23) Kihara, T. Virial coefficients and models of molecules in gases. Rev. Mod. Phys. 1953, 25 (4), 831−843. (24) Mohammadi, A. H.; Anderson, R.; Tohidi, B. Carbon monoxide clathrate hydrates: equilibrium data and thermodynamic modeling. AIChE J. 2005, 51 (10), 2825−2833. (25) Green, D. W.; Perry, R. H. Perry’s Chemical Engineers’ Handbook, 8th ed.; McGraw-Hill: New York, 2008. (26) Stryjek, R.; Vera, J. H. PRSV: An improved Peng−Robinson equation of state for pure compounds and mixtures. Can. J. Chem. Eng. 1986, 64, 323−333.
a Parameters: α, spherical molecular core radius; σ, collision diameter; ε, characteristic energy; k, Boltzmann constant.
Table 8. Acentric Factors (ω) and Critical Properties (Pc, Tc, Zc) Used in This Study25,26 component
Tc/K
Pc/MPa
ω
Zc
ethyne propene water
308.30 364.85 647.29
6.138 4.600 22.09
0.1920 0.1376 0.3438
0.2680 0.2810 0.2290
Results shown in Table 3 and Figure 1 reveal that model predictions are consistent with experimental measurements. It is an indication of the reliability of the suggested modeling approach for the investigated system.
5. CONCLUSIONS Dissociation conditions were experimentally obtained for mixed ethyne and propene hydrates. Additionally, HLV phase equilibria data are reported in terms of equilibrium pressures, temperatures, and vapor phase compositions inside the hydrate stability region. Good agreement was observed between experimental dissociation data and model predictions. The suggested model combined the solid solution theory owed to van der Waals and Platteeuw,2,4,5,11,14,21,22,24 the VPT equation of state12,24 and the NDD mixing rules13,24 suggested by Avlonitis and co-workers. This modeling approach reliably describes the phase behavior of the ethyne + propene + water under hydrate forming conditions. The results reported in the present study can be used to analyze or design hydrate-based processes such as gas separation in which the ethyne−propene system would be involved.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail (A.H.M.):
[email protected], amir_h_mohammadi@ yahoo.com. *E-mail (D.R.):
[email protected]. 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. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Carroll, J. Natural Gas Hydrates, A Guide for Engineers, 2nd ed.; Gulf Professional Publishing: Burlington, MA, 2009. (2) Sloan, E. D. Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Florida, USA, 2008. (3) Suzuki, K. Gas Hydrate in the System of Acetylene-Carbon tetrachloride-Water. Mem. Res. Inst. Sci. Eng., Ritumeikan Univ. 1956, 1, 37−40. (4) Tumba, K.; Hashemi, H.; Naidoo, P.; Mohammadi, A. H.; Ramjugernath, D. Dissociation data and thermodynamic modeling of clathrate hydrates of ethene, ethyne and propene. J. Chem. Eng. Data 2013, 58 (11), 3259−3264. 221
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