Article pubs.acs.org/jced
Liquid Water−Hydrate−Vapor Equilibrium for Methane + Ethane Gas Mixtures: Application of Gas Hydrates for Separation Sheida Soltanimehr, Jafar Javanmardi,* and Khashayar Nasrifar Department of Chemical, Oil and Gas Engineering, Shiraz University of Technology, Shiraz, Iran ABSTRACT: In this communication, liquid water−hydrate−vapor (Lw−H−V) phase diagrams for methane + ethane gas mixtures are predicted using van der Waals−Platteeuw solid solution theory. Experimental measurements were conducted and the results exhibited that methane was effectively separated from ethane by hydrate formation. To perform the experiments, methane + ethane gas mixtures were contacted to excess water at appropriate conditions. Once the hydrate phase was produced, the compositions in the gas and hydrate phases were measured meticulously and reported. Presented in this work, methane was enriched in the residual vapor phase, while ethane was enriched in the hydrate phase. The performed experiments justify the use of gas hydrate as a feasible method for separation. The model predictions of the pressure−composition diagram are also in good agreement with experimental results.
1. INTRODUCTION Natural gas hydrate structures are often classified by structure I, structure II, and structure H (sI, sII, and sH). The hydrate formation condition and the guest molecules determine the structure of hydrate.1 Detailed information on hydrate structures can be found elsewhere.2,3 With suitable size and shape, both methane and ethane can form sI hydrates.4 The hydrate formation conditions for pure methane, pure ethane, and their binary mixtures were measured over a large span of time.5−7 Methane forms sI hydrate as does ethane; however, a binary mixture of methane and ethane is more likely to form sII hydrate at certain conditions.8,9 Sloan et al.9−12 predicted a lower structural transition point (sI → sII) with an upper structural transition point (sI → sII) and employed a Gibbs-free energy minimization method to predict the hydrate phase diagram for the system methane + ethane + water. Recognized by Kini,13 there are four factors determining these structural transition points: First is the guest-to-cage size ratio. Second is the occupancy of the cage. Third is the feed composition, and forth is the number of cavities in each lattice. Natural gas mixtures usually contain large amounts of methane and ethane. These two components have close volatilities; however, a deep separation for mixtures of them is often required in gas and oil processing as well as in ethylene production. Having close volatilities, distillation is not often suggested for separation.14,15 Hydrate separation has attracted attention as a promising means for systems in which distillation is not very appropriate. In recent years,16−18 some research works have been performed regarding separation using hydrate formation. When methane + ethane gas mixtures form hydrate, the concentrations of these components in the gas and hydrate phases are not identical. Compared to ethane, methane hydrate formation occurs at much elevated pressures. Ethane will then form hydrate more easily than methane. Consequently, hydrate © XXXX American Chemical Society
formation might be a viable method for separating the methane + ethane gas mixtures.15,19−22 Zhang et al.15 measured hydrate formation conditions for methane + ethane gas mixtures in the presence of aqueous tetrahydrofuran (THF). Exhibited, ethane was markedly enriched in the vapor phase while methane in the hydrate phase. Sun et al.23 performed hydrate formation conditions measurements for binary gas mixtures containing methane and ethane in the presence of aqueous solutions containing 6 mol percent THF. Comparisons also made with hydrate formation measurements for the same methane + ethane gas mixtures in pure water. Sun et al.23 concluded that the more increasing the composition of ethane in the gas mixture beyond 82%, the more difficult becomes hydrate formation in the presence of the aqueous THF solution than in pure water. Naeiji et al.24 presented a new method based on Langmuir adsorption model for separating methane + ethane gas mixtures using gas hydrate formation. Their results demonstrated that separation of methane from ethane happens at low and high mole fractions of methane in the mixture. Limited data are available for methane + ethane separation using hydrate formation. This work is then justified by confirming and extending available experimental data to a wider range of pressure and composition for the system methane + ethane + water. Furthermore, structural transitions in methane + ethane gas hydrate formation are measured and hydrate phase diagrams are predicted using van der Waals− Platteeuw solid solution theory.25 The agreement between the predictions and experimental data was found to be satisfactory. Received: March 4, 2017 Accepted: June 2, 2017
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DOI: 10.1021/acs.jced.7b00232 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 1. Experimental apparatus for hydrate formation measurements (P is for pressure transmitter, T for temperature transmitter, R for regulator, V for valve and TCS stands for temperature control system).
2. EXPERIMENTAL APPRATUS AND PROCEDURE 2.1. Apparatus. Shown in Figure 1 is the schematic diagram for hydrate measurement device used in this study.26−29 This device is essentially a stainless-steel vessel with 75 cm3 in volume where its content is well mixed with a magnetic stirrer. The apparatus is made to withstand pressures up to 15 MPa. The content of the vessel can be viewed from a glass window held in place. The vessel temperature is maintained by an ethanol bath. The system temperature is measured by a PT-100 thermocouple. A pressure gauge and transducer are used to measure the vessel pressure. The system pressure and temperature are acquiesced by a computerized system. The gas composition is measured and analyzed by gas chromatography (GC) (CP-3800 Varian). In Table 1, the uncertainties of instruments employed in this work are provided in the table footnote. 2.2. Procedure. Methane and ethane from Air Product with claimed purities of 99.99% were used. Distilled water was used for hydrate formation. The hydrate equilibrium cell was first washed with deionized water, dried, and evacuated afterward. Normally, 25 cm3 of distilled water was fed to the cell. By matching the partial pressures, the synthetic gas mixtures were prepared with compositions similar to the real gas mixtures. After adequate mixing, the gas mixtures were sampled and their compositions determined using gas chromatograph (GC). The prepared gas mixtures were then charged to the equilibrium cell. Initially, the system was cooled gradually to a temperature less than estimated hydrate formation temperature. Then, the stirrer was started to facilitate the system equilibrium. During the experiment the pressure and temperature was recorded automatically. When the system pressure was stabilized, the hydrate formation condition was acquiesced. To ensure the system equilibrium, the residual gas was kept in contact with the hydrate phase and water for a long time (normally 4 days).
Then the residual gas was sampled, and its composition was measured using the GC. After the remaining gas was purged, the temperature of the system was increased slowly to the level of ambient temperature. Once the hydrate phase dissociated completely, the compositions of methane and ethane in the hydrate phase were determined by the GC. It is notable that experiments were conducted under excess water conditions. Some gas molecules are always dissolved in water as in industrial applications. This amount should be considered as lost. The plan was to measure the amount of gas that was not dissolved in water.
3. THEORY 3.1. Model. The solid solution theory of van der Waals− Platteeuw25 was employed to predict the hydrate phase diagram (Lw−H−V) for the methane + ethane + water system. The model is based on the identity of chemical potentials at equilibrium for water in the hydrate phase and in the liquid water or ice phase. The chemical potential of water in the hydrate phase reads 2
μwH = μwβ + RT
∑ νm ln(1 − ∑ θmj) m=1
j=1
(1)
μβw
where stands for the chemical potential of water in the empty hydrate lattice, R is the gas constant, T is the system temperature, and vm represents the ratio for the number of cavities of type m to the number of water molecules in the hydrate lattice structure. The parameter θmj is the fractional cavities of type m occupied by a type j gas molecule. The parameter θmj is expressed by θmj = B
Cmj 1 + ∑m = 1 Cmjf j
(2) DOI: 10.1021/acs.jced.7b00232 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Experimental Values and Model Predictions for the System Methane + Ethane at 273.9 Ka experimental
model
cmpd (mol%)
Pb/MPa
feed gas
residual gas/y
hydrate phase/x
residual gas/y
hydrate phase/x
ARDRc
ARDHd
K1
SF
CH4
0.65 0.66 0.69 0.95 1.11 1.55 1.54 1.77 2.34 2.66 0.65 0.66 0.69 0.95 1.11 1.55 1.54 1.77 2.34 2.66
28 31 33 54 71 80 80 80 92 94 73 69 67 46 24 20 20 20 8 6
30 32 43 65 77 91 92 94 98 99 70 68 57 35 23 9 8 6 2 1
14 15 15 29 57 66 66 71 80 90 86 85 85 71 43 34 34 29 20 10
35 36.7 41.35 65.9 77.38 92.4 92.32 95.1 98.5 99.25 65 63.3 58.65 34.1 22.62 7.6 7.7 4.9 1.5 0.75
15.6 15.8 18.2 30.8 57.7 66.4 66.29 70.50 82.53 90.74 84.4 84.2 81.8 69.2 42.3 33.6 33.7 29.5 17.47 9.26
16.6 14.68 3.8 1.3 0.5 1.53 0.35 1.1 0.5 0.25 7.1 4.7 2.89 2.57 1.65 15.5 0.37 18.3 25 25
11.9 5.4 21 6.2 1.27 0.6 0.43 0.7 3.16 0.82 1.86 0.94 3.7 2.5 1.62 1.17 0.88 1.72 12.6 7.4
2.14 2.13 2.86 2.24 1.35 1.37 1.39 1.32 1.22 1.1
2.6 2.7 4.3 4.6 2.5 5.2 5.9 6.4 12.3 11.0
C2H6
a The expanded uncertainties (Uc) in the reported temperatures are ±0.1 K (0.95 of confidence level). bThe expanded uncertainties (Uc) in the reported pressures are about ±0.01 MPa (0.95 of confidence level). cARDH% is calculated as
1 Np
ARDH % =
Np
⎛ |y
1
⎝
∑ ⎜⎜
exp
− ycal | ⎞ ⎟ × 100 ⎟ yexp ⎠
d
%ARD is calculated as
ARDR % =
1 Np
Np
⎛ |xexp − xcal| ⎞ ⎟⎟ × 100 xexp ⎝ ⎠
∑ ⎜⎜ 1
where f j is the gas phase fugacity for hydrate former j. In this work, the Soave−Redlich−Kwong (SRK) equation of state30 was used for calculating the hydrate former fugacity. The parameter Cmj, the Langmuir constant, is calculated from Cmj =
4π κT
∫0
R m − aj
⎛ −ω(r ) ⎞ 2 exp⎜ ⎟r d r ⎝ κT ⎠
where T0 is the reference temperature of 273.15 K, P is the equilibrium pressure, and aw is the activity of water in aqueous phase. The parameters Δμw, Δhw, and Δvw are the chemical potential, molar enthalpy, and molar volume changes from the empty hydrate lattice to the pure liquid water phase, respectively. The number of gas molecules j to water molecule in the hydrate unit cell is expressed by
(3)
where κ is the Boltzmann’s constant, ω(r) is the cell potential, r is the radius, Rm is the radius of cage m, and aj is the spherical core radius of component j, respectively The Langmuir constant is a function of temperature with Kihara potential function parameters as constants. Applying Raman spectroscopic data, Ballard and Sloan12 estimated the Kihara parameters for methane and ethane. These Kihara parameters describe the structural transition for the methane + ethane + water system. These values were used in this work without alteration.11 The chemical potential of water in the liquid water phase is expressed by31−34 ⎛T ⎞ μwL = μwβ − Δμw◦ ⎜ ⎟ + RT ⎝ T0 ⎠ −
∫0
∫T
T
◦
2
nj =
NA
(5)
where NA represents Avogadro’s number. The mole fraction of hydrate phase occupied by component j can be calculated from
xj =
nj ∑j = 1 nj
(6)
3.2. Pressure versus Composition Phase Diagram. Figure 2 depicts the phase diagram for the system methane + ethane at 274.2 K. The predictions were generated using the proposed model with the solid lines indicating the composition for the vapor phase. Shown in Figure 2, the lower and upper transition points occur at yCH4 = 0.722 and yCH4 = 0.996, respectively.12 It is worth mentioning that predictions in this work are in good agreement with the lower and upper
⎛ Δhw ⎞ ⎜ 2 ⎟ dT ⎝ RT ⎠
p
Δvw dP + RT ln(a w )
∑m = 1 θmjvm
(4) C
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The vapor and hydrate equilibrium compositions at 273.9 K are demonstrated in Figure 3. It is worth noting that the predictions compare well with the experimental measurements while temperature slightly differs from 274.2 K.
Figure 2. Pseudo-pressure−composition diagram for the system CH4 + C2H6 + water at 274.2 K.
transition points measured by Raman spectroscopy12 at 274.2 K. The procedure for predicting the phase diagram for the methane + ethane gas mixture is described by (1). The system temperature T and the mole fraction of methane in the gas phase are specified. (2). The initial value of pressure is assumed and the chemical potentials of water in the hydrate phase μHw for both structure I and II and in the liquid water phase μLw are evaluated by eqs 1 and 4, respectively. (3). The chemical potential μHw for both hydrate structures is compared with μLw, and if the difference is appreciable, the value of pressure will be updated using the Newton− Raphson method. Then, starting from step 2 the calculations are repeated until the difference reduces to a predetermined value. In the end, we obtain two pressure values for structure I and II, respectively. The smallest pressure is taken as the hydrate formation pressure and the corresponding structure as the stable hydrate structure. (4). Once the pressure is calculated, point A will be determined in Figure 2. Point A represents the concentration of methane in the gas phase which is in equilibrium with the hydrate phase at the calculated pressure and specified temperature. (5). Using the system temperature, the parameter θmj is evaluated by eq 2. (6). The number of gas molecules j to water molecule in the hydrate unit cell is calculated from eq 5. (7). The fraction of component j in the hydrate phase is calculated from eq 6. Then, point B is determined in Figure 2. Point B represents the concentration of methane in the hydrate phase at the calculated pressure, and specified temperature. If the above-mentioned algorithm is used over the entire mixture composition range, the phase diagram of the mixture will be determined.
Figure 3. Pseudo-pressure−composition diagram for the system CH4 + C2H6 + H2O with the vapor and hydrate equilibrium compositions at 273.9 K.
4. RESULTS AND DISCUSSION The results for partial separation of the gas mixture CH4 (1) + C2H6 (2) using hydrate formation are provided in Table 1. Equilibrium ratio for CH4 between the vapor and hydrate phases (K1) and the separation factor (SF) are calculated from yCH 4 K1 = xCH4 (7) S. F =
yCH xC2H6 4
xCH4yC H 2
6
(8)
where xCH4 and yCH4 are the mole fractions of methane in the hydrate and vapor phase at equilibrium, respectively. Similarly, xC2H6 and yC2H6 are respectively defined as the mole fractions of ethane in the hydrate phase and vapor phase at equilibrium. Ethane hydrate formation occurs at much lower pressure than methane at similar temperatures. Thus, ethane must be enriched in the hydrate phase remarkably better than methane. The experimental measurements provided in Table 1 confirm this behavior. A comparison of the vapor phase composition with the feed composition in Table 1 shows that CH4 definitely stays in the vapor phase. Equilibrium ratios of methane between the vapor and hydrate phases are clearly promising. The largest measured value of K1 was found to be 2.86 and the separation factor was 2.63. These figures demonstrate that hydrate separation can be considered as a viable method for the separation of methane from ethane in their binary gas mixtures. As shown in Figure 4, the separation factor is augmented by increasing the feed pressure which is due to the fact that by increasing the feed pressure the entrapping of ethane in the D
DOI: 10.1021/acs.jced.7b00232 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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factor was decreased by increasing temperature at constant pressure.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: +98-7137354520. Fax: +98-7137354520. ORCID
Jafar Javanmardi: 0000-0002-4146-1490 Funding
The authors wish to express their appreciation to Shiraz University of Technology for support of this work. Notes
The authors declare no competing financial interest.
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NOMENCLATURE ARD average relative deviation a activity aj spherical core radius of component C Langmuir constant f fugacity K1 Equilibrium ratio for CH4 between the vapor and hydrate phases NA Avogadro’s number n number of gas molecules to water molecule P pressure R gas constant, hydrate cage radius r radius T temperature T0 reference temperature (273.15 K) x mole fraction in hydrate phase y mole fraction in vapor phase
Figure 4. Separation factor as a function of pressure for a mixture containing 80% methane + 20% ethane.
hydrate phase is facilitated. Thus, ethane bifurcation enhances in the gas mixture. Increasing temperature, however, decreases the separation factor. As shown in Figure 5, the solubility of ethane in water
Greek Letters
κ Boltzmann’s constant μw chemical potential of water Δhw molar enthalpy differences between the empty hydrate lattice and pure liquid water phase Δνw molar volume differences between the empty hydrate lattice and pure liquid water phase ω(r) cell potential θ fractional hydrate cavities occupied by gas molecule ν number of hydrate cavities per water molecules
Figure 5. Experimental solubility of methane and ethane in water as a function of temperature35,36
decreases sharply than methane with temperature. Therefore, when temperature increases, ethane solubility decreases more effectively than methane. Then the separation factor decreases with increasing temperature.
Subscripts and Superscripts
j m ß H L
5. CONCLUSIONS Upper and lower transition points in methane + ethane gas hydrate mixtures and the hydrate phase diagram for one of these mixtures have been predicted using van der WaalsPlatteeuw theory. The hydrate formation measurements were in good agreement with the Raman spectroscopy data, reported in the literature, for separation of a gas mixture containing methane and ethane. During the course of the experiments, methane was enriched in the residual vapor phase while ethane was in the hydrate phase. The separation factor of methane was found to be high for all performed measurements. Therefore, hydrate formation can be a successful means for methane + ethane gas mixtures separation. Separation factor was increased by increasing the pressure at constant temperature. Conversely, the separation
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component j hydrate cavity empty hydrate lattice hydrate phase liquid water phase
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