Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Investigation on Vapor−Liquid Equilibrium of (Argon + Methane) at the Temperature Range of (95 to 135) K Xiaohong Han,* Yanzhi Wang, Zhangzhang Yang, Yibo Fang, Jiongliang Huang, Xiangguo Xu, and Guangming Chen
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Key Laboratory of Refrigeration and Cryogenic Technology of Zhejiang Province, Institute of Refrigeration and Cryogenics of Zhejiang University, Hangzhou 310027, China
ABSTRACT: Natural gas is gaseous fossil fuel consisting primarily of methane (CH4). Argon (Ar) is a precious gas resource among the nonhydrocarbons in natural gas, and it can be separated from the natural gas; thus, it is very necessary to understand the vapor−liquid equilibrium (VLE) of (Ar + CH4). The investigations on the VLE data of (Ar + CH4) have mostly focused on the temperature range of (>140 K), while studies are relatively scarce below 140 K. In this work, the VLE data of (Ar + CH4) from 95 to 135 K were measured by experiment. Four different mixing rules (HV, MHV1, MHV2, and LCVM) with the same equation of state (PR) and the four equations of state (SRK, PR, PRSV, NM) with the same mixing rule (MHV1) were used to correlate the VLE of (Ar + CH4), respectively. The research results were discussed in detail. In addition, the excess Gibbs free energy of (Ar + CH4) was further analyzed. The results showed that the excess Gibbs free energy of (Ar + CH4) was more than zero, and the curves of excess Gibbs free energy and excess enthalpy of (Ar + CH4) had good symmetry.
■
INTRODUCTION As a highly efficient clean energy, natural gas has a very important position in the industrial and civilian areas. It is attracting more and more attention all over the world, and the proportion of world energy consumption is also increasing. According to the data provided by the US Energy Information and Intelligence Agency, the average growth rate of natural gas consumption in the world over the past decade was 2.3%, and the average growth rate of natural gas production was 2.4%.1 By 2015, world natural gas consumption increased by 1.7%, and global natural gas production grew by 2.2%, of which the US natural gas production growth rate of 5.4% was the largest in the world. The world’s natural gas distribution is very wide, and the global natural gas resources are very rich. Natural gas accounts for 23.8% of the world’s primary energy consumption. By the end of 2015, the proven total reserves of the world’s natural gas were 186.9 trillion cubic meters, which was enough to ensure 52.8 years’ production needs.1 Natural gas is a multicomponent mixture, whose principle component is methane (CH4), and it also contains a small amount of ethane, propane, and other hydrocarbon components; meanwhile, it may contain nitrogen (N2), hydrogen sulfide (H2S), carbon dioxide (CO2), water vapor (H2O), rare gas (helium (He), argon (Ar)), hydrogen (H2), mercury vapor (Hg), and other nonhydrocarbon components, and the weight percentage of each © XXXX American Chemical Society
nonhydrocarbon component in natural gas from different sources is different. Nonhydrocarbon components are a very important constituent part of natural gas. Some nonhydrocarbon components in natural gas can adversely affect the development and utilization of natural gas, but some of the nonhydrocarbon components are enriched to a certain extent which can become a valuable source of gas. Usually, argon is mainly obtained from the separation of air; however, when Ar is enriched to a certain extent in the natural gas, it can also be used as one of the main sources of argon. The literature2 shows that the content of Ar in the Soviet Union gas wells can be as high as 4.92%, which is much higher than that of argon in air; thus, it has good utilization prospects. It can be separated and purified by cryogenic separation methods, and the vapor− liquid equilibrium (VLE) of (Ar + CH4) is the basic and important knowledge. Many researchers have studied the VLE of the mixture (Ar + CH4). For example, Cheung et al.3 studied the solubility of volatile gases in hydrocarbons at low temperatures and gave the VLE data of (Ar + CH4) in the temperature range of (90 to 125 K). The VLE data of N2 + CH4, Ar + CH4, and CO2 + CH4 at Received: April 6, 2018 Accepted: July 11, 2018
A
DOI: 10.1021/acs.jced.8b00280 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
90.67 K were measured by Sprow et al.4,5 Gravelle et al.6,7 studied the VLE properties of (Ar + CH4) at 115.2, 123.4, and 137.1 K with the two-parameter Redlich−Kister equation. Calado et al.8 measured the liquid phase composition of (Ar + CH4) at 115.77 K, and the excess Gibbs free energy of (Ar + CH4) at 115.77 K was correlated. The results showed that the gE−x curve had good symmetry. Duncan et al.9 studied the VLE of the (Ar + CH4) system in the temperature range of (105 to 126 K) by the cyclic method, but only the liquid phase compositions of (Ar + CH4) were measured. Also the corresponding excess Gibbs free energy and enthalpy of mixing were calculated. Christiansen et al.10 studied the VLE of (Ar + CH4) at 150.72, 164.0, and 178.0 K, and the isothermal vapor−liquid equilibrium diagram was given. Miller et al.11 studied the VLE of binary and ternary mixtures (CH4, N2, Ar) at 112 K by vapor phase cycling, and VLE phase diagrams were plotted for the corresponding binary and ternary systems. Jin et al.12 studied the VLE of the binary and ternary mixtures (CH4, N2, Ar) at 122.89 K, and the experimental data of the binary mixtures with (CH4, N2, and Ar) were correlated with the PR equation of state. From the above description, the investigations on the VLE data of (Ar + CH4) mostly focused on the temperature range of >140 K, while the data were relatively scarce below 140 K. Therefore, it is very necessary to measure the VLE of (Ar + CH4) below 140 K, and the detailed discussion and comparison need to be developed.
Peng−Robinson−Stryjek−Vera (PRSV) Equation of State. Stryjek and Vera15 made some improvement and proposed a new expression of the calculation formula on the basis of the PR equation. The expression of the PRSV equation is as follows
(RTc)2 pc Ä ÉÑ 2 ÅÅ | l ÑÑ o o Å o o + ω 0.378893 1.4897153 Å Ñ ( o o ÅÅ ÑÑ o o o o ÅÅ ÑÑ o o o o 2 Å Ñ o Å Ñ − ω 0.17131848 o o 0.5 o Å Ñ Å Ñ − ×m + T 1 (1 ) } Å Ñ r o o ÅÅ ÑÑ 3 o o o o + ω 0.0196554 Å Ñ ) o o Å Ñ o o Å Ñ o o Å Ñ o o 0.5 Å Ñ o o Å +m1(1 + Tr )(0.7 − Tr ) ÑÑ o o Å ÅÇ ÑÖ n ~ (8)
b = 0.077796
b = 0.08664
RTc pc
RT a − 2 V−b V + 2bV − 2b2 ÄÅ ÅÅ ij a pt yzijj T − Tpt Å a = acÅÅÅÅ1 + jjjj − 1zzzzjjj1 − j ÅÅ Tc − Tpt ÅÅÇ k ac {jk ÄÅ ÉÑ ÅÅ ij bpt yzijj T − Tpt yzzÑÑÑÑ ÅÅ zzÑÑ b = bcÅÅÅ1 + jjj − 1zzzjjj1 − zzÑÑ j bc zj ÅÅ T − T c pt k { ÅÇ k {ÑÑÖ
(2)
(3)
where p is the pressure; v is the molar volume; T is the absolute temperature; pc is the critical pressure; Tc is the critical temperature; R is the general gas constant; a and b are parameters dependent on equation of state, respectively; ω is acentric factor; and Tr (= T/Tc) is the reduced temperature. Peng−Robinson (PR) Equation of State. The PR equation of state14 was proposed to compensate for the shortcomings of the RK equation and the SRK equation in calculating the molar volume of the liquid phase. The expression of the PR equation of state is as follows p=
RT a − v−b v(v + b) + b(v − b)
× [1 + (0.37646 + 1.54226ω − 0.26992ω2)(1 −
RTc pc
bc = 0.094451
RTc pc
(14)
bc
Tpt Tc
= 29.7056 (15)
= 1 − 0.1519ω − 3.9462ω 2 + 7.0538ω3
= 0.2498 + 0.3359ω − 0.1037ω 2
(16)
(17)
where Tpt is virtual triple point temperature, and apt, bpt are parameters at the virtual triple point temperature, respectively. The NM equation can accurately predict the properties of the pure component and the phase equilibrium of the mixture. The saturated liquid phase density of the pure component and the mixture, the pure component vapor pressure near the critical point, and the bubble point pressure of the supercritical mixture
2 Tr0.5)]
(5)
b = 0.077796
(12)
(13)
bpt
(RTc) pc
(11)
R2Tc2 pc
bptRTpt
(4)
É2 yzÑÑÑÑ zzÑÑ zzÑÑ zzÑÑ {ÑÑÖ
(10)
ac = 0.497926
a pt
2
a = 0.457235
(9)
p=
R2Tc2 pc 2
RTc pc
where m1 is a parameter related to pure component. More than 90 components’ values of m1 were given in the literature.15 Nasrifar−Moshfeghian (NM) Equation of State. Nasrifar and Moshfeghian16 proposed a new two-parameter cubic state equation in order to improve the computational accuracy of the cubic equation of state without increasing the complexity of the equation. Its expression is shown as follows
MODELS Equations of State. Soave−Redlich−Kwong (SRK) Equation of State. The SRK equation of state13 is expressed as RT a p= − v−b v(v + b) (1)
× [1 + (0.48 + 1.574ω − 0.176ω2)(1 − Tr0.5)]
(7)
a = 0.457235
■
a = 0.42748
RT a − v−b v(v + b) + b(v − b)
p=
(6) B
DOI: 10.1021/acs.jced.8b00280 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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can all be correlated accurately. The predictive ability of the equation can be comparable to the PR equation and the SRK equation.
b=
■
b=
a = bRT
∑ xiαi + i
gE C HVRT
where λ is the characteristic parameter of the contribution degree of HV and MHV1 to α in the LCVM mixing rule, and λ is empirically given to 0.36. NRTL Model. In this work, the NRTL model was used to calculate the excess free energy and activity coefficient of component i. It can be expressed as eqs 26−32)23 gE τ12G12 zyz ji τ G = x1x 2jjj 21 21 + z j RT x 2 + x1G12 zz{ k x1 + x 2G21 ÄÅ ÉÑ 2 ÅÅ i ÑÑ y G τ G Å ÑÑ j z 21 12 12 zz + Ñ ln γ1 = x 22ÅÅÅÅτ21jjj z 2Ñ ÑÑ ÅÅ jk x1 + x 2G21 z{ ( x + x G ) ÑÑÖ 2 1 12 ÅÇ ÄÅ ÉÑ 2 ÅÅ i ÑÑ yz G τ G ÑÑ j 2Å 12 21 21 Å z + Ñ ln γ2 = x1 ÅÅÅτ12jjj z 2Ñ ÑÑ ÅÅ jk x 2 + x1G12 zz{ ( x + x G ) 1 2 21 Ñ ÅÇ ÑÖ g − g22 τ12 = 12 RT g − g11 τ21 = 21 RT
(18)
∑ xibi
(19)
i
where CHV is the characteristic parameter of the HV mixing rule model and has different values for different equations of state: it is −0.6232 for the PR equation. The gE/RT in the equation can be calculated by using the existing various activity coefficient models (generally using the local composition models). MHV1 (Modified Huron−Vidal First-Order) Mixing Rule.20 The MHV1 (modified Huron−Vidal first order) mixing rule is shown as follows ÄÅ E ÉÑ ij b yzÑÑÑ 1 ÅÅÅÅ g ÅÅ α= + ∑ xi lnjjj zzzÑÑÑ + ∑ xiαi j bi zÑÑ CMHV1 ÅÅÅ RT (20) k {ÑÖ i i Ç b=
∑ xibi
yz z {
ij j i k gE ji b zy = ∑ xi lnjjj zzz + j bi z RT i k {
b=
(28) (29) (30)
G12 = exp( −α12τ12)
(31)
G21 = exp( −α12τ21)
(32)
name methane (CH4) argon (Ar)
CAS
purity (mass fraction)
74-82-8
>99.999%
7440-37-1
>99.999%
source Zhejiang Minxing Industrial and Trading Co., Ltd. Zhejiang Minxing Industrial and Trading Co., Ltd.
yz z {
∑ xiαizzzz + q2jjjjα 2 − ∑ xiαi2zzzz i
∑ xibi i
(22)
(23)
where q1 and q2 can be obtained by fitting different equations of state. For the PR equation, q1 = −0.477, q2 = −0.0020. LCVM (Linear Combination of Vidal and Michelsen) Mixing Rule.22 The LCVM (linear combination of Vidal and Michelsen) mixing rule is shown as follows
Figure 1. Schematic diagram of the VLE experimental system. 1, Hydrogen generator; 2, Chromatograph; 3, PC; 4, Six-way valve; 5, Precision gas switch valve; 6, High precision platinum resistance thermometer; 7, Platinum resistance thermometer; 8, PID temperature controller; 9, Self-pressurization dewar; 10, Heater; 11, Insulation Materials; 12, Liquid nitrogen; 13, Gas phase circulation pump; 14, Keithley 2002 data acquisition/switch unit; 15, Equilibrium cell; 16, Thermostated bath; 17, Liquid nitrogen dewar; 18, Pressure transducer; 19, Shut-off valve; 20, Sample; 21, DC regulated power supply; 22, Vacuum pump.
E i y 1 − λ zyzijj g yzz 1−λ ji λ zz + α = jjj + ∑ xi lnjjjjj b zzzzz zzjjj z j C HV z CMHV1 {k RT { CMHV1 i k k bi {
+
(27)
Table 1. Parameters of Experimental Samples
where CMHV1 is the characteristic parameter of the MHV1 mixing rule and has different values for different equations of state: it is −0.53 for the PR equation and PRSV equation, it is −0.593 for the SRK equation, and it is −0.596 for the NM equation. MHV2 (Modified Huron−Vidal Second-Order) Mixing Rule.21 The MHV2 (modified Huron−Vidal second order) mixing rule is shown as follows ij q1jjjjα − j k
(26)
where γ1 is the activity coefficient of component 1; x1 and x2 are the mole fractions of the components; α, τ12, and τ21 are the equation parameters of eqs 26−32; R is the gas constant; and the values of the parameters α, τ12, and τ21 in the NRTL
(21)
i
(25)
i
MIXING RULES The excess free energy mixing rules combined with the cubic equation of state can accurately predict the VLE of the polar system, the nonpolar system, and strong association systems,17 and it can be applied to complex mixtures under high pressure and the VLE of asymmetric systems.18 In this paper, the commonly used excess free energy mixing rules are mainly HV, MHV1, MHV2, and LCVM. HV (Huron−Vidal) Mixing Rule. In 1979, Huron and Vidal proposed the first excess free energy mixing rule, the HV mixing rule,19 and its expressions are shown as follows α=
∑ xibi
∑ xiαi i
(24) C
DOI: 10.1021/acs.jced.8b00280 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 2. Vapor−Liquid Equilibrium Data of the Binary Mixture (Ar(1) + CH4(2))a T/K
p/kPa
x1
y1
T/K
p/kPa
x1
y1
94.93 94.93 94.93 94.93 94.93 94.93 94.93
19.65 129.03 141.66 153.98 181.73 192.03 211.73
0 0.5113 0.5914 0.6848 0.8094 0.8795 1
0 0.9143 0.9324 0.9467 0.9758 0.9826 1
119.94 119.94 119.94 119.94 119.94 119.94 119.94 119.94 119.94
190.62 426.83 601.51 745.88 795.67 825.35 874.62 995.98 1209.00
0 0.1949 0.3753 0.5258 0.5873 0.6142 0.6581 0.7787 1
0 0.6152 0.7675 0.8429 0.8651 0.8952 0.8904 0.9406 1
99.97 99.97 99.97 99.97 99.97 99.97 99.97 99.97 99.97
34.27 111.96 139.52 172.85 198.13 215.61 234.71 276.15 323.00
0 0.225 0.3141 0.4285 0.5105 0.5968 0.6661 0.8294 1
0 0.7521 0.8276 0.8739 0.9006 0.9222 0.9383 0.9694 1
124.92 124.92 124.92 124.92 124.92 124.92 124.92 124.92
267.36 561.09 622.16 769.54 984.97 1032.18 1266.73 1575.90
0 0.1940 0.2458 0.3597 0.5453 0.5876 0.7758 1
0 0.5828 0.6439 0.7341 0.8393 0.8517 0.9256 1
104.84 104.84 104.84 104.84 104.84 104.84 104.84 104.84 104.84
55.54 157.68 201.24 242.46 284.48 310.12 337.67 396.35 466.83
0 0.2247 0.3164 0.4272 0.5082 0.5908 0.6657 0.8255 1
0 0.7165 0.7966 0.8485 0.8848 0.9032 0.9212 0.9646 1
129.89 129.89 129.89 129.89 129.89 129.89 129.89 129.89 129.89
364.90 690.98 771.87 952.15 1241.76 1328.37 1437.98 1635.90 2015.80
0 0.1928 0.2406 0.3478 0.5279 0.5879 0.6695 0.7819 1
0 0.5379 0.6151 0.6953 0.8026 0.8365 0.8744 0.9203 1
109.87 109.87 109.87 109.87 109.87 109.87 109.87 109.87 109.87
87.16 227.34 313.54 337.60 405.20 430.01 477.33 551.06 659.62
0 0.2031 0.3599 0.4081 0.5268 0.5914 0.6661 0.8041 1
0 0.6759 0.8013 0.8259 0.8712 0.8905 0.9138 0.9545 1
134.87 134.87 134.87 134.87 134.87 134.87 134.87 134.87
486.82 879.53 991.59 1184.64 1524.94 1653.90 1787.50 2536.10
0 0.1913 0.2475 0.3389 0.5218 0.5896 0.6695 1
0 0.5203 0.5861 0.6751 0.7956 0.8251 0.8631 1
114.82 114.82 114.82 114.82 114.82 114.82 114.82 114.82 114.82
130.38 318.12 373.99 455.74 553.30 593.08 652.67 748.97 900.03
0 0.1951 0.2816 0.3912 0.5265 0.5863 0.6638 0.8040 1
0 0.6467 0.7279 0.7982 0.8568 0.8782 0.9030 0.9483 1
a
Standard uncertainties are u(T) = 0.011 K, u(p) = 0.64 kPa, and u(x1) = u(y1) = 0.005.
■
equation were obtained by fitting the experimental data. The objective function (OBF) is
EXPERIMENTAL SECTION Samples. The related information about argon (Ar) and methane (CH4) is given in Table 1, and samples CH4 and Ar were without any further purification. Experimental Apparatus. Due to the limited vapor and liquid phase equilibrium data of (Ar + CH4), especially the lack of complete new data in the temperature range below 140 K, VLE data below 140 K are of great significance for the separation of argon from natural gas. In order to fully analyze the
N
OBF =
∑ (ln γ1,calcd − ln γ1,exptl)i2 i=1
(33)
where N is the number of experimental points; γ1,exptl is the experimental activity coefficient; and γ1,calcd is the calculated activity coefficient. D
DOI: 10.1021/acs.jced.8b00280 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 3. Vapor−Liquid Equilibrium Correlation Results of the Binary Mixture (Ar(1) + CH4(2)) by Using PR + Different Mixing Rules PR+MHV1+NRTL
PR+MHV2+NRTL
PR+LCVM+NRTL
T/K
ref
Npa
δpb/%
PR+vdW δy1c
δp/%
PR+HV+NRTL δy1
δp/%
δy1
δp/%
δy1
δp/%
δy1
90.67 94.93 99.97 104.84 109.87 114.82 115.77 119.94 122.89 124.92 129.89 134.87 150.72 164 178
Sprow4 this work this work this work this work this work Calado8 this work Jin12 this work this work this work Christiansen10 Christiansen10 Christiansen10
11 7 9 9 9 9 10 9 12 8 9 8 13 12 8
0.40 0.98 0.51 0.87 0.75 0.83 0.58 0.75 0.57 0.97 0.49 0.50 0.50 0.68 0.86
0.001 0.0014 0.0016 0.0031 0.0038 0.0048 0.0019 0.0079 0.0029 0.0033 0.0049 0.0050 0.0088 0.0082 0.0122
0.19 0.93 0.51 0.84 0.65 0.83 0.47 0.54 0.64 0.66 0.70 0.64 0.34 0.77 0.86
0.0008 0.0025 0.0016 0.0041 0.0027 0.0027 0.0005 0.0095 0.003 0.0031 0.0038 0.0055 0.0087 0.0084 0.0122
0.19 0.95 0.64 0.81 0.55 0.83 0.46 0.65 0.58 0.71 0.70 0.59 0.55 0.56 0.87
0.0008 0.0025 0.0021 0.0035 0.0024 0.0027 0.0005 0.0089 0.0028 0.003 0.0038 0.0055 0.0081 0.0076 0.0122
0.27 0.97 0.50 0.81 0.64 0.62 0.46 0.65 0.59 0.75 0.55 0.54 0.49 0.76 0.87
0.0006 0.0014 0.0016 0.0041 0.0025 0.0029 0.0007 0.0088 0.0028 0.0029 0.0046 0.0053 0.0086 0.0082 0.0123
0.23 0.94 0.55 0.79 0.66 0.83 0.56 0.67 0.6 0.74 0.48 0.58 0.58 0.62 0.86
0.0007 0.0016 0.0014 0.0039 0.0032 0.0024 0.0012 0.0087 0.0029 0.003 0.0049 0.0051 0.0079 0.0079 0.0123
1
a
pexptl − pcalcd
Np
Np indicates the number of data points in the experimental system. bδp = 100 Np ∑i = 1
pexptl
. cδy1 =
1 |y Np 1 exptl
− y1calcd |.
Uncertainty of Temperature Measurement. Temperature measurement uncertainty includes the three parts: (1) Error from the platinum resistance thermometer: as the accuracy of the WZPB-I platinum resistance thermometer is 0.001 K, so uT,1 = 0.001 K. (2) Thermstated bath temperature fluctuations: in our experimental measurement, the thermostated bath temperature fluctuation is less than 5 mK/30 min (0.01 K/h), so uT,2 = 0.01 K. (3) The error from the multifunction data acquisition/switch unit, uT,3 = 0.005 K, for the Keithley 2002 digital multimeter. Therefore, the overall temperature measurement uncertainty is
phase equilibrium properties of methane and argon, experimental data of VLE between methane and argon will be measured. On the basis of these, the phase equilibrium characteristics of the (Ar + CH4) system will be further analyzed in this paper. The VLE experimental data (temperature−pressure−vapor− liquid (T−p−xi−yi)) were measured in an experimental apparatus with a vapor-recirculation type equilibrium cell, shown in Figure 1, very similar to the apparatus from Han et al.24 It mainly included a stainless steel equilibrium cell, a vapor phase circulating pump, a thermostated system, and a measurement system. The equilibrium cell was put into the thermostated bath which is made of copper. The heating wire was uniformly wrapped around the outer wall of the thermostated bath. The cooling capacity was supplied by the liquid nitrogen. A circulation loop from the vapor to liquid phase was used to accelerate the equilibration by a circulating pump (GAHT23.PVS.B, Micropump). The temperature was controlled by the high accuracy temperature controller (Sr253-2IN-0060010, Shimaden, Japan), and the temperature fluctuation in the theromstated bath was less than ±5 mK/30 min. The bath temperature was measured by a four-head 25-platinum resistance thermometer (model: WZPB-I, China) whose accuracy was ±1 mK (ITS). The pressure was measured by a pressure transducer (model: PMP4010, Drunk, F.S. = 1.6 MPa, ±0.04% F.S.). The data were logged by a multifunction data acquisition/switch unit (Keithley 2002). The samples were immediately injected into the gas chromatograph (GC) with a thermal conductivity detector (TCD) (model GC1690, China) by the vapor and liquid sampling valves online, and then the compositions were analyzed. Before the experiment, the GC was calibrated with pure substances of known purity and with the mixed substances of known composition which were prepared gravimetrically. For each experimental measurement point, it needed to be measured at least three times in order to have a good repeatability. Uncertainty Analysis. The process of analysis is similar to the previous work,25 and the uncertainties of temperature (T), pressure (p), and composition (x) are given as follows.
3
uT =
∑ u T,2i
= 0.011 K (34)
i=1
Uncertainty of Composition Measurement. Composition measurement uncertainty includes two parts: (1) Measurement accuracy of GC1690 is 0.3%, so ux,1 = 0.003. (2) Repeatability error of component measurement. In our experimental measurement, the error among the multiple samplings is usually within 0.4%, so ux,2 = 0.004. The overall composition measurement uncertainty is 2
ux =
∑ ux2,i
= 0.005 (35)
i=1
Overall Uncertainty of Vapor Pressure. Pressure measurement uncertainty includes the two parts: (1) Error from the pressure transducer: it can be calculated according to full scale and accuracy of PMP4010 pressure sensor, up,1 = 0.64 kPa. (2) The error from the multifunction data acquisition/switch unit, up,2 = 0.002 kPa for the Keithley 2002 digital multimeter. So the pressure measurement uncertainty is 2
up =
∑ up,2i i=1
= 0.64 kPa (36)
On the basis of Moffat,26 the overall uncertainty of vapor pressure Up is from the pressure measurement uncertainty up, E
DOI: 10.1021/acs.jced.8b00280 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 4. Vapor−Liquid Equilibrium Correlation Results of the Binary Mixture (Ar(1) + CH4(2)) by Using Different Equations of State + (MHV1 + NRTL) Models SRK+MHV1+NRTL
PR+MHV1+NRTL
PRSV+MHV1+NRTL
NM+MHV1+NRTL
T/K
ref
Npa
δpb/%
δy1c
δp/%
δy1
δp/%
δy1
δp/%
δy1
90.67 94.93 99.97 104.84 109.87 114.82 115.77 119.94 122.89 124.92 129.89 134.87 150.72 164 178
Sprow4 this work this work this work this work this work Calado8 this work Jin12 this work this work this work Christiansen10 Christiansen10 Christiansen10
11 7 9 9 9 9 10 9 12 8 9 8 13 12 8
1.71 2.09 0.99 1.11 0.98 0.86 0.81 0.9 0.72 0.63 0.74 0.72 0.35 0.69 1.02
0.0087 0.0017 0.0037 0.0073 0.0043 0.0012 0.0027 0.0062 0.0042 0.0024 0.0046 0.0041 0.0093 0.0072 0.0118
0.19 0.95 0.64 0.81 0.55 0.83 0.46 0.65 0.58 0.71 0.70 0.59 0.55 0.56 0.87
0.0008 0.0025 0.0021 0.0035 0.0024 0.0027 0.0005 0.0089 0.0028 0.003 0.0038 0.0055 0.0081 0.0076 0.0122
0.5 0.8 0.38 0.71 0.63 0.61 0.45 0.59 0.55 0.63 0.46 0.46 0.33 0.36 0.88
0.0010 0.0028 0.0013 0.0039 0.0025 0.0025 0.0007 0.0087 0.003 0.0026 0.0047 0.0046 0.0083 0.0073 0.0122
0.20 1.05 0.49 0.95 0.9 0.89 0.57 0.71 0.47 0.48 0.56 0.54 0.48 0.47 0.67
0.0015 0.0033 0.0018 0.0039 0.0039 0.0028 0.0011 0.0109 0.0034 0.0033 0.0042 0.0050 0.0071 0.0085 0.013
1
a
Np
Np indicates the number of data points in the experimental system; bδp = 100 Np ∑i = 1
temperature measurement uncertainty uT, and composition measurement uncertainty ux. i ∂p y ∑ jjjjj u Xizzzzz = ∂Xi { i=1 k 3
Up =
2
i=1
pexptl
. cδy1 =
1 |y Np 1exptl
− y1calcd |.
and at each experimental temperature, a number of experimental points were measured), and experimental data were shown in Table 2 (vapor pressures of the pure components were included when composition of Ar x1 was equal to 1, and
3
∑ (u(pi ))2
pexptl − pcalcd
(37)
where Xi includes all the variables in the derivation of vapor pressure, that is, the temperature T, mass fraction x, and vapor pressure p. u(p1) is the uncertainty of reading and instrument error, 0.64 kPa; u(p2) is the uncertainty introduced by composition x; and u(p3) is the uncertainty introduced by temperature T. Finally, the relative overall uncertainty of vapor pressure Up/p calculated in the VLE of (Ar + CH4) is below 0.0118. Experimental Procedures. The experimental procedures were as follows. (1) The airtightness of the system was tested by the method of nitrogen filling before the experiment. (2) The system was first evacuated in order to remove the inert gases and other impurities. (3) A desired amount of CH4 and Ar was charged into the equilibrium cell (note: during the charging, charging time was very long because it was very hard for CH4 and Ar to be liquefied quickly even if the equilibrium cell was kept below 120 K. Usually, about 10 h was needed for charging the required refrigerants). (4) The system temperature was set by controlling the temperature of the thermostatic bath. The vapor in the equilibrium cell was circulated continuously with the circulating pump to shorten the equilibrium time. It was shown that 2 h or more was sufficient to reach the thermal equilibrium state for the whole system. (5) After the system was in the thermal balance, the temperature, pressure, and compositions for the system were recorded, respectively. (6) The system was changed to the new set temperature, and the experimental steps were done repeatedly from (4) to (5). (7) The composition for (Ar(1) + CH4(2)) was changed to the new one, and the experimental steps were done repeatedly from (3) to (6). Experimental Data. The experimental data for the system (Ar(1) + CH4(2)) were measured at temperature range of (95 to 135 K) (every 5 K as an experimental temperature point,
Figure 2. Relative pressure deviations (a) and the vapor composition deviations (b) for the binary mixture (Ar(1) + CH4(2)) in the different mixing rules, respectively. ■, PR+HV+NRTL; ☆, PR+MHV1+NRTL; ▲, PR+MHV2+NRTL; ▽, PR+LCVM+NRTL. F
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correlated results were shown in Table 3 and Table 4. The pressure deviations and composition deviations of (Ar + CH4) between experimental results and calculated results from different models were shown in Figures 2−5, and the relationship about excess Gibbs free energy and excess enthalpy with composition of (Ar + CH4) were given in Figures 6 and 7.
the mixture turned to be pure substance Ar. Note: similar work was done in the literature.27).
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RESULTS AND DISCUSSION In this work, the Peng−Robinson (PR) equation-of-state (EOS) with four mixing rules (HV, MHV1, MHV2, and LCVM) and the four equations of state (SRK, PR, PRSV, NM) with MHV1 were used to correlate the VLE data of the mixture (Ar(1) + CH4(2)), respectively, in which the NRTL activity coefficient model was used to calculate the excess Gibbs free energy. Need to explain: PR equation of state combined with four mixing rules was selected to correlate the VLE data of the mixture (Ar (1) + CH4 (2)), this is because PR equation is the most commonly used equation and can overcome the shortcomings of the SRK equation in calculating the molar volume of liquid phase.14 MHV1 mixing rule combined with four equations of state was selected to correlate the VLE data of the mixture (Ar (1) + CH4 (2)), this is because, compared to other mixing rules, MHV1 mixing rule can all attain higher correlation accuracy in predicting phase equilibrium of different types of mixtures in natural gas.5,12,28-35 In order to compare the experimental results and calculated results within the wide temperature range, VLE data of (Ar + CH4) published in other literatures were also added to be correlated with the VLE data in this work together, and the
Figure 4. Pressure−composition phase diagram for the binary mixture Ar(1) + CH4(2) from the PR equation of state and different mixing rules. Experimental data in this work: ▲, 90.67 K; ▽, 94.93 K; ●, 99.97 K; ○, 104.84 K; ■, 109.87 K; ★, 114.82 K; ☆, 119.94 K; □, 124.92 K; ⧫, 129.89 K; △, 134.87 K; ▼, 150.72 K; ◊, 164 K; +, 178 K; pink dashed line, calculated with the PR + HV + NRTL model; orange dotted line, calculated with the PR + MHV1 + NRTL model; blue dash/dotted line, calculated with the PR + MHV2 + NRTL model; gray line, calculated with the PR + LCVM + NRTL model. (Experimental data at 90.67 K, 150.72 K, 164 K, and 178 K were from the literature. Among those temperatures, data at 90.67 K were from Sprow et al.,4 and data at 150.72 K, 164 K, and 178 K were from Christiansen et al.10)
From Figure 2 and Figure 4, the results showed that the calculated accuracy from PR equation combined with four mixing rules (HV, MHV1, MHV2, and LCVM) in the lower temperature were comparable (during the correlation, the basic properties of Ar and CH4 are from Lemmon et al.36). At high temperature, such as 178 K, the calculated results from PR equation combined with the LCVM mixing rule had a large deviation from the experimental values. When the four equations of state (SRK, PR, PRSV, and NM) with the same mixing rule (MHV1) were used to calculate the VLE of (Ar + CH4), it could be found from Figure 3 and Figure 5 that the correlation deviations of the SRK equation + MHV1 were slightly larger than those of other equations of state. Taking the phase equilibrium curve at 90.67 K as an example (Figure 5), the SRK equation + MHV1 had a large deviation between the experimental values and the calculated results for the vapor phase composition of (Ar + CH4); for the liquid phase
Figure 3. Relative pressure deviations (a) and the vapor composition deviations (b) for the binary mixture (Ar(1) + CH4(2)) system from the different equations of state + MHV1 + NRTL models, respectively. ■, SRK + MHV1 + NRTL; ○, PR + MHV1 + NRTL; ▲, PRSV + MHV1 + NRTL; ▽, NM + MHV1 + NRTL. G
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Figure 7. Relationship between excess enthalpy and composition of the binary mixture (Ar(1) + CH4(2)). ■, 94.93 K; □, 99.97 K; ●, 104.84 K; ○, 109.87 K; ▲, 114.82 K; △, 119.94 K; ★, 124.92 K; ☆, 129.89 K; +, 134.87 K.
with the experimental results at the high composition of Ar. The PR equation + MHV1 and PRSV equation + MHV1 had high accuracy for the phase equilibrium prediction of (Ar + CH4). In addition, the excess Gibbs free energy and excess enthalpy of (Ar + CH4) at the experimental temperature were calculated by using the energy parameters obtained by the correlation. The results were shown in Figures 6 and 7. It can be seen from Figures 6 and 7 that the excess Gibbs free energy of (Ar + CH4) was more than zero, and the curves of excess Gibbs free energy and excess enthalpy of (Ar + CH4) had good symmetry.
Figure 5. Pressure−composition phase diagram for the binary mixture (Ar(1) + CH4(2)) from different equations of state and MHV1 + NRTL models. Experimental data in this work: ▲, 90.67 K; ▽, 94.93 K; ●, 99.97 K; ○, 104.84 K; ■, 109.87 K; ★, 114.82 K; ☆, 119.94 K; □, 124.92 K; ⧫, 129.89 K; △, 134.87 K; ▼, 150.72 K; ◊, 164 K; +, 178 K; pink dashed line, calculated with the SRK + MHV1 + NRTL model; orange dotted line, calculated with the PR + MHV1 + NRTL model; blue dashed/dotted line, calculated with the PRSV + MHV1 + NRTL model; gray line, calculated with the NM + MHV1 + NRTL model. (Experimental data at 90.67 K, 150.72 K, 164 K, and 178 K were from the literature. Among those temperatures, data at 90.67 K were from Sprow et al.,4 and data at 150.72 K, 164 K, and 178 K were from Christiansen et al.10).
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CONCLUSIONS VLE data of (Ar+ CH4) are limited in the published literature. Especially VLE data below 140 K are lacking, which have importantly practical significance for the separation of argon from natural gas. On the basis of these, in this paper, the experimental data of methane and argon in the temperature range of (95 to 135) K were measured, and the four different mixing rules (HV, MHV1, MHV2, and LCVM) with the same equation of state (PR) and the four equations of state (SRK, PR, PRSV, NM) with the same mixing rule (MHV1) were used to correlate the VLE of (Ar + CH4). The results showed that they had similar accuracy for four mixing rules with the same EOS at lower temperature, and the deviation for the LCVM mixing rule was larger than that for other mixing rules between the experimental results and calculated results at higher temperature (e.g., 178 K); the calculation accuracy with PR and PRSV equations combined with MHV1 was higher than that with the SRK equation and NM equation combined with MHV1 for (Ar + CH4). In addition, the results showed that the excess Gibbs free energy of (Ar + CH4) was more than zero, and the curves of excess Gibbs free energy and excess enthalpy of (Ar + CH4) had good symmetry.
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Figure 6. Relationship between excess energy and composition of the binary mixture (Ar(1) + CH4(2)). ■, 94.93 K; □, 99.97 K; ●, 104.84 K; ○, 109.87 K; ▲, 114.82 K; △, 119.94 K; ★, 124.92 K; ☆, 129.89 K; +, 134.87 K.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel.: +86 571 8795 3944. Fax: +86 571 8795 394.
composition, they had a good agreement between the calculated results and experimental results at low composition of Ar, whereas there were larger deviations between the calculated results and experimental results at high composition of Ar. At the higher temperature (105 K or higher), taking 124.92 K as an example (shown in Figure 5), the calculated results from the NM equation + MHV1 had larger deviations
ORCID
Xiaohong Han: 0000-0002-6020-7607 Funding
This work has been supported by the National Natural Science Foundation of China (No.51576171) and the Department Project of Technology Office in Zhejiang (2016F50053). H
DOI: 10.1021/acs.jced.8b00280 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Notes
(24) Han, X. H.; Zhang, Y. J.; Gao, Z. J.; Xu, Y. J.; Wang, Q.; Chen, G. M. Vapor-Liquid Equilibrium for the Mixture Nitrogen (N2) + Methane (CH4) in the Temperature Range of (110 to 125). J. Chem. Eng. Data 2012, 57, 1621−1626. (25) Fang, Y. B.; Guan, W. J.; Bao, K. L.; Wang, Y. Z.; Han, X. H.; Chen, G. M. Isothermal Vapor−Liquid Equilibria of the Absorption Working Pairs (R1234yf + NMP, R1234yf + DMETrEG) at Temperatures from 293.15 to 353.15 K. J. Chem. Eng. Data 2018, 63, 1212−1219. (26) Moffat, J. R. Describing the Uncertainties in Experimental Results. Exp. Therm. Fluid Sci. 1988, 1, 3−17. (27) Han, X. H.; Zhang, Y. J.; Gao, Z. J.; Xu, Y. J.; Zhang, X. J.; Chen, G. M. Vapor-Liquid Equilibrium for the Mixture Methane (CH4) + Ethane (C2H6) over the Temperature Range (126.01 to 140.01). J. Chem. Eng. Data 2012, 57, 3242−3246. (28) Donnelly, H. G.; Katz, D. L. Phase Equilibria in the Carbon Dioxide-Methane System. Ind. Eng. Chem. 1954, 46, 511−517. (29) Kaminishi, G.; Arai, Y.; Saito, S.; Maeda, S. Vapor-Liquid Equilibria for Binary and Ternary Systems Containing Carbon Dioxide. J. Chem. Eng. Jpn. 1968, 1, 109−116. (30) Wichterle, I.; Kobayashi, R. Vapor-Liquid Equilibrium of Methane-Ethane System at Low Temperatures and High Pressures. J. Chem. Eng. Data 1972, 17, 9−12. (31) Stryjek, R.; Chappele, P. S.; Kobayash, R. Low-Temperature Vapor-Liquid Equilibriums of Nitrogen-Methane System. J. Chem. Eng. Data 1974, 19, 334−339. (32) Kidnay, A. J.; Miller, R. C.; Parrish, W. R.; Hiza, M. J. LiquidVapor Phase Equilibria in the N2-CH4 System from 130 to 180 K. Cryogenics 1975, 15, 531−540. (33) Al-Sahhaf, T. A.; Kidnay, A. J.; Sloan, E. D. Liquid + Vapor Equilibria in the N2 + CO2 + CH4 System. Ind. Eng. Chem. Fundam. 1983, 22, 372−380. (34) Webster, L. A.; Kidnay, A. J. Vapor-Liquid Equilibria for the Methane-Propane-Carbon Dioxide Systems at 230 and 270 K. J. Chem. Eng. Data 2001, 46, 759−764. (35) Coquelet, C.; Valtz, A.; Dieu, F.; Richon, D.; Arpentinier, P.; Lockwood, F. Isothermal p, x, y Data for the Argon Plus CO2 at Six Temprature from 233.32 to 299.21 K and Pressures Up to 14 MPa. Fluid Phase Equilib. 2008, 273, 38−43. (36) Lemmon, E. W.; Huber, M. L.; Mclinden, M. O. NIST Standard Referencedatabase 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP; Version 9.1; NIST, 2013.
The authors declare no competing financial interest.
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