Vapor–Liquid Equilibrium for the Mixture Nitrogen (N2) + Methane

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Vapor−Liquid Equilibrium for the Mixture Nitrogen (N2) + Methane (CH4) in the Temperature Range of (110 to 125) K Xiao Hong Han, Yu Jia Zhang, Zan Jun Gao, Ying Jie Xu, Qin Wang,* and Guang Ming Chen Institute of Refrigeration and Cryogenics, State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China ABSTRACT: The design and operation of low temperature processes involving natural gas requires the phase equilibrium knowledge about the mixture (nitrogen (N2) + methane (CH4)) over extensive pressure and temperature ranges. In this work, the experimental apparatus for the vapor−liquid equilibrium is built, and vapor−liquid equilibrium data of the mixture (N2 + CH4) have been measured in the temperature range from (110 to 125) K. The experimental method used in this work is a single-cycle type. The vapor−liquid equilibrium experimental data of the mixture (N2 + CH4) are correlated by the Peng−Robinson equation-of-state + the first Modified Huron Vidal mixing rule + Wilson model, and the adjustable parameters of the activity coefficient are given. The correlated results show that they exhibit a good agreement with the experimental data. The average vapor composition deviation and the maximum vapor composition deviation are 0.0057 and 0.0166, respectively; the average relative pressure deviation and the maximum pressure deviation are 0.75 % and 2.25 %, respectively. In addition, no zoetrope exists in the binary system, and the system reveals slightly positive deviations from ideality from the correlation results.

1. INTRODUCTION Nitrogen (N2) is one of the most common nonhydrocarbon components in natural gas.1 In most natural gases, there exists a small amount of N2. However, in some oil-gas fields, N2 has a relatively high content, such as in Tarim Basin oil-gas fields of China, more than 10 % N2 (even up to 32 %) exists in 22 % of natural gas fields;2 N2 covers more in Gar Basin Wuxia region where the volume fraction of N2 in natural gas is up to 84.23 %.3 N2 can play an important role in the determination of the compression power consumption for LNG operation, for example, when the natural gas is liquefied, the more N2 in natural gas, the bigger the power consumption per unit in the system.4 It is well-known that the liquefied nature gas storage and transportation temperature is usually in the temperature ranges of (110 to 125) K because the natural gas needs to be pretreated to remove heavy hydrocarbons, sulfides, carbon dioxide, water, and other impurities under the atmospheric pressure at about −162 °C (∼112 K), then the natural gas is liquefied. Therefore, in the process of LNG, the vapor−liquid equilibrium (VLE) data in the temperature range of (110 to 125) K are needed. In addition, liquefied natural gas is stored in a low temperature about 112 K and a pressure generally no more than 0.1 MPa.5 Thus, in order to minimize the energy consumption in separation, storage, and transportation process, the simulation and optimization of the liquefaction process are necessary to be developed. The accurate vapor−liquid equilibrium data of natural gas at low temperature (110 to 125) K are a basis for the design and operation of low © 2012 American Chemical Society

temperature processes involving natural gas. Therefore, the knowledge about phase equilibrium of the mixture (N2 + CH4) over extensive ranges of pressure and temperature is extremely important for the optimization of the LNG system. The previous researchers had done a lot of work on the binary mixture (N2 + CH4), shown in Table 1.7−19 However, these studies were mainly conducted in the 1960s to the 1970s,6,14−17 and there were few data in some temperature ranges. In recent years, the research about the binary mixture (N2 + CH4) is little.18,19 With the development of the measurement technology, it is necessary to measure the accurate VLE data for the binary mixture (N2 + CH4) in a wide temperature range. The objective of the work is to provide accurate experimental measurements for the binary mixture (N2 + CH4) in temperature ranges from (110 to 125) K. The Peng−Robinson equation-of-state + the first Modified Huron Vidal mixing rule + Wilson (PR + MHV1 +Wilson) model is used to correlate the experimental data, and interactive parameters are obtained.

2. EXPERIMENTAL SECTION 2.1. Samples. CH4 and N2 were both provided by Zhejiang Minxing Industrial and Trading Co., Ltd. with a minimum purity of 99.99 % and 99.999 % (mass fraction), respectively. Received: November 25, 2011 Accepted: March 29, 2012 Published: April 12, 2012 1621

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Table 1. Previous Vapor−Liquid Investigations for the Binary Mixture (N2 + CH4) investigators

year

approximate temp region covered/K

approximate pressure region covered/atm

Rysakov et al.7 Torochesnikov and Levius8 Bloomer and Parent9 Cines et al.10 Bloomer et al.11 Fastovskii and Petrovskii12 Ellington et al.13 Cheung and Wang14 Forg and Wirtz15 Stryjek et al.16 Kidnay et al.17 Shi18 Raabe et al.19

1934 1939 1952 1953 1955 1957 1959 1964 1970 1974 1975 2000 2007

72.63 to 149.5 89 to 133 91 to 191 100 to 172 100 to 187 90 to 150 79 to 187 92 to 124 80 to 180 114 to 183 130 to 180 133.15, 143.15, 153.15 130 to 180

0.5 to 10 0 to 24 1 to 48 1 to 44 7 to 48 1 to 48 0 to 4 1 to 103 1 to 50 1 to 51 4 to 35 5.6 to 50

remarks graphs only dew-bubble point graphs only

graphs only

Figure 1. Schematic diagram of VLE experimental system. 1, chromatograph; 2, six-way valve; 3, dewar; 4, thermostatted bath; 5, equilibrium cell; 6, heater; 7, platinum resistance thermometer; 8, pressure transducer; 9, DC regulated power supply; 10, Keithley 2002 data acquisition/switch unit; 11, PID temperature controller; 12, PC; 13, vacumm pump; 14, sample; 15, self-pressurization dewar; 16, circulation pump.

liquid sampling valves online, 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. For both the liquid and vapor phases, the whole uncertainty of the composition measurement is expected to be within 0.0040 mol fraction. 2.3. Experimental Procedures. The experimental processes were as follows. (1) The system was first evacuated in order to remove the inert gases and other impurities; (2) a known amount of CH4 and N2 were charged into the equilibrium cell. As the CH4 and N2 are difficult to liquefying, the charging time is very long. Usually, about 10 h were needed for charging the required refrigerants; (3) the temperature for the whole system was kept 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 is sufficient to reach the thermal equilibrium state for whole system; (4) after the system is in the thermal balance, the temperature, pressure, and compositions for the system were measured with the four-head 25-platinum resistance thermometer, the pressure transducer, and the GC, respectively. 2.4. Experimental Data. Before the VLE experiment for the mixture (N2(1) + CH4(2)), the saturation pressure

Before use, samples (CH4 and N2) were without any further purification. 2.2. Experimental Equipment. The VLE experimental data (temperature−pressure−vapor−liquid (T−p−xi−yi)) were measured in an experimental apparatus with a recirculating still, shown in Figure 1. It includes a stainless steel equilibrium cell, temperature and pressure measuring systems, refrigeration system, etc. The equilibrium cell was thermostatted in a bath, which is made of copper. Heating wire is uniformly wrapped around the outer wall of the thermostat bath. The cooling capacity is supplied by the liquid nitrogen. A circulation loop from vapor to liquid phase is used to accelerate the equilibration by a circulating pump (GAH-T23.PVS.B, Micropump). The temperature was control by the high accuracy temperature controller ((Sr253-2IN-0060010, Shimaden, Japan) The temperature was measured by a four-head 25platinum resistance thermometer (Model: WZPB-I, China), which has accuracy of ± 1 mK (ITS), and the temperature fluctuation in the thermostated bath is less than ± 3 mK/30 min. The pressure was measured by a pressure transducer (Model: PMP4010, Drunk, FS = 1.6 MPa). The data were logged by a multifunction data acquisition/switch unit (Keithley 2002). The overall temperature uncertainty is within ± 10 mK, and the total pressure measurement uncertainty is within ± 0.65 kPa. The samples were immediately injected into a gas chromatograph (GC) with a thermal conductivity detector (TCD) (model GC1690, China) by the vapor and 1622

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experimental data of CH4 and VLE experimental data for the binary mixture (N2(1) + CH4(2) at 100 K were measured to verify the reliability of the experimental apparatus. The experimental results were shown in Tables 2 and 3 and Figure Table 2. Experimental Data and Reference Data of the Saturation Pressure for Methane T

pexp

pref

100|pexp − pref|/pexp

K

Pa

Pa

%

115.07 120.11 130.15 135.09

134 080 194 650 374 770 496 110

132 930 192 930 371 130 496 110

0.86 0.89 0.97 0.00

Figure 2. VLE data for the mixture (N2(1) + CH4(2)) at 100 K.

2 (in Tables 2 and 3, T is the absolute temperature, K; p is the system pressure; x is the liquid mole fraction; y is the vapor mole fraction; and subscripts exp and ref denote the experimental data and reference data, respectively). The experimental data and the theoretical values (calculated by REFPROP8.020,24) were compared; it is found that they exhibited a good agreement each other, the relative pressure deviation for the saturation pressure of CH4 is within 1 %, and the liquid composition deviation is within 0.01, which suggests that the experimental apparatus is stable and reliable. In this work, the experimental data (T−p−xi−yi) measured for the mixture (N2(1) + CH4(2)) are listed in Table 4. Throughout the work, x indicates the liquid-phase mole fraction, and p indicates the pressure in Pa.

parameters, respectively; Tc is the critical temperature, K; pc is the critical pressure, Pa; and ω is the acentric factor. The MHV1 mixing rule is22 am 1 GE 1 = + bmRT C RT C

bm =

2

a = 0.45724α(T )R Tc /pc

i

∑ xi i

ai biRT

∑ xibi

(5)

(6)

i E

where G is excess Gibbs energy, C is determined by the equation of state, and the subscript m denotes the parameters of the mixture. The excess Gibbs energy GE was calculated by the Wilson model23

3. RESULTS AND DISCUSSION In this work, the Peng−Robinson (PR) equation-of-state (EOS)21and the first Modified Huron Vidal (MHV1) mixing rule22 were used to correlate the VLE data of the mixture (N2(1) + CH4(2)) in which the Wilson activity coefficient model was used to calculate the excess Gibbs free energy. The expression of PR EOS is21 RT a p= − 2 (1) v−b v + 2vb − b2 2

⎛ bm ⎞ ⎟+ ⎝ bi ⎠

∑ xi ln⎜

G(ET , P) RT

= −x1 ln(x1 + Λ12x 2) − x 2 ln(Λ 21x1 + x 2)

(7)

where Λ12 and Λ21 are adjustable parameters. Activity coefficients obtained by the Wilson model are

(2)

ln γ1 = −ln(x1 + Λ12x 2) + βx 2

(8)

ln γ2 = −ln(Λ 21x1 + x 2) − βx1

(9)

where

α (T ) = (1 + (0.37464 + 1.54226ω − 0.26992ω2)(1 − Tr 0.5))2

β=

(3)

b = 0.07780RTc/pc

Λ12 Λ 21 − x1 + Λ12x 2 Λ 21x1 + x 2

(10)

where Λ12 and Λ21 can be expressed as follows:

(4)

where R is the general gas constant, J mol−1 K−1; v is the molar volume, m3 mol−1; a and b are equation of state dependent

Λ12 =

(0) (1) Λ12 + Λ12 ln(T ) RT

(11)

Table 3. Vapor−Liquid Equilibrium Data of the Binary Mixture (N2(1) + CH4(2)) at 100 K pexp

100|pref − pexp|/pexp

pref

xi

yi

kPa

yi,ref

kPa

|yi,ref − yexp|

%

0.8588 0.7489 0.5333 0.4052 0.2675 0.0041

0.9881 0.9752 0.9522 0.9312 0.9000 0.1345

678.89 609.83 485.97 397.26 300.14 38.93

0.9828 0.9719 0.9509 0.9337 0.9008 0.117

672.46 604.54 482.01 401.21 297.36 38.87

0.0053 0.0033 0.0013 0.0025 0.0008 0.0175

0.95 0.87 0.81 0.99 0.93 0.15

1623

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Table 4. Experimental VLE Results for the Binary Mixture (N2(1) + CH4(2)) at the Temperature Range of (110.01 to 123.01) K x1 0.0000 0.0284 0.0515 0.1334 0.1509 0.1689 0.2622 0.3338 0.4956 0.5482 0.7131 1.0000 0.0000 0.0305 0.0425 0.1247 0.1578 0.2275 0.3021 0.4510 0.6470 1.0000

0.0000 0.0296 0.0395 0.1102 0.1532 0.1932 0.2838 0.3619 0.3932 0.5900 1.0000 0.0000 0.0212 0.0363 0.0920 0.1302 0.1645 0.2658 0.3189 0.3497 0.5415 1.0000

y1

pexp/Pa

x1

T = 110.01 K 0.0000 88 05 0.4200 154 244 0.5689 202 782 0.7582 345 091 0.7816 375 132 0.7987 402 465 0.8522 536 627 0.8815 628 458 0.9127 803 962 0.9204 865 055 0.9446 1 058 490 1.0000 1 466 700 T = 112.98 K 0.0000 112 740 0.3940 183 017 0.4872 214 16 0.7168 381 48 0.7588 440 49 0.8192 556 930 0.8542 673 002 0.8969 882 240 0.9331 1 158 000 1.0000 1 735 200 T = 114.99 K 0.0000 132 110 0.3571 205 092 0.4424 230 256 0.6796 390 586 0.7456 472 721 0.7882 553 649 0.8405 711 856 0.8740 853 174 0.8836 904 213 0.9262 1 205 436 1.0000 1 936 000 T = 117.00 K 0.0000 153 920 0.2805 209 606 0.3934 253 697 0.6297 393 285 0.7019 483 085 0.7489 555 426 0.8263 755 756 0.8455 860 776 0.8560 920 000 0.8929 1 268 712 1.0000 2 153 300

0.0000 0.0192 0.0303 0.0730 0.0920 0.1152 0.1939 0.2486 0.2939 0.4826 1.0000

0.0000 0.0208 0.0281 0.0763 0.0890 0.1102 0.1819 0.2159 0.2613 0.4143 1.0000 0.0000 0.0157 0.0275 0.0493 0.0760 0.0863 0.1489 0.1759 0.2208 0.3618 1.0000

y1

pexp/Pa

T = 118.99 K 0.0000 178 110 0.2439 234 866 0.3369 266 955 0.5432 389 056 0.5991 445 366 0.6493 497 194 0.7595 694 255 0.8090 821 521 0.8292 916 143 0.8893 1 286 735 1.0000 2 385 700

Figure 3. Pressure−composition phase diagram for the binary mixture (N2(1) + CH4(2)). Experimental data in this work: ▼, 110.01 K; ○, 112.98 K; ★, 114.99 K; , calculated with PR + MHV1 + Wilson model.

T = 120.96 K 0.0000 204 780 0.2454 269 319 0.3024 290 887 0.5439 433 567 0.5879 465 492 0.6213 525 645 0.7342 722 825 0.7773 810 491 0.8079 935 427 0.8589 1 296 881 1.0000 2 633 900 T = 123.01 K 0.0000 235 610 0.1772 288 583 0.2729 327 139 0.4297 400 725 0.5300 490 130 0.5516 528 443 0.6885 722 400 0.7247 798 300 0.7667 926 760 0.8421 1 320 231 1.0000 2 913 000

Figure 4. Pressure−composition phase diagram for the binary mixture (N2(1) + CH4(2)). Experimental data in this work: ●, 117.00 K; □, 118.99 K; ▲, 120.96 K; ☆, 123.01 K; , calculated with PR + MHV1 + Wilson model.

Λ 21 =

(1) Λ(0) 21 + Λ 21 ln(T ) RT

With the presence of temperature in the equations of Λ12 and Λ21, their values vary with T. Parameters in eqs 11 and 12 are obtained by a nonlinear least-squares method, the object function is shown as follows: 1 OF = Np

2 ⎧ ⎛ pexp − pcal ⎞ ⎪ 2 ⎟ ⎜ ∑ ⎨0.5⎜ ⎟ + 0.5 (y1,exp − y1,cal )j p ⎪ j ⎠j exp ⎩ ⎝ Np

(

+ (y2,exp − y2,cal )j

molecular formula

relative molecular mass

Tc/K

pc/MPa

ω

N2 CH4

NN CH4

28.013 16.043

126.2 190.6

3.42 4.63

0.040 0.007

2

⎫ ⎪ ⎬ ⎪ ⎭

)

(13)

where, Np is the number of experimental points, the subscript cal denotes the calculated data, and j denotes the jth experimental point. The following equilibrium condition for VLE of the mixture (N2(1) + CH4(2)) is

Table 5. Critical Parameters and Acentric Factors for N2 and CH420 substance

(12)

yi φ̑ ivp = xi γipisat φisat

(14)

where y is the vapor phase mole fraction, ϕ is the fugacity coefficient, γ is the activity coefficient, and the superscript sat 1624

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Table 6. Correlated Results of VLE Data for the Binary Mixture (N2(1) + CH4(2)) at Different Temperatures Using the PR + MHV1 + Wilson Model PR + MHV1 + Wilson T/K

Np

Δy

max |ycal − yexp|

δp %

max 100((|pcal − pexp|)/pexp) %

110.01 112.98 114.99 117.00 118.99 120.96 123.01

10 8 9 9 9 9 9

0.0046 0.0033 0.0064 0.0084 0.0037 0.0063 0.0068

0.0098 0.0132 0.0116 0.0166 0.0096 0.0127 0.0145

0.59 0.81 0.68 0.86 0.83 0.98 0.52

1.47 1.62 1.64 1.62 2.55 1.85 1.24

In the correlation, the basic properties of N2 and CH4 are listed in Table 5. The correlated results are shown in Figures 3 and 4 and Table 6; the deviation results are shown in Figures 5 and 6; and the adjustable parameters of the Wilson model are given in Table 7. From the results in Table 6 and Figures 3 to 6, it can be seen that the results correlated by the PR + MHV1 + Wilson model show a good agreement with existing experimental data; the average relative pressure deviation from the PR + MHV1 + Wilson model is 0.75 %, and its maximum relative pressure deviation is 2.55 %; the average vapor composition deviation is 0.0057, and its maximum vapor composition deviation is 0.0166. In addition, from Figures 3 and 4, it can be known that the mixture (N2(1) + CH4(2)) reveals a slightly positive deviation from Roule’s law.

Figure 5. Deviations of pressure for the binary mixture (N2(1) + CH4(2)) from the PR + MHV1 + Wilson model.

4. CONCLUSIONS Isothermal VLE data for the binary mixture (N2 + CH4) were reported. The temperature ranges were explored from (110.01 to 123.01) K at pressures up to 1.4 MPa. The experimental data were correlated with the PR EOS combined with the MHV1 mixing rule and Wilson excess free energy model. The calculated values give a good agreement with the experimental data in this work, and the average deviation for vapor composition and the average relative pressure deviation are 0.0057 and 0.75 %, respectively. The maximum vapor composition deviation is 0.0166, and the maximum relative pressure deviation is 2.55 %. Meanwhile, the adjustable parameters of the Wilson model are given, which suggest that the model used in this work has a good prediction capability. In addition, there is no zoetrope in the binary mixture (N2 + CH4), and the mixture reveals slightly positive deviations from ideality from the correlated results.

Figure 6. Deviations of vapor composition for the binary mixture (N2(1) + CH4(2)) from the PR + MHV1 + Wilson model.

expresses the saturated property parameter for pure refrigerants. For the correlation of the experimental data, a computer program had been developed by applying the least-squares method. The deviations (δp and Δy) listed in tables were defined by

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86 571 87951738. Fax: +86 571 87951738. E-mail: [email protected]. Funding

Δy = ∑|ycal − yexp | j /Np

This work has been supported by the National Natural Science Foundation of China (No. 50806063 and 51176166) and Zhejiang Provincial Natural Science Foundation of China (Y1090455).

(13a)

j

δp = 100·∑|(pcal − pexp )/pexp | j /Np

(14a)

j

Table 7. Constant Values Derived by Fitting the Experimental Data constant values

range

model

a0

a1

b0

b1

temp ranges/K

mole fraction of N2

Wilson

−24.34

5.28

25.76

−5.27

110.01 to 123.01

0.01 to 0.95

1625

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Notes

Other Mixtures. GERG Technical Monograph; Fortschr.-Ber.VDI, VDIVerlag: Düsseldorf, Germany, 2006.

The authors declare no competing financial interest.

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REFERENCES

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