CH4

Article pubs.acs.org/jced

Measurement and Calculation of CO2 Frost Points in CH4 + CO2/CH4 + CO2 + N2/CH4 + CO2 + C2H6 Mixtures at Low Temperatures Xiaojun Xiong, Wensheng Lin,* Rong Jia, Yang Song, and Anzhong Gu Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China ABSTRACT: In published literature, only very limited data for CO2 frost point in natural gas mixture can be found. Measurements and calculations for CH4 + CO2/CH4 + CO2 + N2/CH4 + CO2 + C2H6 mixtures over a wide range of temperature, pressure, and compositions were performed in this work. The measurements were conducted through a simple equilibrium cell by static analytic method utilizing sampling technique. The calculations were carried out by fugacity balance model based on Peng−Robinson (PR) equation of state (EoS) with van der Waals mixing rule. The calculated results agree well with the experimental results, demonstrating the reliability of PR EoS based model. By comparing data obtained from gas mixtures with different nitrogen contents and ethane contents, it is found that both nitrogen and ethane have little effect on CO2 frost point. However, the maximum pressure for CO2 frosting in CH4 + CO2 + N2 ternary mixture increases with nitrogen content; oppositely, it decreases with ethane content in CH4 + CO2 + C2H6 ternary mixture.

1. INTRODUCTION CO2 transformation from gas phase directly to solid phase is called frosting. It usually occurs in low-temperature processes due to a relative high triple point temperature. In natural gas industry, CO2 frost is likely to form into being at the expander outlet, on the trays of demethanizer column or in the heat exchangers or pipelines and leads to hazardous conditions;1,2 hence, the knowledge of CO2 frost point in natural gas mixtures,

Table 2. Theoretical Predictions of CO2 Frost Point in Published Work

Table 1. Published Data of CO2 Frost Point in Natural Gas Mixtures

as the function of temperature, pressure, and composition, is of great practical significance. Some researchers have measured CO2 frost point in different natural gas mixtures, as shown in Table 1. It is obvious that only very limited data are available, which can hardly meet the requirement of natural gas industry. Moreover, most data are available for CH4 + CO2 binary mixtures,3−5 and only a few are for multicomponent natural gas mixtures.4,6,7 Besides, the data collected for multicomponent natural gas mixtures are given at limited compositions4,6,7 within a narrow range of temperature4,6,7 and pressure.7 Consequently, this work attempts to provide CO2 frost data over a wide range of compositions, temperature, and pressure in the region of practical application. In published works,4,7 researchers would like to use dynamic analytic method to measure CO2 frost data through a visualized equilibrium cell, wherein gas mixture with fixed composition is gradually cooled until the solidification is observed. This approach is hard to achieve high accuracy unless a fairly small cooling rate, which may lead to a long experimental time and a

natural gas mixture

T K

kPa

Pikaar3 Agrawal and Laverman4 Zhang et al.5

CH4 + (0−20 %) CO2 CH4 + (0.12−10.67 %) CO2 CH4 + (10.8−54.2 %) CO2 36.50 % CH4 + 63.30 % CO2 + 0.21 % N2 36.50 % CH4 + 63.00 % CO2 + 0.45 % N2 98.36 % CH4 + 0.68 % CO2 + 0.96 % N2 96.13 % CH4 + 2.94 % CO2 + 0.93 % N2 97.06 % CH4 + 1.94 % CO2 + 1.00 % N2 96.11 % CH4 + 1.94 % CO2 + 1.95 % N2 97.053 % CH4 + 1.95 % CO2 + 0.997 % C2H6 96.05 % CH4 + 1.96 % CO2 + 1.99 % C2H6

153−211 137−199

400−4500 172−3043

58 58

191−211

293−4446

17

151−166

1185−4000

5

154−173

175−2445

19

173−184

1240−2240

48

Huafe et al.6

Agrawal and Laverman4

Le and Trebble7

p

© 2015 American Chemical Society

author

data points

author

EoS

natural gas mixture

Agrawal and Laverman5

BWR

Riva et al.8 Zarenezhad and Eggeman9 Zhang et al.6

PR PR SRK

CH4 CH4 CH4 CH4 CH4

+ + + + +

CO2 CO2 + N2 CO2 CO2 CO2

Received: January 17, 2015 Accepted: September 29, 2015 Published: October 12, 2015 3077

DOI: 10.1021/acs.jced.5b00059 J. Chem. Eng. Data 2015, 60, 3077−3086

Journal of Chemical & Engineering Data

Article

Table 3. Chemical Sample Table usage (source) test gas (Shanghai Wetry Standard Gas Co., Ltd.)

chemical name

mole fraction composition

relative expanded uncertainty (0.95 level of confidence)

analysis method

methane−carbon dioxide mixture

CH4: 99.50 %

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

CO2: CH4: CO2: CH4:

methane−carbon dioxide− nitrogen mixture

CO2: 0.50 % N2: 3.00 % CH4: 94.50 % CO2: 0.50 % N2: 5.00 % CH4: 77.00 % CO2: 20.00 % N2: 3.00 % CH4: 75.00 % CO2: 20.00 % N2: 5.00 % CH4: 96.50 %

methane−carbon dioxide−ethane mixture

standard gas (Shanghai Yingjiang Chemical Co., Ltd.)

0.50 % 79.90 % 20.10 % 96.50 %

methane−carbon dioxide mixture

CO2: 0.50 % C2H6: 3.00 % CH4: 94.50 % CO2: 0.50 % C2H6: 5.00 % CH4: 77.00 % CO2: 20.00 % C2H6: 3.00 % CH4: 75.00 % CO2: 20.00 % C2H6: 5.00 % CH4: 99.47 % CO2: CH4: CO2: CH4: CO2: CH4: CO2: CH4: CO2: CH4: CO2: CH4: CO2: CH4:

methane−carbon dioxide− nitrogen mixture

0.53 % 98.99 % 1.01 % 98.00 % 2.00 % 95.01 % 4.99 % 89.96 % 10.04 % 84.96 % 15.04 % 80.21 % 19.79 % 96.50 %

CO2: 0.50 % N2: 3.00 % CH4: 95.00 % CO2: 2.00 % N2: 3.00 % CH4: 92.00 % CO2: 5.00 % N2: 3.00 % CH4: 87.00 % CO2: 10.00 % N2: 3.00 % CH4: 77.00 % CO2: 20.00 % N2: 3.00 % 3078



Article

Table 3. continued usage (source)

chemical name

mole fraction composition

relative expanded uncertainty (0.95 level of confidence)

analysis method

methane−carbon dioxide−ethane mixture

CH4: 96.50 %

1%

GC

1%

GC

1%

GC

1%

GC

1%

GC

CO2: 0.50 % C2H6: 3.00 % CH4: 95.00 % CO2: 2.00 % C2H6: 3.00 % CH4: 92.00 % CO2: 5.00 % C2H6: 3.00 % CH4: 87.00 % CO2:10.00 % C2H6: 3.00 % CH4: 77.00 % CO2: 20.00 % C2H6: 3.00 %

Figure 1. Schematic of the experimental setup: BT, buffer tank; BTT, bidirectional triode thyristor; C, container; CTB, constant temperature bath; DAS, data acquisition system; EC, equilibrium cell; GC, gas chromatography; H2, hydrogen cylinder; He, helium cylinder; HIL, heat insulation layer; HS, heat strip; HW, heat wire; LN2, liquid nitrogen dewar; PC, personal computer; PGi, pressure gauge i; PRP, platinum resistance probe; PT, pressure transducer test gas, test gas cylinder; TR, temperature regulator; Vi, valve i; VP, vacuum pump.

shown in Table 2. It is obvious that most predictions were conducted for CH4 + CO2 binary mixtures, few of them dealt with ternary mixtures. Therefore, this work performed calculations for ternary mixtures as well as binary mixtures using the well-known PR EoS. In this paper, measurement and calculations of CO2 frost points were both conducted. The reliability of measurement was verified by comparing the measured results of this work and other works and the reliability of calculations was checked by performing comparison work between the calculated and measured results. Moreover, to investigate the effects of N2 and C2H6 on CO2 frost point, the experimental and calculated work

high cost of experimental material. Therefore, the static analytic method with sampling technique was used in this work to collect CO2 frost data through a simple equilibrium cell. At a given low temperature, natural gas with sufficient CO2 gradually reaches gas−solid equilibrium in the equilibrium cell, and the equilibrium data of vapor phase is CO2 frost data. As an outward extension of measurement, theoretical calculation is also an effective approach for CO2 frost point prediction. Different researchers have used different equations of state (EoS), such as Bebedict−Webb−Rubin (BWR) EoS,4 Peng− Rabinson (PR) EoS,5,8 and Soave−Redlich−Kwong (SRK) EoS,9 to predict CO2 frost point in natural gas mixture, as 3079



Article

Table 4. CO2 Frost Data for CH4 (1) + CO2 (2) TExp = 193.15 K p

x2

TExp = 188.15 K TCal

p

kPa

%

K

kPa

3038 2746 2418 1752 1620 1389 1051 921 803 533 284

5.46 5.26 5.19 6.85 7.19 8.11 10.29 11.57 12.63 19.32 34.07 TExp = 168.15 K

194.52 193.3 192.18 193.07 192.96 193.02 193.17 192.77 192.83 193.54 193.23

2982 2644 2124 1841 1660 1468 1168 852 654 390 273

x2 %

TExp

TExp = 178.15 K TCal

3.92 3.77 3.75 4.76 4.95 5.17 6.39 8.14 10.25 16.33 22.49 = 158.15 K

p

K

kPa

189.77 188.53 186.97 188.84 188.43 187.86 188.29 188.03 188.02 187.92 187.71

2183 1983 1775 1563 1305 1090 933 768 589 397 278

x2 %

TExp

1.61 1.54 1.58 2.22 2.52 2.83 3.16 3.83 4.67 7.00 9.03 = 153.15 K

TCal K 177.19 176.14 175.81 178.61 178.58 178.35 178.20 178.53 178.18 178.67 177.83

p

x2

TCal

p

x2

TCal

p

x2

kPa

%

K

kPa

%

K

kPa

%

K

1510 1335 1130 953 791 669 562 467 369 277

0.82 0.71 0.91 1.08 1.25 1.45 1.70 2.09 2.52 3.31

168.07 166.07 167.21 167.64 167.63 167.75 167.82 168.19 167.93 167.99

1074 970 865 761 649 561 474 415 341 271

0.48 0.41 0.33 0.39 0.48 0.56 0.66 0.75 0.92 1.13

161.06 159.26 156.77 157.18 157.79 158.11 158.29 158.32 158.56 158.5

1235 996 878 726 652 559 490 437 380 270 219

0.10 0.13 0.16 0.20 0.22 0.25 0.29 0.32 0.36 0.50 0.63

149.32 150.18 150.86 151.5 151.83 151.72 151.92 152.11 152.02 152.07 152.36

TCal

Data points n = 64, average relative deviation ARD = (∑i n= 1((|TCal − TExp|)/TExp))/n = 0.46 %. Expanded uncertainty (0.95 level of confidence) U(T) = 0.3K, U(p) = 10 kPa, relative expanded uncertainty (0.95 level of confidence) Ur(x) = 4 %; x is mole fraction.

2.2. Experimental Setup. The experimental setup is shown schematically in Figure 1. The setup used in the present work has been adopted for measuring solid−liquid equilibrium data11,12 and gas−liquid equilibrium data13 successfully. Somewhat differently, the present work used it to collect gas−solid equilibrium data, that is, CO2 frost data. The experimental setup mainly consisted of three pieces of equipment, the equilibrium cell, the constant temperature bath and the container. The equilibrium cell with a volume of about 350 mL was suspended in the middle of the constant temperature bath. There were two tubes in the equilibrium cell; one connecting to the test gas cylinder across valves 2 and 3 for filling gas, and another connecting to the buffer tank (volume: about 200 mL) across valve 9 for sampling. The sampling tube outside the constant temperature environment was surrounded by a 20 W heat wire to avoid plug problem caused by solidification of CO2. Each time, about 200 mL of sample was quickly withdrawn from the equilibrium cell and stored in the buffer tank. After sampling, the pressure in the equilibrium cell decreased, leading to a disturbance in the equilibrium. So, the next measurement was conducted at a new equilibrium state different from the old one. As a result, the measurement under each experimental condition was performed for only one time. The equilibrium cell was submerged in a constant temperature environment, which is provided by the constant temperature bath. The 5.5 L stainless steel bath, on one hand, was cooled by vapor arising from liquid nitrogen in the container; on the other hand, it was heated by a heating wire controlled by a temperature regulating system, which consisted of a 150 W

were carried out for CH4 + CO2 binary mixtures and CH4 + CO2 + N2 and CH4 + CO2 + C2H6 ternary mixtures at different N2 or C2H6 contents.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The gases with certified compositions used in this measurement are given in Table 3. To avoid insufficient or excessive solid formation of CO2, test gas mixtures were prepared in two types for mixing: one was gas mixture with low CO2 content, such as 99.50 % CH4 + 0.50 % CO2; the other was gas mixture with high CO2 content, such as 79.90 % CH4 + 20.1 % CO2. To investigate the influence of nitrogen and ethane on CO2 frost point, two types of ternary mixtures were prepared: one was gas mixture with 3.00 % N2 or C2H6, and the other was gas mixture with 5.00 % N2 or C2H6. Gas composition was checked by a gas chromatograph using area external standard method.10 As shown in Table 3, 17 known gas mixtures with a relative expanded uncertainty (with a coverage factor k = 2, 0.95 level of confidence) of 1 % were used as standard gases to prepare standard curves. Hydrogen (H2) (Shanghai Pujiang Special Gas Co., Ltd., Shanghai, China) with high checkout sensitivity was chosen as carrier gas. To accelerate the equilibrium process, helium (He) (Shanghai Ji Liang Standard Reference Gas Co., Ltd., Shanghai, China) was used as auxiliary gas filling in the constant temperature bath (CTB). In addition, liquid nitrogen (LN2) (Shanghai Lümin Gas Co., Ltd., Shanghai, China), being a safe and economic coolant, was used in this work. 3080



Article

heat strip, a proportional−integral−differential (PID) temperature regulator (AIJ-3.3 type, Xiamen Yudian Automation Technology Co., Ltd., Xiamen, China), a bidirectional triode thyristor (BTA41-600B type) and a calibrated 100 Ω platinum resistance probe placed in the middle of the bath. In addition, the bottom of the bath was surrounded by heat insulation layer to reduce the vertical temperature difference, and two platinum resistance probes were placed respectively in the top and bottom of the bath to monitor the vertical temperature difference. The comprehensive effects of liquid nitrogen, temperature regulating system and heat insulation layer enabled the bath to keep a constant temperature in the range from 77 K to 200 K with a stability of ± 0.02 K. The constant temperature bath was suspended in the liquid nitrogen biological container (YDS-100B-200 type, Sichuan Yaxi Cryogenic Equipment Co., Ltd., Sichuan, China), which is an open double-wall vessel with a capacity of about 100 L. A plug made of heat insulation material was placed in the container mouth to slow down the vaporization of liquid nitrogen. At the beginning of each experimental run, the container was partially filled with liquid nitrogen from a 195 L dewar. The temperature in the EC was measured by a calibrated 100 Ω platinum resistance probe with a standard uncertainty of 0.1 K. The equilibrium cell pressure was measured by a calibrated pressure transducer (PT) (NS-I1 type, Shanghai Tianmu Automation Instruments Co. Ltd., Shanghai, China) with a standard uncertainty of 3 kPa. Both the temperature signal and pressure signal were collected by a data acquisition system (DAS) (Keithley 2700 type) and recorded by a personal computer (PC) in 10 s intervals. The standard uncertainty of temperature and pressure caused by data acquisition system were 0.06 K and 4 kPa, respectively. In addition, the temperature and pressure at the equilibrium state were consecutively measured for 1 h, so the temperature fluctuation (± 0.1 K) and pressure fluctuation (± 1 kPa) during 1h represented the uncertainty of repeatability. Therefore, the total expanded uncertainty (with a coverage factor k = 2, 0.95 level of confidence) of temperature and pressure were U(T) = 2 × ((0.1 K)2 + (0.06 K)2 + (0.1 K)2)1/2 = 0.3 K and U(p) = 2 × ((4 kPa)2 + (3 kPa)2 + (1 kPa)2)1/2 = 10 kPa, respectively. The composition analysis was conducted by the gas chromatograph (GC 1690 type, Hangzhou Kexiao Chemical Equipment Co., Ltd., Hangzhou, China) and a chromatograph workstation (N2000 type, Zhejiang University Zhida information system engineering co ltd, Zhejiang, China). The accuracy of the gas chromatograph was calibrated according to the Chinese national regulation.14 The uncertainty of the gas composition depends on the uncertainty of chromatographic peak area, carrier gas flow rate, noise of baseline, temperature, and standard gas. The relative standard uncertainty of the chromatographic peak area was calculated to be 0.29 % by injecting the gas into the chromatograph and measuring its peak area six times. The relative standard uncertainty of the carrier gas flow rate was determined to be 0.41 % by checking the flow rate six times. The relative standard uncertainty of the baseline caused by noise was 1.92 %. The relative standard uncertainty of the temperature in gas chromatograph was 0.1 %. The relative standard uncertainty of the standard gas was 0.5 %. As a result, the combined relative standard uncertainty of gas composition was ur(x) = ((0.29 %)2 + (0.41 %)2 + (1.92 %)2 + (0.1 %)2 + (0.5 %)2)1/2 = 2 %, and the relative expanded uncertainty (with a coverage factor k = 2, 0.95 level of confidence) of gas composition was Ur(x) = 2 × 2 % = 4 %. 2.3. Experimental Method. The static analytic method with sampling technique is a well-established method to collect

Figure 2. Comparison of experimental data for CH4 + CO2 binary mixture between this work and other work (a) at the same temperature conditions and (b) at similar temperature conditions.

Figure 3. Comparison between the experimental and the calculated results for CH4 + CO2 binary mixture.

phase equilibrium data. With high reliability and good feasibility, it has been widely used in phase equilibrium study.15,16 In this work, CO2 frost point is the critical condition of CO2 frost formation, which is indeed the temperature, pressure, and composition of vapor phase in equilibrium with solid phase; therefore, the static analytic method with sampling technique can be used to measure CO2 frost point. 2.4. Experimental Procedure. The experiment was performed as the following steps: first, filling three pieces of equipment; second, setting up experimental conditions; third, sampling and analysis. 3081



Article

Table 5. CO2 Frost Data for CH4 (1) + CO2 (2) + N2 (3) CH4 + CO2 + 3 % N2 TExp

p

x2

x3

CH4 + CO2 + 5 % N2 TCal

p

x2

x3

TCal

K

kPa

%

%

K

kPa

%

%

K

193.15

2010 1784 1498 1180 889 685 497 283 2088 1791 1472 1131 783 581 390 276

6.00 6.39 7.04 8.64 11.27 14.04 19.05 32.14 4.12 4.55 5.50 6.73 8.71 11.67 16.92 23.73

3.11 3.45 3.40 3.29 3.27 3.16 2.96 2.50 3.34 3.35 3.44 3.27 3.14 3.15 2.96 2.62

192.59 192.33 191.94 192.16 192.51 192.39 192.55 192.46 188.05 188.05 188.65 188.62 187.97 188.30 188.34 188.47

1920 1765 1592 1402 1198 912 718 532 389 275 1408 1050 853 673 492 267

1.85 2.01 2.25 2.52 2.57 3.22 3.89 5.33 6.75 9.37 0.80 0.83 0.93 1.40 1.64 3.37

3.45 3.44 3.37 3.25 3.19 3.13 3.19 3.12 3.08 3.00 3.07 3.06 3.05 3.03 2.98 2.94

178.04 178.39 178.90 179.18 178.12 178.23 178.09 178.62 178.08 178.10 167.50 165.89 165.43 167.45 166.40 167.83

2200 1740 1450 1223 924 674 432 277 2138 1876 1572 1250 960 775 574 400 268 1930 1622 1332 1032 831 635 424 275

6.32 6.85 7.94 9.25 11.84 15.60 23.32 34.79 4.00 4.48 5.12 5.78 7.07 8.67 11.38 16.04 22.90 1.61 1.63 2.01 2.64 3.28 4.33 6.55 9.91

5.74 5.71 5.58 5.49 5.36 4.52 4.50 4.89 5.47 5.39 5.19 5.03 4.76 5.43 5.25 4.91 5.28 5.62 5.44 5.24 5.29 5.25 5.24 5.07 4.86

194.12 193.07 193.21 193.43 193.59 193.56 193.47 193.20 187.9 188.28 188.39 187.76 187.58 187.83 187.88 188.00 187.72 178.10 175.53 176.38 177.18 177.62 178.09 178.61 178.70

1183 970 786 590 423 273

0.16 0.13 0.15 0.25 0.32 0.48

3.18 3.13 3.11 3.04 2.97 2.93

152.43 150.28 149.93 152.11 151.75 151.9

1703 1564 1260 969 752 570 415 272 1067 882 679 525 400 279

0.41 0.53 0.54 0.77 1.02 1.46 1.95 2.72 0.12 0.24 0.21 0.27 0.31 0.42

5.22 5.03 5.04 4.99 5.01 5.04 5.11 5.18 5.67 5.32 4.86 4.34 4.97 5.13

162.32 164.19 163.10 164.74 165.41 166.55 166.59 166.05 149.61 154.28 151.54 152.02 151.10 151.07

188.15

178.15

168.15

153.15

Data points n = 77, average relative deviation ARD = (∑i n= 1((|TCal − TExp|)/TExp))/n = 0.62 %. Expanded uncertainty (0.95 level of confidence) U(T) = 0.3K, U(p) = 10 kPa, relative expanded uncertainty (0.95 level of confidence) Ur(x) = 4 %; x is mole fraction.

(1) An experimental run started by filling the equilibrium cell, the constant temperature bath and the container as followings: (a) Fill the equilibrium cell with test gas mixture with appropriate CO2 content and it is the key to a successful test. If the test gas mixture contains too much CO2, the thin tube for filling gas in low temperature environment would be blocked, making the pressure in equilibrium cell unable to be read by the pressure transducer placed at the inlet of the thin tube. If the test gas mixture contains too little CO2, no CO2 frosting would occur in the equilibrium cell, which leads to an invalid measurement for CO2 frost point. Therefore, the equilibrium cell filling was accomplished

by carefully mixing two types of test gas mixture (as mentioned in section 2.1) so as to guarantee the CO2 content in test gas being slightly higher than the predicted CO2 frost content. (b) Charge helium into the constant temperature bath to 0.2 MPa to accelerate the procedure of approaching equilibrium. (c) Fill liquid nitrogen into the container up to 25 L. (2) Set a fixed working temperature on the temperature regulator and wait for the equilibrium cell reaching equilibrium. When the temperature in the equilibrium cell maintained at the setting value with a fluctuation of ± 0.1 K and the pressure in the equilibrium kept stable with a fluctuation of ± 1 kPa during a period of 1 h, the 3082



Article

Figure 5. Effect of nitrogen on CO2 frost point: (a) experimental results; (b) calculated results.

Figure 4. Comparison between the experimental and the calculated results for (a) CH4 + CO2 + 3 % N2 and (b) CH4 + CO2 + 5 % N2 ternary mixtures.

3. THEORETICAL CALCULATIONS It is evident that experiment can only be performed under certain operating conditions and offer limited discrete data, which are far not enough for practical use. Thus, theoretical calculations, as an outward extension of experiment, were also conducted in this work. Fugacity balance model based on PR EoS17 with van der Waals mixing rule18 were used for theoretical calculations in the present work. At the CO2 frost point, the fugacity of gas phase should be equal to that of solid phase, as presented in eq 1

steady equilibrium was achieved. Usually, it took about 6 h to cool the equilibrium cell from room temperature to the desired experimental temperature, and it took another 2−3 h to attain steady equilibrium. (3) Once the equilibrium was reached, sampling and analysis were performed as follows: (a) The buffer tank was evacuated to eliminate the influence of last measurement. (b) The sampling tube was heated to avoid plug problem during sampling. (c) Valve 9 was opened to introduce the gas sample into the buffer tank. (d) Valve 10 was opened to wipe out the tube between the buffer tank and the gas chromatograph to eliminate the effect of last measurement. (e) Gas sample was injected into the gas chromatograph for composition analysis, which was repeated for two times and the average value of two measurements was taken as the final test result. (f) Check whether the CO2 content of the final test result is lower than that we have loaded in the cell. If it is lower, it indicates that solid CO2 forms in the cell and the tested result is valid. If not, it means that there is only gas in the cell and tested result is invalid. If this occurs, we will start another experiment run using test gas with higher CO2 content until the tested result is valid. By filling more test gas or releasing some test gas from the equilibrium cell, another experiment run at higher or lower pressure was performed. After a set of experiments under various pressures were completed, other sets of experiments at different temperatures were also accomplished with the same procedures.

f 2g (x 2 , T , p) = f 2s (T , p)

(1)

where f is fugacity; x is fraction in mole; T is temperature in K; p is pressure in kPa; the superscripts “g” and “s” refer to gas phase and solid phase, respectively; the subscript 2 represents carbon dioxide. The gas and solid phase fugacity are, respectively, calculated by eq 2 and 3 f 2g (x 2 , T , p) = x 2φ2g p

(2)

⎡ v2s(p − p sat ) ⎤ 2 ⎥ f 2s (T , p) = p2sat φ2sat × exp⎢ ⎢⎣ ⎥⎦ RT

(3)

where φ is fugacity coefficient and can be derived from PR EOS with van der Waals mixing rule,9 v is specific volume, R is the universal gas constant equal to 8.3145 J/mol·K, the superscript “sat” represents saturated state. The saturated pressure as a function of temperature can be found in literature.9 It is assumed that the specific volume of solid carbon dioxide is a 3083



Article

Table 6. CO2 Frost Data for CH4 (1) + CO2 (2) + C2H6 (3) CH4 + CO2 + 3 % C2H6 TExp

p

x2

x3

CH4 + CO2 + 5 % C2H6 TCal

p

x2

x3

TCal

%K

kPa

%

%

K

kPa

%

%

K

193.15

2010 1820 1488 1158 836 633 429 272 1835 1545 1286 959 738 574 408 277 1640 1336 1036 810 600 418 274 1029 833 649 412 282 273

6.45 6.80 8.04 10.37 11.80 15.94 22.49 33.31 4.27 4.90 6.36 8.32 10.04 12.51 17.31 25.11 1.96 2.35 3.04 3.67 4.69 6.82 9.99 1.18 1.42 1.76 2.77 4.08 0.65

3.07 3.06 3.06 2.96 2.85 3.05 2.80 2.41 3.49 3.50 3.44 3.11 3.05 2.82 2.68 2.44 3.39 3.37 3.19 3.20 3.15 3.07 2.97 3.27 3.46 3.47 3.48 3.05 3.08

193.55 193.34 193.6 194.32 192.42 193.11 192.92 192.43 187.45 187.66 189.17 189.54 189.07 189 189.12 189.19 177.58 178.03 178.54 178.4 178.9 178.9 178.74 169.01 169.26 169.29 169.75 170.09 154.14

2195 1847 1548 1253 924 673 446 274 2055 1790 1514 1200 896 697 464 274 1206 914 676 462 286

5.81 6.77 8.14 9.66 11.40 16.32 23.38 33.65 4.04 4.76 5.61 6.18 7.51 10.18 14.87 23.07 2.72 3.26 4.40 6.08 9.39

5.16 5.94 5.79 5.66 5.62 5.27 4.86 5.14 4.98 5.33 5.47 5.16 5.06 5.25 4.87 5.07 5.31 5.33 5.25 5.14 5.31

192.94 193.46 194.2 194.27 193.11 194.13 193.89 192.65 187.67 188.61 189.18 188.16 187.6 188.63 188.74 188.06 178.79 178.38 178.84 178.66 178.52

644 443 275

1.78 2.24 3.25

5.16 5.06 4.81

169.33 168.4 167.76

188.15

178.15

168.15

153.15

Data points n = 52, Average relative deviation ARD = (∑i n= 1((|TCal − TExp|)/TExp))/n = 0.36%. Expanded uncertainty (0.95 level of confidence) U(T) = 0.3K, U(p) = 10 kPa, relative expanded uncertainty (0.95 level of confidence) Ur(x) = 4 %; x is mole fraction.

obtained in this work were compared with other works, as shown in Figure 2. Figure 2a shows the comparison between this work and Pikaar’s4 at the same temperature conditions. A fairly good consistency is found between two works, demonstrating the reliability of the apparatus and method used in this work. Figure 2b presents the comparison between this work and other works at similar temperature conditions. The results by this work are very close to those of other works utilizing visualized apparatus and dynamic analytic method, which confirms the reliability of this work once again. Because lower temperature desublimates more CO2, the data at 187.7 K and 177.8 K by Le and Trebble8 have slightly lower CO2 content than the data at 188.15 K and 178.15 K by this work, and the results at 178.9 K by Le and Trebble8 and at 168.37 K and 158.21 K by Agrawal and Laverman5 have slightly higher CO2 content than the results at 178.15 K, 168.15 K and 158.15 K by this work. A point-to-point comparison for CH4 + CO2 binary mixture between experiment and calculation is given by Table 1. At given pressures and compositions, the average relative deviation of frost temperature calculation is only 0.46 %. For further comparison, the calculated results at six given temperatures are plotted along with the experimental results in Figure 3. It can be seen that the calculated results fit well with the experimental results. Small deviation and good fitting between the experimental and calculated results suggest that the theoretical model

constant value, independent of pressure temperature, and the value of vs2 is calculated to be 3.1428 × 10−5 m3/mol.4 Substituting the above equations into the fugacity balance equation, eq 1 becomes a complex function of three independent variables, which are x2, T, and p. Given two variables, the third one can be worked out by Matlab programming utilizing bisection method.

4. RESULTS AND DISCUSSION The CO2 frost data were measured and calculated for CH4 + CO2 binary mixtures and CH4 + CO2 + N2 and CH4 + CO2 + C2H6 ternary mixtures at different temperatures and pressures. By comparing the results of gas mixtures with different nitrogen and ethane contents, the effects of nitrogen and ethane on CO2 frost point were discussed. 4.1. CH4 + CO2 Binary Mixture. Although lots of CO2 frost data for CH4 + CO2 binary system have been published, it is still contributive to collect more data to enrich the database. Table 4 presents the experimental data of CH4 + CO2 binary mixture at six constant temperatures, 193.15 K, 188.15 K, 178.15 K, 168.15 K, 158.15 K, and 153.15 K. At the measured pressure and composition, the temperature of CO2 frost point was calculated for comparison, as shown in Table 4. To verify the reliability of the experimental setup and to prove the feasibility of the experimental method, the data 3084



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3 % and 5 %, were tested in this work. The experimental results at five constant temperatures, 193.15 K, 188.15 K, 178.15 K, 168.15 K, and 153.15 K, are summarized in Table 6. Table 6 presents an average relative deviation of 0.36 % between the calculated and measured data. The tested CO2 frost data is drawn against the calculated frosting curves for CH4 + CO2 + 3 % C2H6 ternary mixture in Figure 6a, and that

is applicable for CH4 + CO2 binary mixture in a wide range of temperature, pressure and compositions. As shown, the temperature and pressure have direct effects on CO2 frost content. Generally, higher temperature and lower pressure allow higher CO2 content in the presence of vapor. It can be observed that the space between 193.15 K curve and 188.15 K curve is larger than that of 158.15 K and 153.15 K, which indicates that temperature in higher region affects CO2 frost content more than that in lower region. Each isothermal curve is almost vertical in the higher pressure region and horizontal in the lower pressure region, which implies pressure in lower pressure region plays a more significant role in affecting CO2 content. 4.2. CH4 + CO2 + N2 Ternary Mixture. Practical applications rarely involve binary mixtures, but more involve multicomponent mixtures; hence, the measurements of CH4 + CO2 + N2 ternary mixtures were carried out. Generally, nitrogen content in natural gas varies from zero to 15 %. In this work, ternary mixtures with about 3 % and 5 % nitrogen content were measured and calculated, respectively. The results are presented in Table 5. As Figure 3 pointed out that the desublimation curve at 158.15 K is quite close to that of 153.15 K, the measurements for ternary mixtures were only conducted at five constant temperatures, 193.15 K, 188.15 K, 178.15 K, 168.15 K, and 153.15 K. At given pressures and compositions, the calculated frosting temperatures are compared to the experimental values, as shown in Table 5. The small average relative deviation of 0.69 % between the experimental and the calculated results for CH4 + CO2 + N2 ternary mixtures proves the reliability of PR based fugacity balance model in application of CH4 + CO2 + N2 ternary mixture. At given temperatures, a plot of calculated results against experimental results is drawn for CH4 + CO2 + 3 % N2 and CH4 + CO2 + 5 % N2 ternary mixtures, respectively, in Figure 4a and b. It can be seen that the calculated results agree well with the experimental results, which once again proves that it is reliable to use PR based fugacity balance model to predict CO2 frost point in CH4 + CO2 + N2 ternary mixture.. By comparing CO2 frost data at different nitrogen contents, the effect of nitrogen on CO2 frost point is investigated. As shown in Figure 5a, the experimental results of gas mixtures at different nitrogen contents are consistent with each other. For further comparison, nitrogen is gradually added to the CH4 + CO2 binary mixture until CH4 is completely replaced by nitrogen, and the calculated results are plotted in Figure 5b. Calculated frost points at five given temperatures contribute to five series of CO2 frosting curves. Each series of CO2 frosting curves contains four frosting curves at different nitrogen contents. It can be seen that desublimation curves at different nitrogen contents coincide with each other, which implies that nitrogen addition has little effect on CO2 frost point. However, it should be noted that CO2 frosting curves at different contents have different maximum pressure. With the increase of nitrogen content, the maximum pressure for CO2 desublimation increases as well. That is because the addition of nitrogen to gas mixture enables gas mixture to keep in gas−solid region at higher pressure. 4.3. CH4 + CO2 + C2H6 Ternary Mixture. C2H6 is usually the second largest constituent in natural gas mixtures; therefore, the determination of CO2 frost point in CH4 + CO2 + C2H6 ternary mixture is of great practical importance. In published work, Le and Trebble have measured CH4 + CO2 + C2H6 ternary mixture at two fixed ethane contents, 1 % and 1.95 %; thus, ternary mixtures with higher C2H6 content, about

Figure 6. Comparison between the experimental and the calculated results for (a) CH4 + CO2 + 3 % C2H6 and (b) CH4 + CO2 + 5 % C2H6 ternary mixture.

for CH4 + CO2 + 5 % C2H6 ternary mixture is drawn in Figure 6b. Highly agreed results suggest that the fugacity balance model based on PR equation with van der Waals mixing rule is also feasible for CH4 + CO2 + C2H6 ternary mixture. Figure 7 presents the comparison among gas mixtures with different ethane contents. Both of the measured and the calculated results show clearly that there is little difference among them. At a fixed temperature and pressure, CO2 frost content in various gas mixtures are almost the same. However, a small difference is generated by increasing ethane content, as shown in Figure 7b. The maximum pressure for CO2 frosting obviously declines as ethane content increasing. This can be explained by phase transformation mechanism. The gas−liquid saturated pressure of ethane is similar to the gas−solid saturated pressure of carbon dioxide, implying that ethane condensation occurs while CO2 desublimation takes place. With liquid occurrence, gas mixture turns into gas−liquid−solid phase from gas−solid phase, leaving CO2 solidification technically outside the scope of frost. Consequently, with the addition of ethane, the maximum pressure for CO2 frosting decreases significantly. 3085



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Notes

The authors declare no competing financial interest.

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Figure 7. Effect of ethane on CO2 frost point: (a) experimental results and (b) calculated results.

5. CONCLUSION CO2 frosting usually occurs at low temperature and results in hazardous conditions in the natural gas industry; therefore, it is necessary to predict the CO2 frost point. This work collected CO2 frost data in CH4 + CO2 binary mixture and CH4 + CO2 + N2 and CH4 + CO2 + C2H6 ternary mixtures through a simple equilibrium cell using static analytic method and sampling technique. Also, theoretical calculations utilizing the fugacity balance model were performed for the binaries and ternaries. By comparison, the data of this work for CH4 + CO2 binary mixture are similar to that of other work, which demonstrates the reliability of the apparatus and method used in the present work. The calculated results agree well with the experimental results, proving the applicability of PR EoS based fugacity balance model for the binaries and ternaries. Furthermore, comparison results of gas mixtures at different nitrogen contents shows that the CO2 frost point keeps almost the same and the maximum pressure for CO2 frosting increases as nitrogen content increasing. Somewhat differently, ethane has little effect on CO2 frost point, whereas the maximum pressure for CO2 frosting decreases with ethane content.

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REFERENCES

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The authors are grateful to the support of China’s National Natural Science Fund (No.51076098). 3086


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