Vapor–Liquid Equilibrium Measurements for a Tetrafluoromethane +

Nov 2, 2012 - components in the system and to quicken the equilibrium process. The experimental results were correlated with Peng−. Robinson equatio...
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Vapor−Liquid Equilibrium Measurements for a Tetrafluoromethane + Propane System over a Temperature Range from (142.96 to 293.23) K Yanni Liu,†,‡ Kaihua Guo,*,† and Laiyun Lu† †

School of Engineering, Sun Yat-Sen University, Guangzhou 510275, China School of Civil Engineering, Guangzhou University, Guangzhou 510006, China

‡

ABSTRACT: The isothermal vapor−liquid equilibrium (VLE) for tetrafluoromethane (CF4) + propane (C3H8) system was measured and P, T, and y data were collected at temperatures of (142.96, 163.07, 183.10, 203.26, 223.17, 243.12, 263.15, 283.01, and 293.23) K. A vapor recirculation method was employed to drive the mixing of the two components in the system and to quicken the equilibrium process. The experimental results were correlated with Peng− Robinson equation of state and the van der Waals twoparameters mixing rule. The mean deviations between the correlated and measured vapor compositions were found to be satisfactory within 0.01 and the data showed a good accuracy and consistency.

1. INTRODUCTION Liquefied natural gas (LNG) is considered to be a clean energy and has been widely used in industrial processes and civil life nowadays. The considerable cold energy stored by the LNG could be retrieved instead of directly taken off by seawater. LNG cold energy utilizations, such as power generation, air separation, and intake air cooling, have been carried out in the past few decades.1,2 Recently, a novel cryogenic power cycle with a binary mixture as working fluids and combined with a vapor absorption process has been proposed in our previous work3 to improve the energy recovery efficiency of an LNG cold power generation. In that cycle, the binary mixture of tetrafluoromethane (CF4) and propane (C3H8) has been used as the working fluid and it was found that the proposed cycle was significantly superior to the ordinary organic Rankine cycle (ORC) and the efficiency could be increased by 66.3 %.3 It is significant to get VLE data (e.g., the binary interaction parameter used for the prediction of the mixture thermodynamic properties) of the binary system for the accurate prediction of the novel cryogenic power cycle. However, no VLE data for the CF4 + C3H8 system can be found in NIST/ TRC VLE Floppy Book Database or other literature. Most VLE experiments about the mixture involved in propane are focused on CFC-alternative refrigerants. In order to detect proper substitutes for CFCs and HCFCs in HVAC&R applications, special attention has been paid to the mixtures of propane + hydrofluorocarbons (HFCs). Bobbo et al.4−7 measured VLE properties of propane (R290) + HFCs such as difluoromethane (R32), pentafluoroethane (R125), 1,1,1,3,3,3hexafluoropropane (R236fa), and 1,1,1,2,3,3,3-heptafluoropropane (R227ea) and correlated the experimental data by using the Redlich−Kwong−Soave (RKS) equation of state (EoS) and the Huron−Vidal (HV) mixing rule with the nonrandom two-liquid (NRTL) model for the excess energy. Valtz et al.8,9 also © 2012 American Chemical Society

measured R290 + R32 and R227ea binary systems and correlated the VLE data by using RKS EoS with a modified HV and Wong− Sandler mixing rules and found better fitting results for these azeotropic systems. Kim et al.10 measured and correlated the VLE data for R290 + R32 and R125 systems with Peng− Robinson (PR) EoS and the van der Waals mixing rule and obtained satisfactory results. Lim et al.11−14 measured VLE data for R290 + R32, R227ea, 1,1,1,2-tetrafluoroethane (R134a), and 1,1,1-trifluoroethane (HFC-143a) as well as propylene (R1270) and compared the correlations by means of Carnahan−Starling− De Santis (CSD) and PR EoS with Wong Sandler mixing rule and found that PR EoS can give more accurate results. Park et al.15,16 performed VLE experiments for R290 + R125 and 1,1difluoroethane (R152a) and calculated the azeotropic behaviors of these binary systems by using CSD, PR, and RKS EoS with the van der Waals mixing rule. Im et al.17 had surveyed VLE data for the R290 + R143a system and correlated the experimental data with Peng−Robinson Stryjek−Vera (PRSV) EoS and Wong Sandler mixing rule. Gong et al.18,19 measured the VLE for R290 + R134a and trans-1,3,3,3-tetrafluoropropene (R1234ze (E)) and correlated the data with PR EoS and HV mixing rule. There are a few experimental studies on the binary mixtures involved in tetrafluoromethane (CF4). Zhu et al.20,21 measured the VLE data on CF4 + methane (CH4) and ethane (C2H6) and obtained the binary interaction parameters with the purpose of improving the thermodynamic efficiency of miniature mixed refrigerant Joule−Thomson refrigerators. Yu and Guo22 performed the VLE experiment on CF4 and nitrogen (N2) to improve the thermodynamic efficiency of the cryogenic mixture Received: July 18, 2012 Accepted: October 25, 2012 Published: November 2, 2012 3611

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Figure 1. Schematic diagram of visualized vapor−liquid equilibrium experimental apparatus. 1, sapphire cell; 2, blind cell; 3, oil heater; 4, thermal insulation; 5, absolute pressure transducer; 6, four-way sampling valve; 7, vapor recirculation pump; 8, vapor handling measuring pump; 9, gas chromatograph; 10, Agilent working station; 11, magnetic driven stirrer; 12, fan; 13, two-stage compression refrigerator; 14, cooling water pipe; 15, controller box; 16, data acquisition computer; 17, three-layer visualized observation window; 18, gas bottle; 19, liquid nitrogen dewar; 20, vacuum pump; 21, electromagnetic control valve; 21, absolute pressure transducer; V1−V17, valves.

top of the sapphire cell and driven to circulate by the circulation pump with a volume flow rate of (2 to 120) cm3·min−1 and mixed with the liquid phase at the bottom of the sapphire cell”.22 The temperature fluctuation of the air-bath, which was cooled by a two-stage compression refrigeration for above 203 K and by liquid nitrogen for lower temperature, was controlled within ± 0.1 K and that of the sapphire cell within ± 0.01 K. The temperatures were measured with Pt100 platinum resistance thermometers. The Pt100 platinum resistance thermometer for the sapphire cell was calibrated by a Pt25 standard platinum resistance, which was manufactured by Yunnan Measuring Appliance Ltd. and calibrated by Chinese National Institute of Measurement and Testing. The uncertainty was less than ± 0.01 K. The pressure was surveyed by two absolute pressure transducers, one by Keller PA33 pressure transducer with a full scale of 2 MPa and an uncertainty of ± 200 Pa, and the other by Mensor 6100 with a full scale of 10 MPa and an uncertainty of ± 1 kPa. The pressure reading from the Mensor 6100 was used when the pressure was higher than 1 MPa, and the pressure reading from Keller PA33 was used for the lower pressures in this work. The mixture composition measurement was performed using a gas chromatograph (Agilent HP 6890N) equipped with a thermal conductivity detector (TCD). Samples for calibration of the GC curve were made based on mass basis by a high-accuracy Sartorius CP225 balance, which has a accuracy of 0.1 mg in the range of 220 g. After careful calibration, all the sample data were on a straight line and the uncertainty was within ± 0.002 in mole fraction over the whole range of concentrations. The vapor composition data reported in this work were determined with the calibration curve. 2.3. Experimental Procedure. At first, the sapphire cell and all pipelines were evacuated at ordinary temperature. Then the system was filled with a certain amount of C3H8 and re-evacuated three times to guarantee the removal of all residual gases. Then a

refrigerant cycles (MRC) for gas liquefaction systems. Schneider23 had reviewed and discussed their previous systematic data24 at extremely high pressure with a thermodynamic and phase-theoretical point of view for the selected binary families of a fluorinated component (such as CF4, CHF3, and SF6) + a hydrocarbon (such as CH4, C2H6, and C3H8). Schneider23 showed that, at a high-pressure supercritical condition, the binary system of CF4 + C3H8 can have liquid−liquid equilibrium (LLE). However, the vapor−liquid−liquid equilibrium (VLLE) may not exist at a cryogenic and moderate pressure condition. This argumentation has been confirmed in the present study. In this work, the VLE data for CF4 + C3H8 system in a temperature range of (142.96 to 293.23) K were measured with a high-precision cryogenic visualization equilibrium instrument, which contains a high-pressure sapphire cell in a well-controlled cryogenic air bath and a chromatogram system for vapor composition analysis. The experimental data were correlated with the Peng−Robinson equation of state and the van der Waals two-parameters mixing rule, and the results were discussed.

2. EXPERIMENTAL SECTION 2.1. Chemicals. Chemicals of tetrafluoromethane (CF4) and propane (C3H8) were employed for VLE measurement. CF4 was supplied by Beijing LINGGAS Ltd. with a guaranteed mole fraction purity of 99.999 %, and C3H8 was provided by Shenzhen Shente Industrial Gases Co. Ltd. with a guaranteed mole fraction purity of 99.99 %. In both materials, no impurity was detected by gas chromatography, and they were used directly without further purification. 2.2. Apparatus. The apparatus has been reported in detail previously and already applied to get reliable data for nitrogen (N 2 ) + tetrafluoromethane (CF 4 ) system. 22 The same experimental setup of our previous work22 now is presented again in Figure 1 for one to see conveniently. “The setup is based on a vapor recirculation method. On the basis of the vapor recirculation method, the vapor phase was drawn out from the 3612

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Table 1. Experimental Data of Tetrafluoromethane (1) + Propane (2) System and Comparison with the Calculated Results Pa/kPa

a

yb

ycal

1.1 4.8 10.0

0.7118 0.9479 0.9715

0.7795 0.9723 0.9871

1.3 1.5 1.8 2.3 3.0 3.6 3.7

0.1169 0.206 0.2904 0.4628 0.5885 0.6581 0.6532

0.1075 0.2190 0.3052 0.4564 0.5835 0.6530 0.6624

7.3 10.7 14.3 16.0 27.5 41.3

0.1834 0.3755 0.5385 0.5795 0.736 0.8358

0.1940 0.3742 0.5317 0.5814 0.7564 0.8378

27.4 32.3 39.2 51.9 71.7 111.1

0.0998 0.2243 0.3692 0.5231 0.6501 0.7705

0.0875 0.2239 0.3595 0.5151 0.6478 0.7712

87.1 110.8 140.5 175.8 289.8

0.1765 0.3399 0.4722 0.577 0.7364

0.1806 0.3524 0.4862 0.5865 0.7438

186.1 220.8 278.6 305.5 431.4 657.5

0.0792 0.2225 0.3731 0.4298 0.5707 0.7102

0.0951 0.2315 0.3838 0.4351 0.5906 0.7204

408.2 448.3 507.2 614 691.4 884.5 934.5

0.1227 0.1896 0.2737 0.388 0.4522 0.5569 0.5733

0.1447 0.2151 0.2986 0.4096 0.4687 0.5712 0.5908

767.3 946.8 1193.7 1429.3 2006.2

0.1257 0.2676 0.3978 0.4798 0.5972

0.1541 0.2936 0.4174 0.4957 0.6082

961.1 1077.4 1268.9 1519.4 2044.8

0.0844 0.1607 0.2603 0.3491 0.4766

0.1089 0.1897 0.2909 0.3851 0.5067

Δ(ycal − y) T= 0.0677 0.0244 0.0156 T= −0.0094 0.0130 0.0148 −0.0064 −0.0050 −0.0051 0.0092 T= 0.0106 −0.0013 −0.0068 0.0019 0.0204 0.0020 T= −0.0123 −0.0004 −0.0097 −0.0080 −0.0023 0.0007 T= 0.0041 0.0125 0.0140 0.0095 0.0074 T= 0.0159 0.0090 0.0107 0.0053 0.0199 0.0102 T= 0.0220 0.0255 0.0249 0.0216 0.0165 0.0143 0.0175 T= 0.0284 0.0260 0.0196 0.0159 0.0110 T= 0.0245 0.0290 0.0306 0.0360 0.0301

Pa/kPa

yb

ycal

Δ(ycal − y)

142.96 ± 0.01 K 21.6 29.7 60.7 163.07 ± 0.01 K 5.8 12.8 22.7 51.3 102.5 150.8

0.9925 0.9971 0.9965

0.9944 0.9962 0.9988

0.0019 −0.0009 0.0023

0.7991 0.9001 0.9451 0.975 0.987 0.9911

0.7850 0.9031 0.9458 0.9766 0.9890 0.9931

−0.0141 0.0030 0.0007 0.0016 0.0020 0.0020

183.10 ± 0.01 K 82 132 313.6 505 669.4

0.9134 0.9479 0.977 0.9849 0.9878

0.9183 0.9493 0.9792 0.9884 0.9923

0.0049 0.0014 0.0022 0.0035 0.0045

203.26 ± 0.01 K 213.4 436.9 886.4 1219.5 1397.5 1475.5 223.17 ± 0.01 K 528.2 998.6 1492 1980.5

0.8777 0.9328 0.9655 0.9713 0.9743 0.9766

0.8790 0.9390 0.9688 0.9790 0.9850 0.9881

0.0013 0.0062 0.0033 0.0077 0.0107 0.0115

0.8467 0.9117 0.9337 0.9437

0.8532 0.9155 0.9384 0.9506

0.0065 0.0038 0.0047 0.0069

243.12 ± 0.01 K 1033.3 1654.9 2436.5 3581 3917.1

0.8025 0.8619 0.8912 0.9007 0.8977

0.8099 0.8670 0.8947 0.9026 0.9079

0.0074 0.0051 0.0035 0.0019 0.0102

263.15 ± 0.01 K 1240.9 2020.3 2825.8 3555.6 4373 4978.7

0.6655 0.7678 0.8107 0.8276 0.8287 0.8245

0.6761 0.7734 0.8126 0.8272 0.8280 0.8122

0.0106 0.0056 0.0019 −0.0004 −0.0007 −0.0123

283.01 ± 0.01 K 2765 4092.3 5071.8 6009.4

0.6749 0.7296 0.7351 0.6987

0.6802 0.7280 0.7288 0.6863

0.0053 −0.0016 −0.0063 −0.0124

293.23 ± 0.01 K 2517.4 3495.5 4683.5 5988.6

0.5504 0.6291 0.6711 0.6533

0.5708 0.6413 0.6712 0.6513

0.0204 0.0122 0.0001 −0.0020

P uncertainty is ± 200 Pa for P ≤ 1 MPa and is ± 1 kPa for P > 1 MPa. by uncertainty is ± 0.002 in mole fraction. 3613

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Table 2. Basic Thermodynamic Parameters of CF4 and C3H8 component

chemical formula

molecular weight

TC/K

PC/MPa

ω

tetrafluoromethane (1) propane (2)

CF4 C3H8

88.005 44.097

227.51 369.90

3.7500 4.2567

0.177 0.1524

predicted amount of C3H8 was filled into the system by an expected pressure. Meanwhile the air bath started to be chilled by the two-stage compression refrigeration system. When a setting temperature, which exceeds the dew point of C3H8, was reached, the second material, CF4 (the volatile substances), was added into the system slowly to a desired pressure. The vapor circulation and equilibrium test procedure is now quoted from our previous work22 here. “The substances in the system were circulated with the vapor circulation pump to make the two components mixed uniform. Then the air bath was further cooled down to the test temperature. When two phases (vapor and liquid) appeared in the sapphire cell (the vapor-liquid interface can be observed through the multilayer-glass observing window fitted on the wall of the air bath), the test system was kept at steady for an enough long time. When the equilibrium state was assumed to be reached (the temperature fluctuation of the sapphire cell and the air bath were within 0.01 K and 0.1 K, respectively, and the pressure fluctuation was less than 1 kPa), the data of temperature and pressure were recorded, and the vapor in the sapphire cell was sampled through the sampling valve and sent to the gas chromatograph for analyzing.” For the next composition test, which was kept at the same temperature, more amount of CF4 was added and the system was compressed to another pressure. Then the above procedures were repeated. After the different-composition tests at the same temperature were finished, we adjusted the system to another temperature and perform the equilibrium tests for the next setting temperature. For each equilibrium state, at least three samples of the vapor phase were withdrawn and analyzed by the GC, and the average value was used in this work. The vapor volume in the tested cell was about 60 mL and the volume of the sampling valve was only 5 μL. Thus, there were hardly any pressure drop during the sampling process and the sequent samplings had nearly no influence on the equilibrium of the system. The uncertainties of the three samples were within 0.8 ‰.

N

σ2 =

∑ (yi − yi ,cal )2 i=1

(1)

where N is the number of the experimental data points and yi and yi,cal are the ith experimental and calculated vapor mole fraction, respectively. The van der Waals mixing rule with two parameters, one for the attractive force parameter (a) and the other for the molar covolume parameter (b), was applied for this work, and a and b were calculated from eqs 2 and 3 N

a=

N

∑ ∑ xixj

aiaj (1 − kij) (2)

i=1 j=1 N

b=

N

∑ ∑ xixj i=1 j=1

1 (bi + bj)(1 − βij) 2

(3)

where kij and βij are the two adjustable interaction parameters, kij = kji and βij = βji and if i = j, kij = βij = 0. They are adjusted to fit the experimental data with the objective function in eq 1. When βij= 0, the van der Waals two-parameter mixing rule will be reduced to the ordinary one-parameter mixing rule. The van der Waals one-parameter mixing rule, which is simple and has been commonly applied to binary mixtures, was first used to correlate the experimental results. The experimental data and the correlation results at 293.23 K are shown in Figure 2. It can be

3. RESULTS AND DISCUSSION 3.1. Experimental Data. The isothermal experimental P, T, and y data of CF4 + C3H8 system were measured at nine temperatures (142.96, 163.07, 183.10, 203.26, 223.17, 243.12, 263.15, 283.01, and 293.23) K. The experimental results are listed in Table 1. 3.2. Data Correlation. The correlation was conducted by means of Peng−Robinson equation of state (PR EoS)25 and the van der Waals mixing rule with two interaction parameters,26 which were suitable for calculating the phase behavior of the nonpolar and even slightly polar mixtures. The basic parameters for each pure substance, such as the critical temperature (TC), critical pressure (PC), and acentric factor (ω), were attained from commercial software of Refprop 7.0,27 and they are listed in Table 2. The basic idea in this regression analysis is to minimize the deviation between the predicted and experimental data. In the correlation, the objective function for regression was

Figure 2. Vapor−liquid equilibrium of the CF4 + C3H8 system at 293.23 K.

seen that the deviations between the experimental and the calculated curve (the dash line) was obvious, particularly near to the critical area. The maximum difference between the experimental and the calculated data was about 0.05. To improve the correlations, modifications of the temperature-dependent function α(T) in the attractive term of the PR EoS had been mainly proposed by some existed literatures. Of the models containing component-dependent parameters, those of Nasrifar and Bolland28 have been extensively studied. The expressions are 3614

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Figure 3. Vapor−liquid equilibrium for CF4 + C3H8 system at different temperatures: ■, 293.23 K; ◆, 283.01 K; ●, 263.15 K; ▲, 243.12 K; ▼, 223.17 K; ★, 203.26 K; □, 183.10 K; ○, 163.07 K; ☆, 142.96 K; −, calculated with PR equation of state and the van der Waals two parameter mixing rule. (The right part figure is enlarged to show clearly those low-pressure test data and their correlations.)

⎧[1 + m(1 − T )]2 T ≤ 1 r r ⎪ α(T ) = ⎨ b1 b3 b2 ⎪ Tr > 1 ⎪T + T2 + T3 ⎩ r r r

expected to get satisfied results. The van der Waals two parameter mixing rule is much simpler than the “EoS + Gibbs free energy” model and easier to be applied for correlation of the experimental data to get the binary interaction parameters and for prediction equilibrium states in engineering. The PR EoS together with the van der Waals two-parameter mixing rule were employed for correlating VLE data in this work. The result calculated with the two-parameter mixing rule at 293.23 K is plotted as the solid line in Figure 2. It can be seen that the consistency the experimental data with calculated results is improved considerably. By taking the temperature dependent on the two interaction parameters into consideration, kij and βij were correlated with a linear function for the whole temperature range as follows:

(4)

By using this modification, considerably inaccuracies were also found in the critical region. The second improvement focuses on the modifications to van der Waals one parameter mixing rule by taking concentration effect into account. The concentrationindependent mixing rule proposed by Stryjek−Vera29 and Mathias−Klotz−Pransnitz30 were used and there was found no considerable improvement. By using van der Waals oneparameter mixing rule, the attention concentrates on the adjustment to the attractive parameter (a), and the adjustment for molar covolume (b) is not considered. However, for nonperfect fluids, excess volume for condensed phase may not be trivial, and the volumetric effect for mixture system may be not neglegirable, especially for the compressed vapor−liquid state and near to the critical region. For the data correlation, the intermolecular interactions are more significant in liquid phase rather than in vapor. However, for the present CF4 + C3H8 system, the experimental VLE data can not be fitted well without consideration of both attractive and covolume intermolecular interaction parameters, kij and βij, even for limited p−T−y data. In fact, the van der Waals two-parameter mixing rule can take into account of the intermolecular interactions not only for vapor phase but also for condensed liquid phase. Thus we may expect that if the data of the composition of liquid phase were available, the two-parameter mixing rule applied in this work may also show some effectiveness for full p−T−y−x data correlation. Among the modern approaches for description of mixture phase equilibrium as presented in the literature,4−9 the “EoS + Gibbs free energy” models, such as Huron−Vidal and Wong− Sandler mixing rules seem to be the most appropriate for modeling mixtures with highly polar components. The basic concept related to this type of models are to adjust both the attractive parameter a and the molar covolume b, where these two parameters are related to each other and the excess mixing energy may be modeled with a solution theory such as NRTL model. This type of mixing rules will affect both a and b parameters in EoS. As mentioned before, The van der Waals two parameter mixing rule also works for adjustment of the intermolecular interactions in both vapor and condensed liquid phases. Thus we proposed to use the van der Waals twoparameter mixing rule for correlation of the VLE data and

kij = −0.0756 + 5.9892 × 10−4T

(5)

βij = 0.0566 − 4.6583 × 10−4T

(6)

The correlations at different temperatures are shown in Figure 3 and Table 1. It can be seen that the test data show a good consistency with the calculated results and the deviations are rather small for all of the isotherms, even for those around the critical area. The overall mean deviation on vapor-phase mole fraction is 0.01, which was calculated as MDV =

1 N

N

∑ |yi − yi ,cal | i=1

(7)

For some higher temperature tests in this experiment, the critical temperature of CF4 was exceeded and the retrograde phenomena can be seen for some CF4-rich compositions, as shown in Figure 3. In all tested temperatures, there was no separation of liquid phases observed, and it is confirmed that no VLLE state exists in these cryogenic and moderate pressure conditions.

4. CONCLUSIONS The isothermal VLE data for tetrafluoromethane (CF4) + propane (C3H8) system at (142.96, 163.07, 183.10, 203.26, 223.17, 243.12, 263.15, 283.01, and 293.23) K were measured. The Peng−Robinson equation of state (PR EoS) with van der Waals one parameter mixing rule was first used and it was found inaccuracy for correlation of the VLE data around the critical region. To improve the prediction model, PR EoS and the van der Waals mixing rule with two interaction parameters were 3615

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employed. The basic concept related to the van der Waals twoparameter mixing rule is similar to those of the type “EoS + Gibbs free energy” model for mixtures with highly polar components. The van der Waals two-parameter mixing rule is much simpler than “EoS + Gibbs free energy” model but effective for correlation the experimental data. By applying the PR EoS and the van der Waals mixing rule with two temperature-dependent interaction parameters, we have got satisfied correlation results. The calculated and measured VLE data have shown a smaller overall mean deviation of 0.01 and a good consistency for all isotherms in the whole tested temperature range, even around the critical region.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86 20 39332893. Fax: +86 20 39332895. Funding

The authors are grateful for support from the National Natural Science Foundation of China (Grant No. 51076169), the Natural Science Foundation of Guangdong Province (Grant No. 9251027501000001), the Key Laboratory of LNG Cryogenic Technology, the Education Department of Guangdong Province, China (Program No. 39000-321101) and the SYSU-BP LNG Center (Program No. 99103-9390001). Notes

The authors declare no competing financial interest.

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REFERENCES

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dx.doi.org/10.1021/je300806e | J. Chem. Eng. Data 2012, 57, 3611−3616