Article pubs.acs.org/jced
Determination of the Critical Properties of C6−C10 n‑Alkanes and Their Binary Systems Using a Flow Apparatus Yang Liu, Ying Zhang, Mao-gang He,* and Nan Xin Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, P. R. China ABSTRACT: A flow apparatus was established to measure the critical properties of pure components and mixtures. The critical points are visually determined by observing the critical opalescence. The measurement can be carried out up to 10 MPa for pressure and 773 K for temperature. Critical temperatures (Tc) and critical pressures (pc) of pure compounds (hexane, heptane, octane, nonane, and decane) and their binary mixtures were measured. Experimental data for hexane + heptane, hexane + octane, hexane + decane, heptane + octane, and heptane +decane are available in the open literature and compare well with our data. On the other hand, the critical properties of hexane + nonane, heptane + nonane, octane + nonane, octane + decane, and nonane + decane systems were presented for the first time in this paper. All the experimental data are correlated by the Redlich− Kister equation.
1. INTRODUCTION Critical properties of pure substances and mixtures are important design and characterization parameters for both practical and theoretical research. These properties provide the boundary conditions for the supercritical region in which supercritical fluid extraction can be performed. The locus of critical points tells phase change boundaries for mixtures, which is also one of the bases for the binary phase diagrams proposed by Scott and van Konynenburg.1 In addition, critical properties would be commonly used in calculating pvT properties, transport properties, and the prediction of thermodynamic property based on the corresponding states principle. In order to improve the accuracy of prediction and extend the range of applicability of predictive equations of state, experimental data for critical points of mixtures are necessary. C6−C10 normal alkanes are the main components of fuel, which are widely used in power machines, for example, internal engine and aviation aircraft. They are also the fundamental materials in chemical engineering. The critical parameters of them and their mixtures are necessary to be known. The common experimental techniques for measuring critical parameters include sealed tube methods, open tube methods, flow methods, spontaneous boiling methods, and pvT methods.2 For most organic substances the visual method is usually the best technique to measure the critical temperature.3 The flow method4−9 is widely used to measure critical parameters of pure compounds and mixtures, for the critical temperature and critical pressure can be measured at the same time. In this work, a flow viewtype apparatus was built. The critical temperatures and critical pressures of five pure compounds: hexane, heptane, octane, nonane, and decane were measured and compared with literature databases. Moreover, the critical properties of the ten binary systems: hexane + heptane, hexane + octane, hexane + nonane, © 2014 American Chemical Society
hexane + decane, heptane + octane, heptane + nonane, heptane + decane, octane + nonane, octane + decane, and nonane + decane were also experimentally determined. The pure alkanes and their mixtures measured in this work are all thermally stable.
2. EXPERIMENTAL SECTION 2.1. Material. Compounds used in this work were purchased from commercial sources and used without any further purification. The purities and the suppliers of the compounds are listed in Table 1. Table 1. Suppliers and Purities of the Used Chemicals chemical hexane heptane octane nonane decane
purity > > > > >
99 99 99 99 99
% % % % %
supplier Tianjin Tianjin Tianjin Tianjin Tianjin
Guangfu Guangfu Guangfu Guangfu Guangfu
2.2. Measurement Method and Equipment. The low residence time flow method was used to measure the critical properties. The sample was pumped rapidly through a view cell at a temperature, pressure, and flow rate which results in critical opalescence and meniscus disappearance in the observation chamber of the cell. Thermal decomposition or reaction was minimized because the residence time of the fluid at high temperatures was kept low. Received: August 12, 2014 Accepted: October 1, 2014 Published: October 13, 2014 3852
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Table 2. Experimental Uncertainties in Critical Temperature, Critical Pressure, and Mole Fraction temp/K PRT, u1 temperature measurement circuit, u2 temperature control system, u3 measurement repeatability, urep combined uncertainty, uc pressure transducer, u1 pressure measurement circuit, u2 pressure control system, u3 measurement repeatability, urep combined uncertainty, uc
Figure 1. Experimental system of the low-residence time flow method. ST, sample tank; DP, dual piston pump; V, valve; VP, vacuum pump; PH, preheater; TC, thermocouple; PRT, platinum resistance thermometer; PT, pressure transducer; BV, back pressure valve.
The experimental apparatus established in this study is shown in Figure 1. The measurement can be carried out up to 10 MPa for pressure and 773 K for temperature. Compared to the conventional apparatus presented by Rosenthal and Teja,4 a novel experimental cell was developed as shown in Figure 2;
mol number of first component, u1 mol number of first component, u2 purity, uP combined uncertainty, uc
0.02 0.001 0.005 0.2 0.2 pressure/kPa 1.25 0.2 0.8 5 5.2 mol fraction < 0.0001 < 0.0001 0.006 0.006
and the system was evacuated by a vacuum pump. At the beginning of critical point measurement, the experimental cell temperature was set higher than the estimated critical temperature. The degassed sample was pumped into the system, entering the bottom of the tube and exiting through the top. As the sample was pumped through the system, it was seen to flash to vapor inside the tube. When the pressure increased, this effect was no longer visible. When the temperature was close to the critical point, the gas−liquid meniscus became faint and eventually vanished at the critical point. During this process, the critical opalescence could be observed. After the critical point was exceeded, the critical opalescence disappeared, and only one transparent phase was left. Then, the cell was cooled slowly. With the temperature decreased to the critical value, the critical opalescence reappeared; the color went from colorless to yellow, to red-yellow, and to black. Then the gas−liquid meniscus reappeared, and two phases formed. At the points the meniscus disappeared and reappeared, the system was assumed to reach the critical points. Care was taken to adjust the position of the meniscus. When the critical opalescence steadily appeared near the end of the PRT, the temperature measured by the PRT was assumed to be the critical temperature, and the pressure was noted as well. The critical point of the material was visually observed at three or four flow rates. For each measurement, the whole process was repeated at least three times, and the average values were taken as the experimental data. After every measurement, the system was purged with nitrogen. In the work, the binary mixtures were all measured over the whole range of concentration. 2.4. Assessment of Experimental Uncertainties. The expanded uncertainties in critical temperature and critical pressure can be given by10
Figure 2. Experimental cell. 1, sample inlet; 2, sample cell; 3, PRT; 4, heater; 5, sample outlet; 6, thermal insulation layer.
a quartz glass tube is adopted instead of the conventional sight glass, which is more effective for heating the sample uniformly. Moreover, a temperature sensor can be installed into the tube directly, and the front end of the temperature sensor will be in the critical phenomena region, which can improve the measuring accuracy of the critical temperature. The heaters were cast into the thermal insulation layer which was made of silica fiber particles, so the heating uniformity would be improved further. The instrument of the experimental system mainly included a temperature sensor (Fluke 5608-12 PRT, measurement uncertainty: ± 0.02 K), pressure transmitter (Rosemount 3051S; 0−10 MPa, accuracy: ± 0.025%), digital multimeter (Keithley 2002), dual piston pump (LabAlliance 1500, flow control: 0.001 mL/min), temperature controller (Shimaden FP23, PID: 0.1), and electronic balance (Mettler Toledo ME204, 0.1 mg). 2.3. Experimental Procedure. The critical properties for pure substances and binary mixtures were determined by visual observation. Before the measurement, the sample was degassed
U = kuc = k
∑ (ui)2
(1)
where ui is the uncertainty of each influencing factor, uc is the combined standard uncertainty composed by each uncertainty of influencing factor, and k is the confidence coefficient which is usually taken to be 2 or 3. When k = 2, the degree of confidence is 95%; when k = 3, the degree of confidence is 99%. In this study, the confidence coefficient of the compound uncertainty is taken to be 2. 3853
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Table 3. Experimental Critical Temperatures and Pressures for Pure Compounds this worka
a
DIPPR
NIST
compounds
Tc/K
pc/MPa
Tc/K
pc/MPa
hexane heptane octane nonane decane
507.79 540.14 568.92 594.52 617.73
3.033 2.736 2.496 2.278 2.106
507.60 540.20 568.90 594.60 617.70
3.025 2.740 2.490 2.290 2.110
Tc/K 507.60 540.00 568.90 595.00 617.80
pc/MPa
± ± ± ± ±
0.5 2.0 0.5 1.0 0.7
3.02 2.74 2.49 2.30 2.11
± ± ± ± ±
0.04 0.03 0.01 0.04 0.08
Standard uncertainties u(Tc) = ± 0.4 K, and u(pc) = ± 0.01 MPa.
Table 4. Critical Temperatures and Critical Pressures of Binary Systems: Hexane + Heptane, Hexane + Octane, and Heptane + Octanea this work x1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
b
Tc/K hexane+ heptane 537.41 534.58 531.71 528.64 525.61 522.15 518.62 515.02 511.43 hexane + octane 564.53 559.83 554.93 549.44 543.43 537.15 530.62 523.54 515.83 heptane + octane 566.40 563.89 561.32 558.61 555.71 552.80 549.81 546.74 543.49
Table 5. Critical Temperatures and Critical Pressures of Binary System: Hexane + Decanea this workb
literature 13 pc/MPa
x1
2.796 2.831 2.866 2.903 2.937 2.967 2.996 3.021 3.030
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
2.595 2.674 2.751 2.826 2.899 2.956 3.001 3.032 3.055
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
2.541 2.575 2.601 2.633 2.659 2.680 2.701 2.723 2.730
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Tc/K heptane + octane 537.45 534.65 531.65 528.55 525.45 522.05 518.55 514.95 511.35 hexane + octane 564.45 559.75 554.85 549.35 543.35 537.05 530.45 523.45 515.75 heptane + octane 566.35 563.85 561.25 558.55 555.65 552.75 549.75 546.65 543.45
pc/MPa 2.796 2.831 2.865 2.900 2.935 2.964 2.988 3.010 3.030
Tc/K
pc/MPa
x1
Tc/K
pc/MPa
609.60 602.16 594.63 585.60 576.74 565.61 553.57 539.52 524.75
2.306 2.470 2.636 2.801 2.945 3.052 3.157 3.185 3.170
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
609.55 602.05 594.35 585.45 576.25 565.45 553.25 539.25 524.35
2.306 2.472 2.635 2.798 2.944 3.067 3.152 3.190 3.164
Table 6. Critical Temperatures and Critical Pressures of Binary System: Heptane + Decanea
2.597 2.672 2.746 2.821 2.893 2.950 2.995 3.031 3.052
this workb
2.547 2.579 2.608 2.635 2.661 2.685 2.707 2.727 2.744
literature 9
x1
Tc/K
pc/MPa
x1
Tc/K
pc/MPa
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
613.27 606.10 600.97 594.71 587.76 579.15 571.84 562.80 552.11
2.225 2.310 2.395 2.476 2.581 2.664 2.736 2.764 2.782
0.1012 0.2037 0.2983 0.4091 0.4875 0.5599 0.6899 0.8070 0.8950
613.04 605.72 601.82 594.49 588.53 581.93 572.54 561.29 552.21
2.2184 2.3184 2.3800 2.4731 2.5511 2.6327 2.7108 2.7573 2.7538
a
x1 represent the mole fraction of heptane. bStandard uncertainties u(x)= ± 0.012, u(Tc)= ± 0.4 K, and u(pc)= ± 0.01 MPa.
uncertainties in critical temperature, critical pressure, and mole fraction in this work are estimated to be less than ± 0.4 K, ± 0.01 MPa, and ± 0.012, respectively as shown in Table 2.
x1 represent the mole fraction of the first component. bStandard uncertainties u(x) = ± 0.012, u(Tc) = ± 0.4 K, and u(pc) = ± 0.01 MPa.
3. RESULTS AND DISCUSSION To verify the reliability of the experimental system, the critical properties of pure hexane, heptane, octane, nonane, and decane were measured and compared with DIPPR11 and NIST12 databases. The comparison results are listed in Table 3. Our experimental data agree well with those in literature. The deviations between our data and DIPPR for temperatures and pressures are within ± 0.2 K and ± 0.012 MPa, respectively. All our data are in the range for the values of critical points which NIST database gives. The critical temperatures and critical pressures of hexane + heptane, hexane + octane, heptane + octane, hexane + decane, and heptane + decane binary mixtures were measured and compared with the experimental data in refs 9, 13, and 14 which
(2)
where n1 and n2 are the mole numbers of first and second component. The expanded uncertainty in mole fraction is given by ⎛ ∂x ⎞2 2 ⎛ ∂x ⎞2 2 Ux = kuc = k ⎜ ⎟ un + up 2 ⎟ un + ⎜ ⎝ ∂n2 ⎠ 2 ⎝ ∂n1 ⎠ 1
x1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
a x1 represent the mole fraction of hexane. bStandard uncertainties u(x)= ± 0.012, u(Tc)= ± 0.4 K, and u(pc)= ± 0.01 MPa.
a
The mole fraction x is calculated by n1 x= n1 + n2
literature 14
(3)
where un1 and un2 are the uncertainties of n1 and n2 and up is the uncertainty caused by chemical purity. The expanded 3854
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Table 7. Critical Temperatures and Critical Pressures of Binary Systems:a Hexane + Nonane, Heptane + Nonane, Octane + Nonane, Octane + Decane, and Nonane + Decaneb x1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Tc/K
pc/MPa
hexane + nonane 589.91 584.60 581.01 573.39 567.76 560.50 553.32 541.70 529.01 heptane + nonane 589.58 585.47 581.66 576.80 572.12 567.30 562.53 556.49 550.58 octane + nonane 592.47 590.09 587.55 584.73 581.92 579.81 577.55 574.37 572.21
x1
2.456 2.583 2.715 2.812 2.895 2.974 3.054 3.119 3.121
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
2.392 2.447 2.499 2.566 2.631 2.674 2.714 2.742 2.767
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Tc/K
pc/MPa
octane + decane 614.21 610.47 606.73 601.97 597.31 592.20 586.83 581.35 576.46 nonane + decane 615.70 613.66 611.84 609.39 607.11 605.32 603.48 600.81 597.91
2.185 2.247 2.304 2.349 2.396 2.430 2.471 2.510 2.507
Figure 3. Fractional deviations ΔTc = Tc(expt) − Tc(calc) of the experimental critical temperatures Tc(expt) of binary mixtures: hexane + heptane, hexane + octane, and heptane + octane from values Tc(calc) estimated from fitted equation. ●, This work, with error bars representing the expanded uncertainty; red circles, ref 13.
2.147 2.176 2.198 2.223 2.243 2.261 2.274 2.283 2.286
2.339 2.371 2.398 2.42 2.441 2.463 2.486 2.506 2.504
Figure 4. Fractional deviations Δpc = pc(expt) − pc(calc) of the experimental critical pressures pc(expt) of binary mixtures: hexane + heptane, hexane + octane, and heptane + octane from values pc(calc) estimated from fitted equation. ●, This work, with error bars representing the expanded uncertainty; red circles, ref 13.
Standard uncertainties u(x)= ± 0.012, u(Tc)= ± 0.4 K, and u(pc)= ± 0.01 MPa. bx1 represent the mole fraction of the first component. a
Table 8. Coefficients of Redlich−Kister Equations binary mixtures
c1/K
c2/K
c3/K
d1/ MPa
hexane + heptane hexane + octane hexane + nonane hexane + decane heptane + octane heptane + nonane heptane + decane octane + nonane octane + decane nonane + decane
6.195 20.620 66.170 54.856 4.868 19.279 33.810 1.810 15.401 4.986
−0.740 1.279 48.193 18.587 0.360 20.218 11.282 0.232 1.629 5.543
−2.397 0.372 36.479 −10.097 −0.063 14.760 7.429 7.033 6.483 6.101
0.203 0.519 0.958 1.475 0.164 0.451 0.617 0.217 0.369 0.201
d2/ MPa
d3/ MPa
0.043 0.203 0.336 0.838 0.009 0.126 0.453 −0.005 0.096 0.026
0.159 0.153 0.778 0.500 0.086 0.372 0.389 0.276 0.258 0.094
n
Tc = x1Tc,1 + x 2Tc,2 +
∑ cjx1x2(2x1 − 1) j ‐ 1 j=1 n
pc = x1pc,1 + x 2pc,2 +
∑ djx1x2(2x1 − 1) j ‐ 1 j=1
(4)
where Tc,i and pc,i are the critical temperature and pressure of the component i, n is set as 3 in the correlation, xi is the mole fraction of the component i, and cj and dj are the empirical constants and obtained with least-square method by minimizing the relative mean standard deviation (RMSD). For the binary mixtures, Tc or pc can be regarded as the sum of the ideal contribution (the first two terms of the equation) and the nonideal contribution. The coefficients for each binary mixture are given in Table 8, and the AAD and RMSD are shown in Table 9. The maximum average absolute deviations were 0.11 % for critical temperature and 0.28 % for critical pressure. The minimum correlation coefficients (R2) are 0.9993 for critical temperatures and 0.9975 for critical pressures. The critical temperatures and critical pressures obtained by this work are shown in Figure 3−8 as relative deviations from the values predicted from eq 4. Critical temperatures and
are shown in Tables 4, 5, and 6. The experimental critical temperatures and critical pressures of the five binary systems: hexane + nonane, heptane + nonane, octane + nonane, octane + decane, and nonane + decane were measured for the first time in this study, and the experimental data are shown in Table 7. The classical Redlich−Kister equation15 is a commonly used empirical model for the critical parameter correlation analysis.16,17 The experimental critical temperature and pressure data of each binary mixture were fitted by 3855
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Table 9. AAD, RMSD, and R2 of Redlich−Kister Equationsa temperature AAD/%
RMSD/K
R2
AAD/%
RMSD/MPa
R2
hexane + heptane hexane + octane hexane + nonane hexane + decane heptane + octane heptane + nonane heptane + decane octane + nonane octane + decane nonane + decane
0.007 0.014 0.112 0.033 0.006 0.069 0.066 0.028 0.047 0.022
0.04 0.07 0.66 0.19 0.03 0.43 0.43 0.18 0.31 0.15
0.9999 0.9999 0.9994 0.9999 0.9999 0.9993 0.9997 0.9995 0.9996 0.9995
0.075 0.115 0.282 0.227 0.069 0.278 0.265 0.074 0.141 0.044
0.002 0.003 0.007 0.006 0.002 0.007 0.007 0.002 0.004 0.001
0.9993 0.9996 0.9992 0.9998 0.9994 0.9975 0.9991 0.9990 0.9992 0.9996
1 Note: AAD = N a
pressure
binary mixtures
N
∑ i=1
|uij ,cal − uij ,exp| uij ,exp
⎡1 , RMSD = ⎢ ⎢⎣ N
⎤0.5
2⎥
∑ (uij ,exp − uij ,cal) i
⎥⎦
uij is critical temperature or critical pressure.
Figure 7. Fractional deviations ΔTc = Tc(expt) − Tc(calc) of the experimental critical temperatures Tc(expt) of binary mixtures: hexane + nonane, heptane + nonane, octane + nonane, octane + decane, and nonane + decane from values Tc(calc) estimated from fitted equation. Colored points, experimental points by this work, with error bars representing the expanded uncertainty.
Figure 5. Fractional deviations ΔTc = Tc(expt) − Tc(calc) of the experimental critical temperatures Tc(expt) of binary mixtures: hexane + decane and heptane + decane from values Tc(calc) estimated from fitted equation. ●, This work, with error bars representing the expanded uncertainty; blue square, ref 9; red triangle, ref 14.
Figure 6. Fractional deviations Δpc = pc(expt) − pc(calc) of the experimental critical pressures pc(expt) of binary mixtures: hexane + decane and heptane + decane from values pc(calc) estimated from fitted equation. ●, This work, with error bars representing the expanded uncertainty; blue square, ref 9; red triangle, ref 14.
Figure 8. Fractional deviations Δpc = pc(expt) − pc(calc) of the experimental critical pressures pc(expt) of binary mixtures: hexane + nonane, heptane + nonane, octane + nonane, octane + decane, and nonane + decane from values pc(calc) estimated from fitted equation. Colored points, experimental points by this work, with error bars representing the expanded uncertainty.
critical pressures obtained from refs 9, 13, and 14, are also shown in Figures 3−6. All the deviations of critical temperatures are between ± 0.25 %, and all the deviations of critical
pressures are between ± 1 %, include the values obtained from refs 9, 13, and 14. 3856
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(12) Mallard, W. G.; Linstrom, P. J. NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology: Gaithersburg, MD, 2005. (13) Kay, W. B.; Hissong, D. W. The critical properties of hydrocarbons I. Simple mixtures. Proc. Am. Pet. Inst., Div. Refin 1967, 47, 653−722. (14) Pak, S. C.; Kay, W. B. The Critical Properties of Binary Hydrocarbon Systems. Ind. Eng. Chem. Fundam. 1972, 11, 255−267. (15) Redlich, O.; Kister, A. T. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 1948, 40, 345−348. (16) Han, K. W.; Xia, S. Q.; Ma, P. S.; Yan, F. Y.; Liu, T. Measurement of critical temperatures and critical pressures for binary mixtures of methyl tert-butyl ether (MTBE) plus alcohol and MTBE plus alkane. J. Chem. Thermodyn. 2013, 62, 111−117. (17) Soo, C. B.; Théveneau, P.; Coquelet, C.; Ramjugernath, D.; Richon, D. Determination of critical properties of pure and multicomponent mixtures using a “dynamic−synthetic” apparatus. J. Supercrit. Fluids 2010, 55, 545−553.
4. CONCLUSION As presented in this work, our new apparatus is capable of measuring the critical properties of pure and multicomponent systems. The capacity of the apparatus was studied for the measurement of critical points of pure n-alkanes (hexane, heptane, octane, nonane, and decane) and critical properties of their binary mixtures. The experimental results of the systems (hexane + heptane, hexane + octane, heptane + octane, hexane + decane, and heptane + decane) show good agreement with the literature data. The experimental critical temperatures and critical pressures of the five binary systems, hexane + nonane, heptane + nonane, octane + nonane, octane + decane, and nonane + decane, were measured for the first time. All the experimental values were correlated by the classical Redlich−Kister equation. The maximum average absolute deviations were 0.11 % for critical temperature and 0.28 % for critical pressure.
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AUTHOR INFORMATION
Corresponding Author
*Tel: +86-29-8266-3863. Fax: +86-29-8266-8789. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (NSFC No. 51106129) and the Fundamental Research Funds for the Central University (No. XJTU-HRT-002).
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REFERENCES
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