A static analytical apparatus for vapour pressures and (vapour + liquid) phase equilibrium measurements with an internal stirrer and view windows

J. Chem. Thermodynamics xxx (2014) xxx–xxx

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A static analytical apparatus for vapour pressures and (vapour + liquid) phase equilibrium measurements with an internal stirrer and view windows Hao Guo a,b, Maoqiong Gong a,⇑, Xueqiang Dong a, Jianfeng Wu a,⇑ a b

Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, P.O. Box 2711, Beijing 100190, China University of Chinese Academy of Sciences, Beijing 100039, China

a r t i c l e

i n f o

Article history: Received 10 January 2014 Received in revised form 13 March 2014 Accepted 13 March 2014 Available online xxxx Keywords: Static analytical apparatus Saturated vapour pressures (Vapour + liquid) equilibrium Isobutane 1,1,1,3,3-Pentafluoropropane

a b s t r a c t A new static analytical apparatus for reliable vapour pressures and (vapour + liquid) equilibrium data of small-scale cell (150 mL) with internal stirrer and view windows was designed. In this work, the compositions of the phases were analyzed by a gas chromatograph connected on-line with TCD detectors. The operating pressure ranges from (0 to 3000) kPa, and the operating temperature range from (293 to 400) K. Phase equilibrium data for previously reported systems were first measured to test the credibility of the newly developed apparatus. The test included vapour pressure of 1,1,1,3,3-pentafluoropropane (R245fa) and isobutane (R600a), VLE of the (R600a + R245fa) system from T = (293.150 to 343.880) K. The measured VLE data are regressed with thermodynamic models using Peng–Robinson EoS with two different models, viz. the van der Waals mixing rule, and the Huron–Vidal mixing rule utilising the non-random two-liquid activity coefficient model. Thermodynamic consistency testing is also performed for the newly measured experimental data. Ó 2014 Published by Elsevier Ltd.

1. Introduction Organic-fluid mixtures have received increasing attention as working media for refrigeration, heat pump and power generation cycles due to their potential for environment-friendly and their favourable characteristics for improving system performance [1–3]. Phase equilibrium data are of great importance in calculation of thermodynamics properties and optimization of thermodynamics cycles. The objective of this paper is to provide a new static analytical apparatus with internal stirrer and view windows for reliable vapour pressures and (vapour + liquid) equilibrium data of pure and mixed organic fluids above room temperature. The (R600a + R245fa) system was selected to test the credibility of the apparatus. The data of the saturated vapour pressures were correlated by a Wagner type equation [4], and the VLE data were correlated with thermodynamic models using Peng–Robinson EoS (PR EoS) [5] with two different models, namely the van der Waals (vDW) mixing rule [6], and the Huron–Vidal (HV) mixing rule [7] utilising the non-random two-liquid (NRTL) activity ⇑ Corresponding authors. Tel./fax: +86 10 82543728 (M. Gong). Tel./fax: +86 10 62627843 (J. Wu). E-mail addresses: [email protected] (M. Gong), [email protected] (J. Wu).

coefficient model [8]. To the best of our knowledge, the experimental data of (R600a + R245fa) system is reported by Sbobb et al. [9]. The detailed comparisons will be presented in the following sections. 2. Experiment description and theoretical models 2.1. Equilibrium apparatus The apparatus designed in this paper is based on the staticanalytic method with an internal stirrer and view windows which allows for the analysis of vapour pressure and (vapour + liquid) phase at equilibrium. A schematic of the apparatus is shown in figure 1. 2.1.1. Equilibrium cell The equilibrium cell consists of the cell assembly and an internal stirrer. The cell was made of stainless steel with the volume of 150 mL and enclosed with two Si–Al glasses each held by two mobile flanges. There are two other flanges and a charging port on the cell wall. The upper flange is used to hold the internal stirrer. The lower flange containing four different diameters holes restricts different diameters capillaries to enter into the equilibrium cell for sampling (one vapour-phase capillary at the top of

http://dx.doi.org/10.1016/j.jct.2014.03.014 0021-9614/Ó 2014 Published by Elsevier Ltd.

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H. Guo et al. / J. Chem. Thermodynamics xxx (2014) xxx–xxx

16 3

column and analyzed. This sampling method provides a tiny dead volume neglected comparing the volume of the cell to avoid the influence to the equilibrium state in the cell. Since the sample system is isolated, there was no change in interior conditions for the sample.

4 67

5

1 9 15 14 13 10 11

2

8

12 FIGURE 1. A schematic of the experimental apparatus. 1. Feed system; 2. Digital controller; 3. Digital controller; 4. Temperature and pressure indicator; 5. GC; 6,7. Motors; 8. Vacuum pump; 9. Vacuum vessel; 10. Cooling coil; 11. isothermal liquid bath; 12. Electric heater; 13. Equilibrium cell; 14. Stirrers; 15. Pressure transducer; 16. N2-filled system.

the cell and three liquid-phase capillaries at different elevation with 0.35 mm inner diameter in the cell) and pressure measurement lines with 0.5 mm inner diameters. The internal stirrer contains an axis with many blades and two ceramic bearings, which is controlled by a speed controller. 2.1.2. Isothermal environment for the equilibrium cell In this apparatus, the equilibrium cell is immersed into the isothermal liquid bath. Silicone oil is used as the heating medium in the liquid bath for high temperatures. In order to decrease heat leaks, the equilibrium cell is fixed a suitable position within the oil bath that about 50 mm of the oil is above the upper of the equilibrium cell. To overcome the heat losses at high temperatures, a vacuum environment and thermal insulation materials surround thermostatic bath. A 100 X standard platinum resistance thermometer is inserted into the bath to monitor temperatures of the bath. A 25 X standard platinum resistance thermometer is used to measure the temperatures of the equilibrium cell and inserted into the cell with a 316 stainless steel casing. The oil bath temperature is controlled by adjusting the heat loads of cooling water and an electric heater using Shimaden SR 253 digital controllers. A stirrer with a speed controller is located in the liquid bath to obtain uniform temperature distributions. 2.1.3. Sampling method The accurate sampling for vapour and liquid phase is achieved using a six-port-automatic-sample-injection (SPASI) valve equipped with the GC in which the sample is loaded through four stainless steel capillaries with the same 0.35 mm internal diameters and fine needle valves in the front of SPASI valve. The capillaries lied in different height for vapour and liquid sampling are welded in the flanges of thermostat bath and vacuum vessel, and the parts exposed in environment are held a temperature close to oil bath temperature maintained by electric heat bands. The needle valves from Swagelok are turned off when no sampling is taken. Figure 2 shows a schematic flow diagram of the SPASI value. In the pushing mode, the sample quantitative loop is loaded through the capillaries. In the sample mode, rotation of the rotor 60°, the sample in the loop is injected in the chromatographic

2.1.4. Pressure, temperature and composition measurements The pressure measurement system includes a digital pressure transducer (Mensor CPT6001) and a sensitive diaphragm pressure transducer (GE DRUCK). The accuracy of digital pressure transducer is 0.01% FS over the ranges of (0 to 1.5) MPa and (0 to 3) MPa. The diaphragm pressure transducer separates the sample from an N2-filled system with the digital pressure transducer. The accuracy of the transducer is 0.04% FS with the pressure difference adjustable range of (0 to 40) kPa and the temperature range is (233 to 400) K. The combined uncertainty of pressure measurement is estimated to be within ±500 Pa. A 25 X standard platinum resistance thermometer (calibrated by the Cryogenic Metrology Station of the Chinese Academy of Sciences based on the 1990 International Temperature Scale (ITS 90)) is used for temperature measurements (with a uncertainty of ±5 mK (k = 2)). The temperature values are logged using the FLUKE 1594A data acquisition unit. The total uncertainty of the temperature measurement is estimated to within ±5 mK. The compositions of the phase in equilibrium cell are analyzed by a Shimadzu GC2014 gas chromatograph equipped with a thermal conductivity detector (TCD). The GC must be calibrated with mixtures of known composition obtained gravimetrically before the VLE data are measured. The uncertainties of vapour and liquid mole fractions measurements are estimated to be less than ±0.005. 2.2. Experimental procedure The experimental system is evacuated using an oil vacuum pump. Then a certain amount of the less volatile component is introduced into the cell. In the experimental process, the temperature controller is set to the desired temperature and the internal stirrer is started. When the temperature in the cell reaches the desired value for at least 1 h and the fluctuation in the cell is less than ±3 mK for at least 10 min, the equilibrium state is considered to be achieved. Then the saturated vapour pressures of the first component can be obtained. Then the appropriate more volatile component is then forced into the cell. Once equilibrium is established, samples of the the vapour and liquid phases are taken. The sixway automatic sampling valve could be used to clean the capillary and sample quantitatively. The vapour and liquid mole fractions at the equilibrium state are measured by the on-line gas chromatograph. At least 3 samples leading to a repeatable mole fraction within 0.2% are taken. VLE data for other compositions are measured by introducing an adequate amount of the more volatile component step by step. At last, the cell is evacuated and the saturated vapour pressures of the more volatile pure component are measured. 2.3. Theoretical models 2.3.1. Statured vapour pressures The experimental data of statured vapour pressures were correlated by a Wagner type equation [4]. The Wagner type equation is given by the expression:

ln

p Tc ¼ ða0 s þ a1 s1:5 þ a2 s2:5 þ a3 s5 Þ; pc T

s¼1

T ; Tc

Please cite this article in press as: H. Guo et al., J. Chem. Thermodyn. (2014), http://dx.doi.org/10.1016/j.jct.2014.03.014

ð1Þ

ð2Þ

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H. Guo et al. / J. Chem. Thermodynamics xxx (2014) xxx–xxx

(a) Chromatographic column

(b) Chromatographic column Helium

Rotor

Rotor

Stator

Stator

Equilibrium cell

Sample quantitative loop

Sample quantitative loop

Helium

Equilibrium cell

FIGURE 2. A schematic diagram of six-port-automatic-sample-injection valve: (a) pushing mode; (b) sample mode.

where p is the pressure, pc is the critical pressure, Tc is the critical temperature, T is the temperature, and a0, a1, a2 and a3 are constants of the Wagner equation.

The HV mixing rule [7] is given by the following expression:

"

# X aii  g E 1 ;  a¼b xi bii C i X

ð12Þ

2.3.2. (Vapour + liquid) phase equilibrium data correlations The measured VLE data were regressed with thermodynamic models using Peng–Robinson (PR) EoS [5] with two different models, the van der Waals (vDW) mixing rule [6], and the Huron–Vidal (HV) mixing rule [7] utilising the non-random two-liquid (NRTL) [8] activity coefficient model (PR-vDW and PR-HV-NRTL mode). The PR EoS [5] is expressed as follows:

where g E1 is the excess Gibbs free energy at infinite pressure, C is a numerical constant equal to 0.623225 for the PR EoS. The NRTL activity coefficient model [8] is applied to calculate the excess Gibbs free energy by means of the following form:

RT aðTÞ p¼  v  b v ðv þ bÞ þ bðv  bÞ

P g E1 X j sji Gji xj ¼ xi P RT l Gli xl i

ð3Þ

with

R2 T 2c

aðTÞ

pc

ð4Þ

;

RT c b ¼ 0:077796 ; pc

ð5Þ

h

i2

aðTÞ ¼ 1 þ ð0:37464 þ 1:54226x  0:26992x2 Þð1  T 0:5 r Þ ; T ; Tc

ð6Þ ð7Þ

where p is the pressure, R is the gas constant (R = 8.314 J  K–1  mol1), T is the temperature, v is the molar volume, a is a function of temperature, b is a constant, x is the acentric factor, Tc is the critical temperature, pc is the critical pressure. The vDW mixing rule [6] is expressed:

a¼

XX xi xj aij ; i

b¼

xi bii ;

ð13Þ

i

ð14Þ

with

aðTÞ ¼ 0:457235

Tr ¼

b¼

ð8Þ

j

X xi b i

ð9Þ

i

with

aij ¼ ð1  kij Þðai aj Þ1=2 ;

ð10Þ

where kii = 0, kij (=kji ) is the binary interaction parameter and the following temperature dependence of the parameters is used: vdW

kij ¼ aVdw þ bij ij

Tþ

cvdW ij T

:

ð11Þ

sij ¼

Aij ; T

ð15Þ

Gji ¼ expðaji sji Þ;

ð16Þ

aji ¼ aij ;

ð17Þ

where sii = 0, aii = 0, and aji , sij and sji are the binary interaction parameters that are temperature dependent as the following expression: NRTL

sij ¼ aNRTL þ ij

bij T

þ

cNRTL ij T2

;

ð18Þ

In this paper, aij = 0.3. The minimization of the sum of the absolute relative deviation between the calculated and experimental pressures is used as the objective function to correlate the experimental data:

F¼

! N X jpexp  pcal j ; pexp i¼1

ð19Þ

where N is the number of the experiment points measured, pexp and pcal refers to the pressures from experiment and calculation, respectively. In this work, thermodynamic consistency testing using the point test of Van Ness et al. [10] was performed for the measured VLE data. The proposed standard of thermodynamic consistent is that the average absolute deviation (AAD) of vapour composition should be less than 0.01 for the point test:

! N jyi exp  yical j 1X : AAD y ¼ N i¼1 yi exp

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H. Guo et al. / J. Chem. Thermodynamics xxx (2014) xxx–xxx

TABLE 1 Mole fraction purity, critical parameters (Tc pc) and acentric factors x for R245fa and R600a [11]. Fluids

CAS No.

Mole fraction purity

Tc (K)

pc (MPa)

x

R245fa R600a

460-73-1 75-28-5

0.990 0.999

427.16 407.81

3.651 3.629

0.3776 0.184

TABLE 4 Constants of the Wagner equation (a0, a1, a2 and a3) for R600a and R245fa. Fluids

a0

a1

a2

a3

R600a R245fa

7.11604 7.12074

2.334056 0.683257

3.30698 1.59636

2.345343 20.6733

The R245fa was supplied by Zhejiang Lantian Environmental and Chemical Engineering Co. Ltd with a declared mole fraction purity of 0.990. R600a was provided by Beijing AP BAIF Gases Industry Co. Ltd with a declared mole fraction purity of 0.999. Both of the materials were subjected to purity checks detected by gas chromatography using the thermal conductivity detector (TCD). It was verified that no significant impurities were found for all materials. Table 1 gives mole fraction purity, critical temperature Tc, critical pressure pc, and acentric factor x for R245fa and R600a [11].

0

100

1

-1

(pexp-pcal)/pexp

3. Materials

-2 -3 -4 -5 200

4. Results and discussion

240

280

320

360

400

T/K To verify reliability of the apparatus for statured vapour pressures and phase equilibrium data measurements and accuracy of the experimental procedure, vapour pressures data of pure R245fa and R600a and VLE system of (R600a + R245fa) over the

temperature range from (293.150 to 343.880) K were measured using the apparatus.

TABLE 2 Experimental vapour pressures pexp for R600a.a

a

FIGURE 3. Relative deviations of the experimental vapour pressure data of R600a from equation (1): h, this work; e, Miyamoto [12]; s, Glos [13]; 4, Galicia–Luna [14]; ., Lim [15]; J, Kayukawa [16]; —, NIST REFPROP 9.0 [11].

T/K

pexp/MPa

T/K

pexp/MPa

T/K

pexp/MPa

293.584 293.582 295.580 297.581 299.590 301.611 303.616 305.630 307.642 309.650 311.661

0.3067 0.3067 0.3256 0.3452 0.3659 0.3876 0.4102 0.4339 0.4586 0.4842 0.5109

313.685 315.704 317.727 319.724 321.751 323.820 325.769 327.732 329.743 331.718 333.710

0.5387 0.5679 0.5981 0.6290 0.6617 0.6961 0.7309 0.7653 0.8027 0.8408 0.8805

335.742 337.793 339.845 341.752 343.782 345.859 347.859 349.905 351.906 353.911

0.9225 0.9662 1.0115 1.0545 1.1025 1.1531 1.2044 1.2563 1.3098 1.3651

u(T) = 0.005 K, u(p) = 500 Pa.

4.1. Statured vapour pressures The measured vapour pressures of pure R600a and R245fa in the temperature range from (293 to 353) K are presented in tables 2 and 3, respectively. Regressed values of the constants a0, a1, a2, and a3 in are shown in table 4. Figures 3 and 4 present the relative deviations of the available experimental and calculated vapour pressure data from equation (1) for R600a and R245fa. Figure 3 shows the data of Miyamoto [12] which shows good agreement with equation (1) to within 0.4% above T = 310 K. The data of Glos et al. [13] and NIST REFPROP 9.0 [11] agree well with equation (1) within 0.4% above 250 K.

7

TABLE 3 Experimental vapour pressures pexp for R245fa.a

a

6

T/K

pexp/MPa

T/K

pexp/MPa

295.076 295.570 296.570 297.570 298.572 298.574 298.576 298.577 299.608 300.612 300.614 301.618 302.627 303.638 304.645 305.652 306.664

0.1322 0.1347 0.1399 0.1452 0.1506 0.1507 0.1507 0.1507 0.1565 0.1624 0.1624 0.1684 0.1746 0.1810 0.1876 0.1943 0.2012

307.673 308.683 309.698 310.718 311.739 313.710 315.739 317.763 318.777 319.771 321.709 323.730 325.715 327.677 329.669 330.677

0.2083 0.2157 0.2233 0.2311 0.2391 0.2552 0.2726 0.2908 0.3003 0.3099 0.3291 0.3499 0.3716 0.3940 0.4179 0.4304

331.699 333.707 335.726 337.741 338.755 339.773 341.825 343.825 345.866 347.855 348.865 348.867 349.863 350.862 351.867 352.873

0.4434 0.4696 0.4971 0.5259 0.5408 0.5561 0.5879 0.6204 0.6546 0.6895 0.7076 0.7077 0.7259 0.7446 0.7638 0.7833

u(T) = 0.005 K, u(p) = 500 Pa.

5

100

pexp/MPa

(pexp-pcal)/pexp

T/K

4 3 2 1 0 -1 -2

250

300

350

400

T/K FIGURE 4. Relative deviations of the experimental vapour pressure data of R245fa from equation (1): h, this work; s, Pan [17]; 4, Wang [18]; J, Nicola [19]; e, Ahmar [20]; ", Sotani [21];—, NIST REFPROP 9.0 [11].

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H. Guo et al. / J. Chem. Thermodynamics xxx (2014) xxx–xxx

TABLE 5 Experimental and calculated vapour pressures (pexp and pcal), mole fractions of the liquid and vapour phases of R600a (x1exp, y1exp and y1cal), absolute deviations of pressures (Dp) and vapour compositions (Dy) between experimental and calculated data for the binary system of {R600a (1) + R245fa (2)}. Experimental data

a

Calculated data with PR-vDW model

Calculated data with PR-HV-NRTL model

pexp/MPa

x1exp

y1exp

pcal/MPa

y1cal

Dpb/MPa

Dyc

pcal/MPa

y1cal

Dpb/MPa

Dyc

0.1227 0.1535 0.2089 0.2487 0.3103 0.3277 0.3363 0.3383 0.3376 0.3346 0.3274 0.3022

0.000 0.022 0.079 0.130 0.353 0.486 0.669 0.758 0.808 0.875 0.927 1.000

0.000 0.207 0.443 0.540 0.662 0.687 0.739 0.767 0.790 0.822 0.874 1.000

0.1229 0.1534 0.2147 0.2525 0.3182 0.3277 0.3341 0.3354 0.3346 0.3303 0.3226 0.3007

0.0000 0.2035 0.4449 0.5402 0.6704 0.6948 0.7284 0.7566 0.7800 0.8254 0.8783 1.0000

T = 293.150 K 0.0002 0.0001 0.0058 0.0038 0.0079 0.0000 0.0022 0.0029 0.0030 0.0043 0.0048 0.0015

0.0000 0.0035 0.0019 0.0002 0.0084 0.0078 0.0106 0.0104 0.0100 0.0034 0.0043 0.0000

0.1229 0.1522 0.2102 0.2460 0.3144 0.3277 0.3367 0.3383 0.3376 0.3335 0.3256 0.3007

0.0000 0.2005 0.4367 0.5304 0.6671 0.6975 0.7349 0.7612 0.7821 0.8230 0.8727 1.0000

0.0002 0.0013 0.0013 0.0027 0.0041 0.0000 0.0004 0.0000 0.0000 0.0011 0.0018 0.0015

0.0000 0.0065 0.0063 0.0096 0.0051 0.0105 0.0041 0.0058 0.0079 0.0010 0.0013 0.0000

0.1779 0.2627 0.3281 0.4139 0.4390 0.4507 0.4512 0.4535 0.4521 0.4483 0.4374 0.4047

0.000 0.060 0.128 0.348 0.485 0.644 0.680 0.766 0.810 0.870 0.937 1.000

0.000 0.348 0.497 0.634 0.671 0.717 0.730 0.765 0.791 0.825 0.877 1.000

0.1773 0.2668 0.3347 0.4233 0.4390 0.4481 0.4494 0.4503 0.4488 0.4432 0.4289 0.4027

0.0000 0.3470 0.4958 0.6420 0.6752 0.7115 0.7221 0.7551 0.7784 0.8211 0.8924 1.0000

T = 303.150 K 0.0006 0.0041 0.0066 0.0094 0.0000 0.0026 0.0018 0.0032 0.0033 0.0051 0.0085 0.0020

0.0000 0.0010 0.0012 0.0080 0.0042 0.0055 0.0079 0.0099 0.0126 0.0039 0.0154 0.0000

0.1773 0.2627 0.3268 0.4178 0.4383 0.4507 0.4523 0.4536 0.4523 0.4468 0.4320 0.4027

0.0000 0.3416 0.4869 0.6374 0.6761 0.7163 0.7270 0.7585 0.7801 0.8195 0.8878 1.0000

0.0006 0.0000 0.0013 0.0039 0.0007 0.0000 0.0011 0.0001 0.0002 0.0015 0.0054 0.0020

0.0000 0.0064 0.0101 0.0034 0.0051 0.0007 0.0030 0.0065 0.0109 0.0055 0.0108 0.0000

0.2503 0.4257 0.5409 0.5761 0.5937 0.5955 0.5933 0.5876 0.5729 0.5316

0.000 0.125 0.335 0.463 0.652 0.767 0.813 0.870 0.929 1.000

0.000 0.451 0.614 0.645 0.705 0.762 0.792 0.822 0.887 1.000

0.2491 0.4377 0.5531 0.5761 0.5921 0.5938 0.5911 0.5832 0.5666 0.5288

0.0000 0.4536 0.6115 0.6508 0.7035 0.7509 0.7775 0.8206 0.8831 1.0000

T = 313.150 K 0.0012 0.0120 0.0122 0.0000 0.0016 0.0017 0.0022 0.0044 0.0063 0.0028

0.0000 0.0026 0.0025 0.0058 0.0015 0.0111 0.0145 0.0014 0.0039 0.0000

0.2491 0.4257 0.5427 0.5720 0.5937 0.5964 0.5939 0.5861 0.5694 0.5288

0.0000 0.4434 0.6047 0.6495 0.7078 0.7547 0.7799 0.8204 0.8803 1.0000

0.0012 0.0000 0.0018 0.0041 0.0000 0.0009 0.0006 0.0015 0.0035 0.0028

0.0000 0.0076 0.0093 0.0045 0.0028 0.0073 0.0121 0.0016 0.0067 0.0000

0.3440 0.4113 0.5422 0.6952 0.7440 0.7663 0.7684 0.7647 0.7563 0.7366 0.6856

0.000 0.032 0.120 0.345 0.470 0.651 0.766 0.825 0.870 0.931 1.000

0.000 0.165 0.386 0.596 0.633 0.692 0.760 0.789 0.822 0.887 1.000

0.3416 0.4136 0.5582 0.7142 0.7441 0.7651 0.7667 0.7610 0.7517 0.7291 0.6824

0.0000 0.1762 0.4072 0.5888 0.6338 0.6948 0.7481 0.7859 0.8225 0.8884 1.0000

T = 323.150 K 0.0024 0.0023 0.0160 0.0190 0.0001 0.0012 0.0017 0.0037 0.0046 0.0075 0.0032

0.0000 0.0112 0.0212 0.0072 0.0008 0.0028 0.0119 0.0031 0.0005 0.0014 0.0000

0.3416 0.4086 0.5422 0.7010 0.7390 0.7673 0.7702 0.7647 0.7554 0.7323 0.6824

0.0000 0.1722 0.3971 0.5824 0.6327 0.6987 0.7515 0.7876 0.8223 0.8858 1.0000

0.0024 0.0027 0.0000 0.0058 0.0050 0.0010 0.0018 0.0000 0.0009 0.0043 0.0032

0.0000 0.0072 0.0111 0.0136 0.0003 0.0067 0.0085 0.0014 0.0003 0.0012 0.0000

0.6210 0.8740 1.1201 1.2043 1.2422 1.2422 1.2342 1.2174 1.1841 1.1051

0.000 0.105 0.341 0.511 0.649 0.766 0.817 0.873 0.935 1.000

0.000 0.307 0.532 0.604 0.687 0.759 0.786 0.827 0.887 1.000

0.6167 0.8741 1.1377 1.2057 1.2310 1.2320 1.2236 1.2050 1.1684 1.1040

0.0000 0.3060 0.5322 0.6153 0.6805 0.7482 0.7850 0.8336 0.9021 1.0000

T = 343.880 K 0.0043 0.0001 0.0176 0.0014 0.0112 0.0102 0.0106 0.0124 0.0157 0.0011

0.0000 0.0010 0.0002 0.0113 0.0065 0.0108 0.0010 0.0066 0.0151 0.0000

0.6167 0.8536 1.1201 1.2062 1.2400 1.2425 1.2334 1.2134 1.1741 1.1040

0.0000 0.3003 0.5267 0.6146 0.6824 0.7496 0.7851 0.8320 0.8990 1.0000

0.0043 0.0204 0.0000 0.0019 0.0022 0.0003 0.0008 0.0040 0.0100 0.0011

0.0000 0.0067 0.0053 0.0106 0.0046 0.0094 0.0009 0.0050 0.0120 0.0000

Standard uncertainties u are u(x) = u(y) = 0.005, u(T) = 0.005 K and u(p) = 500 Pa. Declared mole fraction purities: R600a (0.999), R245fa (0.990). Dp ¼ pexp  pcal . Dy ¼ y1exp  y1cal .

b c

However, the deviations increase rapidly below 250 K. The data of Galicia–Luna [14] and Lim [15] and Kayukawa [16] show relative deviations within 1% at temperatures from (273.15 to 406.97) K. Figure 4 shows that the data of Pan et al. [17], Wang [18], Nicolar

[19] and NIST REFPROP 9.0 [11] agree well with equation (1) within 0.5% within the temperature range from (280.000 to 383.000) K and within 1% above 383.000 K. However, the relative deviations increase rapidly below 280 K. The data of Ahmar et al. [20] exhibit

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H. Guo et al. / J. Chem. Thermodynamics xxx (2014) xxx–xxx

1.2

2.5

1.0

1.5

(a)

2.0

(pexp-pcal)/pexp× 100

p /MPa

6

0.8 0.6 0.4

1.0 0.5 0.0 -0.5 -1.0 -1.5

0.2

0.0

0.0

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

1.0

x1

1.0

x1,y1

0.015

FIGURE 5. VLE data for {R600a (1) + R245fa (2)} system at different temperatures: 293.150 K (j,h); 303.150 K (d,s); 313.150 K (N,4); 323.150 K (.,5); 343.880 K (,}); (. . .) calculated by PR-vDW model; (—), calculated by PR-HV-NRTL model.

(b)

0.010

2

y1exp-y1cal

0.005

(a)

(pexp-pcal)/pexp× 100

1

-0.005 -0.010

0

-0.015 0.0

-1

0.2

0.4

-2 -3 0.0

0.2

0.4

0.6

0.8

1.0

x1 0.020 0.015

(b)

0.010 0.005

y1exp-y1cal

0.000

0.000 -0.005 -0.010 -0.015 -0.020 -0.025 0.0

0.2

0.4

0.6

0.8

1.0

x1 FIGURE 6. Deviations plot against mole fraction for the {R600a (1) + R245fa (2)} system using PR–vDWs model: (a) deviation of pressure and (b) deviation of vapour mole fraction: T = 293.150 K (h); 303.150 K (s); 313.150 K (4); 323.150 K (5); 343.880 K (}).

relative deviations less than 1% at temperatures from (353.37 to 413.54) K. The relative deviations of Sotani’s data [21] are 0.06% to 2.82 at temperatures from (293.25 to 426.12) K. 4.2. VLE measurements The experimental and correlated VLE data using the PR–vDW model and PR–HV–NRTL model of test system (R600a + R245fa)

x1

0.6

0.8

1.0

FIGURE 7. Deviations plot against mole fraction for the {R600a (1) + R245fa (2)} system using PR–HV–NRTL model: (a) deviation of pressure and (b) deviation of vapour mole fraction: T = 293.150 K (h); 303.150 K (s); 313.150 K (4); 323.150 K (5); 343.880 K (}).

are reported in table 5 and plotted in figure 5, respectively. Table 5 summarizes the experimental and calculated vapour pressures (pexp and pcal) of the system, the mole fraction of the liquid and vapour phases of R600a (x1exp and y1exp), the calculated mole fraction of the vapour phase (y1cal), the deviations of pressures (Dp) and vapour compositions (Dy) between the experimental and the calculated data. Figures 6 and 7 give the deviations of pressures and vapour compositions between the experimental and the calculated data using PR-vDW and PR-HV-NRTL model, respectively. The values of the adjustable parameters, the average absolute relative deviation of pressure (AARD p) and the average absolute deviation of vapour phase mole fraction (AAD y) of the systems using different models at each temperature are reported in table 6. As shown in table 6, all the measured VLE data stratify the point test. Table 6 shows that PR-HV-NRTL model gives a better representation of the experimental data than the PR-vdW model. The constants of temperature dependent model parameters in the vDW mixing rule and NRTL model, the average absolute relative deviation of pressure (AARD p) and the average absolute deviation of vapour phase mole fraction (AAD y) for the system are reported in table 7. It is demonstrated that the NRTL model with temperature dependence provides a more satisfactory correlation than the vdW model. The VLE data of (R600a + R245fa) system at temperatures (293.15 to 313.15) K were reported in the literature [9]. Figure 8 gives comparisons between the data in the literature and this work using the PR-HV-NRTL model at three temperatures. The data in

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7

H. Guo et al. / J. Chem. Thermodynamics xxx (2014) xxx–xxx

TABLE 6 Adjustable parameters (kij in vDW mixing rules, Aij and Aji in NRTL model), average absolute relative deviation of pressure (AARD p) and average absolute deviation of vapour phase mole fraction (AAD y) of different models for {R600a (1) + R245fa (2)} system. T/K

PR-vdW model

293.150 303.150 313.150 323.150 343.880 a b

PR-HV-NRTL model

kij

AARD p/%a

AAD yb

Aij/K

Aji/K

AARD p/%a

AAD yb

0.1537 0.1549 0.1569 0.1569 0.1525

0.98 1.01 0.88 0.89 0.73

0.0053 0.0058 0.0043 0.0055 0.0051

438.4077 423.6940 412.0319 407.6154 392.0703

307.7135 303.6975 296.9574 280.5330 246.0412

0.47 0.36 0.32 0.40 0.48

0.0061 0.0052 0.0052 0.0046 0.0054

P AARD p ¼ ð100=NÞ N i¼1 ððjpi exp  pical jÞ=pi exp Þ. P AAD y ¼ N ððjy i exp  yical jÞ=yi exp =NÞ. i¼1

TABLE 7 vdWs NRTL NRTL NRTL NRTL Constants of temperature dependant model parameters (avdWs , b12 and cvdWs of k12 in vDW mixing rule, aNRTL and cNRTL of s12 and s21 in NRTL model), 12 12 12 , b12 , c 12 , a21 , b21 21 average absolute relative deviation of pressure (AARD p) and average absolute deviation of vapour phase mole fraction (AAD y) for the {R600a (1) + R245fa (2)} system.

avdWs 12

vdWs

b12 0.0002504

0.00476

cvdWs 12

vDW model AARD p/%a AAD yb

25.39437

0.97

cNRTL 12

aNRTL 21

425942.3

7.79504

0.0054 NRTL model

aNRTL 12

NRTL

b12 1994.83

3.341995 a b

NRTL

b21 4849.815

cNRTL 21

AARD p/%a

AAD yb

661575.4

0.41

0.0053

P AARD p ¼ ð100=NÞ N i¼1 ððjpi exp  pical jÞ=pi exp Þ: P AAD y ¼ N ððjy  yical jÞ=yi exp =NÞ: i exp i¼1

0.60

respectively. The AAD y for the literature data is less than that of this work, while the AARD p is more than that of this work.

0.55 0.50

p /MPa

0.45

4.3. Azeotrope

0.40

The obvious azeotropic behaviour can be found at each temperature in figure 5. The pressure and composition at azeotropic point should meet the following relationship [22]:

0.35 0.30 0.25

dp ¼ 0: dx1

0.20 0.15 0.10 0.0

0.2

0.4

x1,y1

0.6

0.8

1.0

FIGURE 8. Comparisons between the data of reference and this work at T = (293.15, 303.15, and 313.15) K for the {R600a (1) + R245fa (2)} system: 293.150 K (j,h) [9]; 303.150 K (d,s) [9]; 313.150 K (N,4) [9]; (—), calculated by PR-HV-NRTL model.

TABLE 8 Azeotropic composition x1,az and pressure paz calculated with different models for the {R600a (1) + R245fa (2)} system at each temperature. T/K

293.150 303.150 313.150 323.150 343.880

PR–vDW model

PR–HV–NRTL model

x1,az

paz

x1,az

paz

0.754 0.745 0.734 0.726 0.715

0.3354 0.4505 0.5943 0.7676 1.2345

0.761 0.751 0.741 0.733 0.720

0.3383 0.4537 0.5967 0.7709 1.2449

this work show good agreement with the literature data. The AAD y and AARD p of the data in literature [9] were calculated using the PR-HV-NRTL model with the parameters in table 7. They are 0.0034% and 0.53% at temperatures of (293.15 to 313.15) K,

ð21Þ

Table 8 shows the characteristics of the azeotrope (pressure paz and composition x1,az) calculated using different models at each temperature. The data of paz and x1,az obtained using PR-HV-NRTL model are more than those gained using the PR-vDW model. The maximum absolute deviations of paz and x1,az are 0.0104 and 0.007, respectively.

5. Conclusions This paper presented the vapour pressure of 1,1,1,3,3-pentafluoropropane (R245fa) and isobutane (R600a), VLE of (R600a + R245fa) system from T = (293.150 to 343.880) K using a new apparatus based on the static-analytic method with an internal stirrer and view windows. The saturated vapour pressures data were correlated by a Wagner type equation and compared with NIST REFPROP 9.0 and literature data. The deviations showed that the experimental data show good agreement with literature within temperature range measured. The VLE data were regressed with the PR-vdW and PR-HV-NRTL models. The best results were obtained with the PR-HV-NRTL model. The VLE systems also show good thermodynamic consistency. Good agreement was also obtained for VLE data of the system between experimental and literature data. The azeotropic behaviour could be found for the system studied over the temperature ranges studied.

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H. Guo et al. / J. Chem. Thermodynamics xxx (2014) xxx–xxx

Acknowledgements This investigation has been financially supported by the National Basic Research Program of China under the contract number of 2010CB710701 and the National Natural Sciences Foundation of China under the contract number of 5110672. References [1] [2] [3] [4] [5] [6] [7] [8] [9]

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[11] E.W. Lemmon, M.L. Huber, M.O. Mclinden, Reference fluid thermodynamic and transport properties (REFPROP), NIST Standard Reference Database 2.3, Version 8.0, Physical and Chemical Properties Division, National Institute of Standards and Technology, Gaithersburg, MD, 2009. [12] H. Miyamoto, J. Takemura, M. Uematsu, J. Chem. Thermodyn. 36 (2004) 919– 923. [13] S. Glos, R. Kleinrahm, W. Wagner, J. Chem. Thermodyn. 36 (2004) 1037–1059. [14] L.A. Galicia-Luna, A. Ortega-Rodriguez, J. Chem. Eng. Data 45 (2000) 265–271. [15] J.S. Lim, Q.N. Ho, J.Y. Park, B.G. Lee, J. Chem. Eng. Data 49 (2004) 192–198. [16] Y. Kayukawa, M. Hasumoto, Y. Kano, K. Watanabe, J. Chem. Eng. Data 50 (2005) 556–564. [17] J. Pan, J.T. Wu, Z.G. Liu, J. Chem. Eng. Data 51 (2006) 186–189. [18] Z.W. Wang, Y.Y. Duan, J. Chem. Eng. Data 49 (2004) 1581–1585. [19] G.D. Nicola, J. Chem. Eng. Data 46 (2001) 1619–1622. [20] E.E. Ahmar, A. Valtz, P. Paricaud, et al., Int. J. Refrig. 35 (2012) 2297–2310. [21] T. Sotani, H. Kubota, Fluid Phase Equilib. 161 (1999) 325–335. [22] A. Bejan, Advanced Engineering Thermodynamics, second ed., John Wiley & Sons, New York, 1997.

JCT 14-36

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