Isobaric vapor∓liquid equilibrium for binary system

Fluid Phase Equilibria 382 (2014) 133–138

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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Isobaric vapor–liquid equilibrium for binary system of methyl myristate + methyl palmitate at 0.5, 1.0 and 1.4 kPa Ruru Chen a , Hui Ding b, *, Mingchao Liu a , Jinlong Qi a , Hang Zhou a , Ning Chen a a b

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China School of Environmental Science and Engineering, Tianjin University, Tianjin 300072, China

A R T I C L E I N F O

A B S T R A C T

Article history: Received 26 May 2014 Received in revised form 2 September 2014 Accepted 4 September 2014 Available online 8 September 2014

Isobaric vapor–liquid equilibrium (VLE) data for the binary system of methyl myristate + methyl palmitate at 0.5, 1.0 and 1.4 kPa were measured by a VLE modified Othmer still. The esters used in this paper are the major components of biodiesel. The experimental data in the vaccum conditions passed the Wisniak consistency test and point consistency test of Van Ness test, which ensure the reliability of experimental data. Furthermore, these VLE data were correlated with Nonrandom two-liquid (NRTL) activity coefficient model and Wilson model, and predicted by UNIFAC and Dortmund (modified UNIFAC) models. The results indicate that the calculated values of these four models agree well with the experimental data. ã 2014 Elsevier B.V. All rights reserved.

Keywords: Vapor–liquid equilibrium Methyl myristate Methyl palmitate NRTL model UNIFAC model Dortmund (modified UNIFAC) model

1. Introduction Biodiesel, which consists of a blend of fatty acid methyl or ethyl esters, has become more attractive recently. Made from an increasingly diverse mix of resources including agricultural oils, recycled cooking oil, soybean oil and animal fats, it is a renewable, clean-burning diesel replacement that is sustainable and improving our environment [1,2]. Several processes for biodiesel fuel production have been developed, among which transesterification has been the most common method used to produce biodiesel [3]. The phase equilibrium data involving the fatty esters are very essential physicochemical properties for the design, modeling, simulation and optimization of the production of biodiesel. In the open literature, for the kind of components made of biodiesel only some VLE binary data are reported so far. Rose et al. [4] measured VLE data of methyl myristate and methyl palmitate system at 4.0, 5.3, 6.7 and 13.3 kPa, but they only gave four experimental points for each of defined pressure. To test the performance of differential scanning calorimetry (DSC), Akisawa et al. [5] obtained VLE data of methyl myristate and methyl palmitate system at 3.9997 kPa. Costa et al. [6] determined the solid–liquid phase diagram of methyl myristate and methyl palmitate, but they did not give the VLE data

* Corresponding author. Tel.: +86 22 2740 4701; fax: +86 22 2740 4705. E-mail address: [email protected] (H. Ding). http://dx.doi.org/10.1016/j.fluid.2014.09.006 0378-3812/$ – see front matter ã 2014 Elsevier B.V. All rights reserved.

of the two substances. Shimoyama et al. [7] measured the VLE for methanol + methyl myristate system at 493–543 K. For the binary system of methyl palmitate and methyl stearate, isobaric VLE data at 0.1, 1, 5 and 10 kPa were reported by Hou et al. [8]. Considering the scarcity of the VLE data of the methyl esters and their importance to the biodiesel industry, our interest focuses on the VLE properties under reduced pressure for the mixtures of methyl myristate and methyl palmitate. In this work, the binary vapor–liquid equilibrium (VLE) data for the mixture of methyl myristate and methyl palmitate were determined at 0.5, 1.0 and 1.4 kPa in a modified Othmer still. The obtained VLE data were verified with the Wisniak test [9] and Van Ness test [10] to check thermodynamic consistency. In addition, the Nonrandom two-liquid (NRTL) and Wilson models were regressed with the experimental data, and a group contribution (UNIFAC) and Dortmund (modified UNIFAC) models were applied to predict the VLE data. 2. Experimental 2.1. Materials The sources and purity levels of the chemicals used in this study are reported in Table 1. In the two reagents, no impurities were detected by gas chromatography (GC 2060, China) with flame ionization (FID), thus both of the chemicals were used without further purification.

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R. Chen et al. / Fluid Phase Equilibria 382 (2014) 133–138

Nomenclature

A,B, C D Lk Wk T 0i DSoi R F A12, A21 N ajk, bjk, cjk P Pis Rk , Q k T u ViL xi, yi exp cal

a gi s ’i ; ’si

constants of Antoine equation term defined by Eq. (3) term defined by Eq. (4) term defined by Eq. (5) boiling point of component i molar entropy of vaporization of component i universal gas constant term defined by Eq. (6) parameters of NRTL and Wilson equations the number of experimental data points the interaction parameter of UNIFAC and Dortmund models the total pressure vapor pressure of pure component i the volume parameter and the area parameter for group k, respectively temperature standard uncertainty liquid mole volume of pure liquid i liquid and vapor composition i mole fraction experimental calculated parameters of NRTL equation the activity coefficient of component i average standard deviation the fugacity coefficients of component i in the mixture vapor phase and in the pure state

2.2. Apparatus and procedure The experimental apparatus where measurements were carried out was a circulation VLE still (a modified Othmer still) [11]. Its reliability for VLE measurements was verified in our previous papers [8,12]. The apparatus are presented in Fig. 1. The internal volume of the still was about 50 cm3, of which 40 cm3 was occupied by the liquid solution. The temperature was measured by a mercury thermometer whose accuracy is
0.1 K, while the pressure was measured with Pirani vacuum gauge with an accuracy of
1%. In each experiment, about 40 cm3 mixtures were fed into the still and then starting vacuum pump (Pferffer DUO 2.5, Germany). The liquid started to be heated after the desired pressure was reached and stable. The vapor was condensed in the condensing coil, and immediately returned to the equilibrium chamber through the vapor-phase sampling port. When the pressure and temperature maintained constant at least 45 min, the equilibrium was assumed to be established. The vapor and liquid samples were withdrawn simultaneously to be dissolved by hexane and analyzed by GC.

Table 1 Materials description. Chemical name

Source

Methyl myristate Methyl palmitate

Shanghai Haiqu 0.999 Chemical Co., Ltd., China Shanghai Haiqu 0.999 Chemical Co., Ltd., China

a

Gas chromatography.

Mass fraction purity

Purification method

Analysis method

None

GCa

None

GC

Fig. 1. Experimental setup for VLE measurement. 1, mercury thermometer; 2, equilibrium chamber; 3, silicone oil; 4, liquid-phase sampling port; 5, heating bar; 6, ground joint; 7, condensing coil; 8, four-way pipe; 9, cold trap; 10, vapor-phase sampling port; 11, vacuum pump; 12, latex rubber tube; 13, buffer tank.

2.3. Analysis All the samples of the equilibrium phases were analyzed by GC with a FID detector. The GC was calibrated with standard solutions that were prepared gravimetrically by an electronic balance (FA2004N, uncertainty of
0.0001 g). The deviations between the compositions of the gravimetrically composed samples indicated a standard uncertainty 0.001 of mole fraction. The GC column is PC-88 column(30 m  0.45 mm  2.55 mm). The carrier gas is nitrogen with a constant flow rate of 1 mL/min. Temperature of injector, detector and oven were kept at 523.15 K, 533.15 K and 473.15 K, respectively. For each sample, the final composition was determined from the average of three analyses. 3. Results and discussion 3.1. The experimental data Isobaric VLE of the mixture of methyl myristate and methyl palmitate were determined at 0.5 kPa, 1.0 kPa, and 1.4 kPa. These data were in parallel tested for three times, and the averaged data

Table 2 VLE data for temperature T, mole fraction x1 and mole fraction y1 for the system methyl myristate (1) + methyl palmitate (2) at 0.5 kPaa . T/K

x1

y1

g1

g2

435.51 433.98 433.46 432.25 430.32 428.09 424.46 419.56 416.88 415.27 414.48 413.81 412.03

0.0000 0.0682 0.1003 0.1499 0.2170 0.3007 0.3996 0.5484 0.6975 0.7684 0.8621 0.9128 1.0000

0.0000 0.1898 0.2600 0.3562 0.4650 0.5755 0.6800 0.7955 0.8815 0.9142 0.9515 0.9701 1.0000

– 1.037 0.987 0.952 0.931 0.915 0.955 1.016 1.004 1.019 0.982 0.977 1.002

1.002 0.940 0.912 0.892 0.886 0.882 0.934 1.029 1.030 1.064 1.056 1.068 –

a

The standard uncertainty is u(P) = 0.01 p, u(T) = 0.1 K, and u(x1) = u(y1) = 0.001.

R. Chen et al. / Fluid Phase Equilibria 382 (2014) 133–138 Table 3 VLE data for temperature T, mole fraction x1 and mole fraction y1 for the system methyl myristate (1) + methyl palmitate (2) at 1.0 kPaa .

135

Table 7 Parameters of the models used to correlate VLE data for the binary system and rootmean-square deviations at 0.5, 1.0, 1.4 kPa.

T/K

x1

y1

g1

g2

Methyl myristate (1) + methyl palmitate (2)

450.97 447.08 446.01 445.23 442.40 440.62 437.74 434.77 432.04 430.46 429.64 429.12 428.42

0.0000 0.0813 0.1418 0.1678 0.2432 0.3488 0.4759 0.5882 0.7428 0.8080 0.8778 0.9270 1.0000

0.0000 0.2100 0.3253 0.3615 0.4685 0.5911 0.7101 0.7896 0.8833 0.9159 0.9464 0.9673 1.0000

– 1.169 1.084 1.052 1.057 1.001 0.995 1.016 1.013 1.034 1.020 1.010 0.998

0.998 1.012 0.969 0.979 1.013 0.980 0.981 1.036 1.042 1.082 1.125 1.177 –

Model

A12a

A21a

0.5 kPa Wilson NRTL

0.6282 323.917

1.5960 69.691

1.0 kPa Wilson NRTL

0.6930 53.117

1.4 kPa Wilson NRTL

1.7392 16.692

a a

The standard uncertainty is u(P) = 0.01 p, u(T) = 0.1 K, and u(x1) = u(y1) = 0.001.

Table 4 VLE data for temperature T, mole fraction x1 and mole fraction y1 for the system methyl myristate (1) + methyl palmitate (2) at 1.4 kPaa . T/K

x1

y1

g1

g2

459.02 455.97 454.96 452.34 450.48 448.95 446.18 442.06 440.01 438.21 437.22 436.11

0.0000 0.0840 0.1313 0.2006 0.2427 0.3440 0.4704 0.5955 0.7302 0.8229 0.9306 1.0000

0.0000 0.2106 0.3004 0.4080 0.4649 0.5869 0.7052 0.7919 0.8739 0.9188 0.9688 1.0000

– 1.116 1.059 1.045 1.060 1.004 0.987 1.038 1.018 1.024 0.996 1.003

1.003 0.979 0.954 0.978 1.010 0.960 0.956 1.057 1.051 1.117 1.145 –

a

Component

Antoine constants B

A Methyl myristate

5.9342 1350.1 9.63335 4003.649 Methyl palmitate 7.53530 2285.800 9.23356 3810.4368 a

c

s Tb /K

s y1b

– 164.167

0.82 0.65

0.0172 0.0076

1.2730 90.919

– 135.004

0.45 0.37

0.0049 0.0066

0.4188 115.027

– 62.121

0.48 0.36

0.0070 0.0073

Wilson, Aij = Lij; NRTL, Aij = gij  gjj.

sT ¼

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX exp 2 u ðT cal Þ i T i t i¼1

N

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX u ðycal yexp Þ2 1;i 1;i t i¼1 ; s y1 ¼ . N

system temperature T. The Antoine constants [15,16] for each component are listed in Table 5. ’i and ’si are the fugacity coefficient of component i in the mixture vapor phase and the pure saturated vapor, respectively. R is the gas constant and V Li is the liquid molar volume of pure component i. In this work, the vapor s could be regarded as ideal gas at  reduced  pressure, thus ’i and ’i V L ðPPs Þ are equal to 1; and the term exp i RT i is approximately equal to 1 at low pressure. Therefore, equation can be written as Pyi ¼ g i xi Psi

(2)

3.2. Consistency tests of experimental data

The standard uncertainty is u(P) = 0.01 p, u(T) = 0.1 K, and u(x1) = u(y1) = 0.001.

Table 5 Parameters of the Antoine equationa .

b

b

a

Pressure range (mmHg)

Wisniak test [9] is used to check the thermodynamic consistency of all the experimental data. The test can be described by the following equations. R1 R1 j Lk dx1  0 W k dx1 j D ¼ 100  R 01 (3) R1 0 Lk dx1 þ 0 W k dx1

C 113.000 301.9132 166.000 278.11662

0.1–6b 2–20c 0.1–6b 2–20c

Lk ¼

AB Antoine equation: log10 ðPsi Þ ¼ ðT273:15þCÞ where Psi is in mmHg and T in K. Taken from ref. [15]. Taken from ref. [16].

are listed in Tables 2–4. The tabulated activity coefficient (g i) was calculated from the following equation [13,14] ! V Li ðP  Psi Þ s s ’i Pyi ¼ g i xi Pi ’i exp (1) RT In this equation, yi and xi are the compositions of component i in the vapor and liquid phases, respectively, and P is the total pressure in the equilibrium system. Psi is the vapor pressure of pure component i which was calculated from the Antoine equation at

ST 0i xi Ds0i Sxi Ds0i  T

Wk ¼

(4)

  RT y Sxi lng i  Sxi ln i 0 yi Sxi Dsi

(5)

where T 0i is the boiling point of component i; Ds0i is the molar entropy of vaporization of component i; xi and yi are liquid and vapor phase molar fractions; R is the universal gas constant; T is the temperature; k denotes each experimental point. The isobaric VLE was considered as thermodynamically consistent if the deviation D less than 3–5. The results of the consistency test are listed in Table 6, indicating that all the VLE data are thermodynamically consistent. Table 8 Group volume Rk and area Qk.

Table 6 Results of the Wisniak thermodynamic consistency test.

Group

P/kPa

L

W

D

0.5 1.0 1.4

1.396 2.031 1.859

1.496 1.983 1.905

3.45 1.20 1.22

CH3 CH2  CH2COO

UNIFAC

Dortmund

Volume Rk

Area Qk

Volume Rk

Area Qk

0.9011 0.6744 1.6764

0.8480 0.5400 1.4200

0.6325 0.6325 1.2700

1.0608 0.7081 1.4228

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R. Chen et al. / Fluid Phase Equilibria 382 (2014) 133–138

Table 9 Group interaction parameter ajk. Model name

Parameter

Group

CH3

CH2

CH2COO 

UNIFAC

ajk

CH3 CH2 CH2COO

0 0 114.8

0 0 114.8

232.1 232.1 0

Dortmund

ajk

CH3 CH2 CH2COO CH3 CH2 CH2COO CH3 CH2 CH2COO

0 0 632.22 0 0 3.3912 0 0 0.3928  102

0 0 632.22 0 0 3.3912 0 0 0.3928  102

98.656 98.656 0 1.9294 1.9294 0 0.3133  102 0.3133  1102 0

bjk

cjk

modeling capability test [18]. In this paper, the NRTL activity coefficient model was used. The criterion is described as following equation [19]

Dy ¼

N 1X 100jyexp  ycal i j i N i¼1

(6)

in which N is the number of experimental data; the superscript exp indicates experimental data; and the superscript cal indicates values calculated with the NRTL equation. The test suggested that if the mean absolute deviation Dy is less than 1, the experimental data was considered to be thermodynamically consistent. The checking results for the system at 0.5, 1.0, 1.4 kPa are 0.6347, 0.4473 and 0.5179, respectively, indicating the thermodynamic consistency of all the experimental data. 3.3. Data regression

Fig. 2. T  x1  y1 diagram of the methyl myristate (1) + methyl palmitate (2) system at 0.5 kPa: &, & experimental data in this study; —, correlated results by the NRTL model; —, correlated results by the Wilson model; --, predicted results by the UNIFAC model; . . . , predicted results by the Dortmund model.

The isobaric VLE data were correlated with the models of the Wilson and NRTL with Matlab software by minimizing the following objective function F [20] F¼

2 X N X exp 2 ðycal ki  yki Þ

(7)

k¼1 i¼1

Here the experimental results of the binary system can also be tested by the point consistency method of the Van Ness test described by Fredenslund et al. [17], which is regarded as a

Fig. 3. T  x1  y1 diagram of the methyl myristate (1) + methyl palmitate (2) system at 1.0 kPa: &, & experimental data in this study; , correlated results by the NRTL model; —, correlated results by the Wilson model; --, predicted results by the UNIFAC model; . . . , predicted results by the Dortmund model.

where N is the number of experimental data points. The superscripts cal and exp presents the calculated values and experimental data, respectively. yki denotes the vapor composition

Fig. 4. T  x1  y1 diagram of the methyl myristate (1) + methyl palmitate (2) system at 1.4 kPa: &, & experimental data in this study; , correlated results by the NRTL model; —, correlated results by the Wilson model; --, predicted results by the UNIFAC model; . . . , predicted results by the Dortmund model.

Table 10 Regression and prediction results for methyl myristate (1) + methyl palmitate (2). Experimental data

Calculated data NRTL

exp

Wilson

4y

T /K

4T

a

cal

4T/K

y1

0.0000 0.1607 0.2289 0.3255 0.4400 0.5596 0.6729 0.7994 0.8886 0.9215 0.9578 0.9747 1.0000

0.0000 0.0291 0.0311 0.0307 0.025 0.0159 0.0071 0.0039 0.0071 0.0073 0.0063 0.0046 0.0000 0.0129

435.51 433.45 432.46 430.96 428.97 426.60 423.98 420.42 417.28 415.93 414.28 413.44 412.03

0.00 0.53 1.00 1.29 1.35 1.49 0.48 0.86 0.40 0.66 0.20 0.37 0.00 0.66

0.00 0.69 0.25 0.28 0.36 0.61 0.66 0.01 0.07 0.44 0.19 0.03 0.00 0.28

0.0000 0.1983 0.3139 0.3574 0.4672 0.5905 0.7067 0.7894 0.8821 0.9156 0.9485 0.9701 1.0000

0.0000 0.0117 0.0114 0.0041 0.0013 0.0006 0.0034 0.0002 0.0012 0.0003 0.0021 0.0028 0.0000 0.0030

450.97 447.74 445.67 444.85 442.65 439.96 437.15 434.95 432.27 431.23 430.17 429.45 428.42

0.00 0.04 0.64 0.21 0.42 0.78 1.00 0.51 0.10 0.40 0.16 0.00 0.36

0.0000 0.1943 0.2852 0.3997 0.4602 0.5836 0.7038 0.7965 0.8760 0.9222 0.9703 1.0000

0.0000 0.0163 0.0152 0.0083 0.0047 0.0033 0.0014 0.0046 0.0021 0.0034 0.0015 0.0000 0.0051

459.02 455.96 454.35 452.16 450.92 448.18 445.18 442.60 440.18 438.70 437.13 436.11

x1

y1

0.5 kPa 435.51 433.98 433.46 432.25 430.32 428.09 424.46 419.56 416.88 415.27 414.48 413.81 412.03 ADc

0.0000 0.0682 0.1003 0.1499 0.2170 0.3007 0.3996 0.5484 0.6975 0.7684 0.8621 0.9128 1.0000

0.0000 0.1898 0.2600 0.3562 0.4650 0.5755 0.6800 0.7955 0.8815 0.9142 0.9515 0.9701 1.0000

0.0000 0.1847 0.2583 0.3585 0.4721 0.5861 0.6914 0.8081 0.8915 0.9231 0.9587 0.9757 1.0000

0.0000 0.0051 0.0017 0.0023 0.0071 0.0106 0.0114 0.0126 0.0100 0.0089 0.0072 0.0056 0.0000 0.0063

435.51 434.66 433.46 431.69 429.46 426.92 424.21 420.65 417.55 416.22 414.55 413.67 412.03

0.00 0.68 0.00 0.56 0.86 1.17 0.25 1.09 0.68 0.94 0.06 0.15 0.00 0.50

1.0 kPa 450.97 447.08 446.01 445.23 442.40 440.62 437.74 434.77 432.04 430.46 429.64 429.12 428.42 AD

0.0000 0.0813 0.1418 0.1678 0.2432 0.3488 0.4759 0.5882 0.7428 0.8080 0.8778 0.9270 1.0000

0.0000 0.2100 0.3253 0.3615 0.4685 0.5911 0.7101 0.7896 0.8833 0.9159 0.9464 0.9673 1.0000

0.0000 0.1962 0.3101 0.3535 0.4644 0.5907 0.7102 0.7943 0.8864 0.9187 0.9499 0.9698 1.0000

0.0000 0.0138 0.0152 0.0080 0.0041 0.0004 0.0001 0.0047 0.0031 0.0028 0.0035 0.0025 0.0000 0.0045

450.97 447.77 445.76 444.95 442.76 440.01 437.08 434.78 431.97 430.90 429.83 429.15 428.42

1.4 kPa 459.02 455.97 454.96 452.34 450.48 448.95 446.18 442.06 440.01 438.21 437.22 436.11 AD

0.0000 0.0840 0.1313 0.2006 0.2427 0.3440 0.4704 0.5955 0.7302 0.8229 0.9306 1.0000

0.0000 0.2106 0.3004 0.4080 0.4649 0.5869 0.7052 0.7919 0.8739 0.9188 0.9688 1.0000

0.0000 0.1950 0.2858 0.3999 0.4601 0.5830 0.7034 0.7968 0.8770 0.9230 0.9700 1.0000

0.0000 0.0156 0.0146 0.0081 0.0048 0.0039 0.0018 0.0049 0.0031 0.0042 0.0012 0.0000 0.0052

459.02 455.93 454.32 452.13 450.90 448.17 445.18 442.57 440.11 438.61 437.06 436.11

b

Dy ¼ yexp  ycal i . i DT = Texp  Tcal. Pn

c

ADyi ¼

i¼1

jyexp ycal j 1;i 1;i ; ADT N

Pn ¼

i¼1

/K

y1

cal

cal

Dortmund

4y

T /K

4T/K

y1

0.0000 0.1756 0.2472 0.3447 0.4566 0.5704 0.6771 0.7970 0.8840 0.9172 0.9547 0.9726 1.0000

0.0000 0.0142 0.0128 0.0115 0.0084 0.0051 0.0029 0.0015 0.0025 0.003 0.0032 0.0025 0.0000 0.0052

435.51 433.07 431.95 430.31 428.24 425.87 423.32 419.95 417.01 415.74 414.18 413.38 412.03

0.00 0.91 1.51 1.94 2.08 2.22 1.14 0.39 0.13 0.47 0.30 0.43 0.00 0.89

0.00 0.66 0.34 0.38 0.25 0.66 0.59 0.18 0.23 0.77 0.53 0.33 0.00 0.38

0.0000 0.1867 0.3009 0.3448 0.4574 0.5858 0.7071 0.7925 0.886 0.9191 0.9511 0.9717 1.0000

0.0000 0.0233 0.0244 0.0167 0.0111 0.0053 0.0030 0.0029 0.0027 0.0032 0.0047 0.0044 0.0000 0.0078

450.97 448.10 446.16 445.37 443.22 440.49 437.58 435.28 432.46 431.36 430.25 429.49 428.42

0.00 0.01 0.61 0.18 0.44 0.77 1.00 0.54 0.17 0.49 0.09 0.00 0.36

0.0000 0.1895 0.2788 0.3921 0.4523 0.5761 0.6986 0.7944 0.8772 0.9249 0.9727 1.0000

0.0000 0.0211 0.0216 0.0159 0.0126 0.0108 0.0066 0.0025 0.0033 0.0061 0.0039 0.0000 0.0087

459.02 456.10 454.56 452.46 451.26 448.60 445.65 443.04 440.52 438.94 437.22 436.11

cal

cal

4y

Tcal/K

4T/K

0.0000 0.2062 0.2855 0.3906 0.5062 0.6184 0.7189 0.8268 0.9023 0.9305 0.9622 0.9771 1.0000

0.0000 0.0164 0.0255 0.0344 0.0412 0.0429 0.0389 0.0313 0.0208 0.0163 0.0107 0.0070 0.0000 0.0220

435.51 432.56 431.26 429.41 427.14 424.63 422.07 418.84 416.19 415.10 413.78 413.12 412.03

0.00 1.42 2.20 2.84 3.18 3.46 2.39 0.72 0.69 0.17 0.70 0.69 0.00 1.42

0.00 1.02 0.15 0.14 0.82 0.13 0.16 0.51 0.42 0.90 0.61 0.37 0.00 0.40

0.0000 0.2175 0.3428 0.3894 0.5053 0.6314 0.7450 0.8219 0.9036 0.9319 0.9590 0.9764 1.0000

0.0000 0.0075 0.0175 0.0279 0.0368 0.0403 0.0349 0.0323 0.0203 0.0160 0.0126 0.0091 0.0000 0.0196

450.97 447.54 445.32 444.44 442.14 439.28 436.42 434.27 431.75 430.82 429.89 429.27 428.42

0.00 0.46 0.69 0.79 0.26 1.34 1.32 0.50 0.29 0.36 0.25 0.15 0.00 0.49

0.00 0.13 0.40 0.12 0.78 0.35 0.53 0.98 0.51 0.73 0.00 0.00 0.38

0.0000 0.2205 0.3188 0.4385 0.5000 0.6220 0.7371 0.8236 0.8960 0.9368 0.9772 1.0000

0.0000 0.0099 0.0184 0.0305 0.0351 0.0351 0.0319 0.0317 0.0221 0.0180 0.0084 0.0000 0.0201

459.02 455.54 453.76 451.43 450.14 447.38 444.46 442.02 439.77 438.42 437.01 436.11

0.00 0.43 1.20 0.91 0.34 1.57 1.72 0.04 0.24 0.21 0.21 0.00 0.57

cal

R. Chen et al. / Fluid Phase Equilibria 382 (2014) 133–138

T /K

T

a

UNIFAC

4y

b

y1cal

jT exp T cal i j i . N

137

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of component k at i point. The regression binary interaction parameters of the NRTL and Wilson models are listed in Table 7. Besides, the root-mean-squared deviations (RMSD) of the vapor phase mole fraction and the temperature between the experimental data and the calculated values are presented in Table 7 as well. 3.4. Data prediction The UNIFAC group contribution method is a reliable and fast tool for predicting liquid-phase activity coefficients at moderate pressures and temperatures [21]. It is the best-known and most successful method presently used for predicting vapor–liquid equilibrium. In this paper, based on the experimental VLE data, the predictive capability of the UNIFAC and Dortmund (modified UNIFAC) models was test for VLE calculations. All of the group volume, area parameters together with the group interaction parameters about UNIFAC model and Dortmund model are listed in Tables 8 and 9, respectively. Figs. 2–4 compare graphically the simulated regression and prediction results with experimental data at 0.5 kPa, 1.0 kPa and 1.4 kPa, respectively. The four models values, including the calculated vapor compositions and calculated temperature, are listed in Table 10. In addition, the deviation and the average mean deviation of vapor molar fraction and temperature between model values and experimental data are also shown in Table 10. As seen from Table 10 and Fig. 2–4, all these four models represent satisfactorily for the VLE properties of the methyl myristate and methyl palmitate systems at all studied pressures. It is observed that the results simulated by the NRTL model are slight better than those of other models. The average mean deviations for NRTL model in vapor molar fraction, y, and temperature, T, are no more than 0.0063 and 0.50 K, respectively. Besides, it can be seen that the results calculated by Dortmund model showed the largest deviation for methyl myristate and methyl palmitate system at all studied pressures. The largest average mean deviations for Dortmund model in vapor molar fraction, y, and temperature, T, are 0.0220 and 1.42 K, respectively, at 0.5 kPa. At the pressure of 0.5 kPa, the average mean deviation of Wilson model in temperature is lower than those obtained from UNIFAC model, while, on the contrary, the average mean deviation in vapor composition is higher than those of UNIFAC model. However, the Wilson model is better correlated with the experimental data than the UNIFAC model at 1.0 and 1.4 kPa. In general, the results calculated by the four models at 0.5 kPa seemed slight worse than those at 1.0 and 1.4 kPa. From the view of industrial application, all the four models can be used to calculate the VLE of the binary system of methyl myristate and methyl palmitate. 4. Conclusions Isobaric VLE data were determined for the binary system of methyl myristate and methyl palmitate at 0.5 kPa, 1.0 kPa and 1.4 kPa. All the experimental data passed the Wisniak and Van Ness thermodynamically consistency test. The experimental VLE data were regressed with NRTL and Wilson models, and predicted by UNIFAC and Dortmund (modified UNIFAC) models. The comparison of experimental data with the calculated values obtained from the four models indicates that the experimental and calculated

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