~ ' 1":

ELSEVIER Fluid Phase Equilibria 107 (1995) 257-267

i l K [

Isothermal vapour-liquid equilibrium data for the systems n-pentane with n-hexane, n-octane and n-decane

Peter Rice, Ali E1-Nikheli

Dept. of Chemical Engineering, Loughborough University of Technology, Loughborough, Leics. LE l l 3TU

Received 22 July 1994; accepted in final form 26 December 1994

A b s t r a c t

Measurements of isothermal VLE for the systems n-pentane with n-hexane at 298.7, 303.7 and 308.7 K, n-octane at 303.7, 308.7 and 313.7 K and n-decane at 317.7 and 333.7 K are presented. These data can be used for the design of industrial equipment or with the data for the n-pentane + n-propanol system (Rice et al., 1990) for testing thermodynamic theories. The data satisfied the point-to-point consistency test. Using the maximum likelihood method the data was correlated with the Wilson (1964), the NRTL (Renon and Prausnitz, 1968) and the UNIQUAC (Abrams and Prausnitz, 1975) equations. Prior to this vapour pressure measurements were made to evaluate the equipment and enthalpies of vaporization were calculated. Both these parameters showed acceptable agreement with literature values.

Keywords: Data; Vapour-liquid equilibria; Isothermal; Binary; n-pentane; n-hexane; n-octane, n-decane

1. Introduction

VLE data for the n-alkane systems are of interest to industry. Also data for binary systems obtained on the same apparatus showing increasing deviations from ideality can be used to test mixture theories.

2. Experimental

The VLE data were measured using a still, pressure stabilizer, temperature control and measuring device, a gas chromatograph, a chart recorder and a computer integrator. The equipment is shown schematically in Fig. 1. The equilibrium still used was a Lobodest Model 0601/U recirculating still similar to that described by Gutsch and Knapp (1982). The still, which is all glass, is provided with a Cottrell pump to ensure adequate mixing of the liquid and vapour and to maintain the liquid at a certain level. The still had a tubular boiler provided with an immersion heater. Equilibrium liquid and vapour samples were taken using magnetically controlled valves. The sampling mechanism ensured

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258 P. Rice, A. El-Nikheli / Fluid Phase Equilibria 107 (1995) 257-267

8

9 - 2 0

14

lSq4-

16-

17

N I N O i

21

22

3

Fig. 1. VLE still and other equipment: 1, filler; 2, mixing chamber; 3, immersion heater; 4, Cottrell pump; 5, equilibrium chamber; 6, compensation heating-jacket; 7, thermometer position; 8, micro-sample removal point vapour phase in miscibility gap; 9, cool vapour-phase; 10, shut-off valve; 11, sample receiver for condensed vapour phase; 12, micro-sample removal point for vapour phase; 13, micro-sample removal point for liquid-phase; 14, liquid-phase cooler; 15, shut-off valve; 16, sample receiver for liquid phase; 17, magnetic stirrer; 18, solenoid coils for electrical actuation of 9 and 10; 19, venting-cocks for removal of sample-receivers; 20, vacuum measuring instrument; 21, electronic digital thermometer; 22, electronic control unit; 23, automatic pressure- and vacuum-stabilizer VKI.

that the total pressure inside the still remained constant during sampling. A mixing chamber, provided with a magnetic stirrer, ensured adequate mixing of recycled vapour and liquid streams. Separation of equilibrium phases was achieved in the equilibrium chamber, which consisted of a silver-jacketed vacuum double-walled cylinder surrounded by a heating mantle at a temperature 1 K lower than the inside temperature. The fluctuations of pressure in the system were kept to a minimum by a buffer tank and pressure was controlled by a Fischer VKI automatic vacuum-pressure controller to ___ 0.068 kPa. The equilibrium pressure inside the system was measured by a mercury manometer and a Bourdon gauge. A set of mercury-in-glass thermometers, graduated in 0.2 K increments (calibrated by the National Bureau of Standards), was used to measure the temperature inside the equilibrium chamber, the boiler and the mantle.

P. Rice, A. El-Nikheli / Fluid Phase Equilibria 107 (1995) 257-267 259

300

250

r ~

150

I00

~kO ~ D

121 []

,o []

K1

D

0. I 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Liquid or vapour composition x or y

Gr i~o l d This work

0.9

Fig. 2. VLE data obtained for the system benzene-toluene at 120°C compared with the data of Griswold et al. (1943).

The equilibrium samples were analysed in a gas chromatograph (INTERSMAT IGC 10) with a thermal conductivity detector and an electric computing integrator (MINIGRATOR Model 23000-11; Spectra Physics). Chromatographic calibrations covering the complete range of compositions for each of the binary mixtures studied were carried out. Equilibrium compositions were estimated from areas under peaks using the calibration curves.

Reliability of the results was checked by measuring the vapour pressures of some normal alkanes and VLE of a known binary mixture. The results of vapour pressure measurements were found to agree with values found in the literature (American Petroleum Institute, 1977) with average deviations between experimental and literature values of less than 1%. VLE measurements at 393.7 K for the binary system benzene + toluene were found to agree also with those of Griswold et al. (1943) (Fig. 2).

2.1. Materials

All chemicals used in the measurements were either research or Analar grade. All chemicals were obtained from BDH Chemicals with minimum purity of 99.93 mol%, percentage maximum limit of impurity of 0.03 and maximum percentage non-volatile matter of 0.01 all for n-decane. Measured densities, using a 10 ml pycnometer, refractive indices and normal boiling points agreed with those found in the literature (Table 1). Gas chromatographic analysis indicated no secondary peaks and therefore the chemicals were used as received.

3. Results and discussion

3.1. Vapour pressure

Vapour pressures for the pure components were measured and correlated with the Antoine equation:

B In P = A (1)

t + C

260 P. Rice, A. EI-Nikheli / Fluid Phase Equilibria 107 (1995) 257-267

Table 1 Purities and source of pure chemicals

Compound Source Minimum %Maximum %Non-volatile purity (mol%) limits of purity matter

n-Pentane BDH 99.95 0.03 0.002 Chemicals

n-Hexane BDH 99.95 0.03 0.002 Chemicals

n-Octane BDH 99.95 0.03 0.002 Chemicals

n-Decane BDH 99.93 0.03 0.010 Chemicals

where P is the pressure in kPa., t is the temperature in°C, and A, B and C are constants given in Table 2. As noted previously, the measurements agree with those found in American Petroleum Institute tables (1977) to within ___ 1%.

Plots of In P against 1/T gave straight lines, with a correlation coefficient better than 0.995, so that mean values of enthalpy of vaporization for the temperature range were calculated as

d(ln P ) A n = - R 1 (2)

The values obtained were 27.46, 31.24, 36.14 and 44.56 kJ kg -1 for n-pentane, n-hexane, n-octane and n-decane, respectively. Corresponding values from the literature (Majer and Svoboda, 1985) were 26.2, 31.0, 36.0 and 44.2 kJ kg -1. Also, using the Antoine constants the variation of enthalpy of vaporization with temperature was calculated as

BT AH=PAV(t+C)2 (3)

where AV = V~ - V L.

Table 2 Constants A, B and C used in Antoine's equation

Compound A B C Temp. AAD range (K) A P(Pa)

n-Pentane 13.9652 2576.79 239.889 287.95- 376.0 316.55

n-Hexane 13.6773 2631.42 221.922 285.35- 341.3 339.45

n-Octane 13.5151 2852.23 195.326 306.7- 344.2 395.2

n-Decane 13.3888 3096.52 178.965 314.25 - 631.9 443.85

P. Rice, A. EI-Nikheli / Fluid Phase Equilibria 107 (1995) 257-267 261

55

~ 5 0 . . • *

~45 ' * . * . .

"~40 0 (~ O000OmO O ~ ...

~'35

"A ~ 2 5 [] ,qit~.,~ • D D

m 20 I I I 250 300 350 400

Temperature (K)

*:g

I

450

Large open symbols- Majer & Svoboda Small filled symbols- from this work

O A o

n-pentane n-hexane n-octane n-de, cane

500

Fig. 3. Enthalpy of vaporization, calculated from vapour pressure, versus temperature for n-pentane, n-hexane, n-octane and n-decane.

If for the low pressures used in the present experiments P V = R T and V C >> V L then

T 2 A H = RB ( t + C)2 (4)

Vapour molar volumes were estimated using the SRW equation (1972) while the Spencer and Danner (1972) modification of the Rackett equation was used to estimate liquid molar volumes.

Calculated values of enthalpy of vaporization using Eq. (4) are shown in Fig. 3 compared with the data from Majer and Svoboda (1985). Our calculations show a much smaller variation of enthalpy of vaporization with temperature than that given in Majer and Svoboda (1985). The difference increases as the chain length increases.

3.2. VLE data

Experimental P, T, x, y data for the binary systems n-pentane with n-hexane at 298.7, 303.7 and 308.7 K, n-octane at 303.7, 308.7 and 313.7 K and n-decane at 317.7 and 333.7 K are given in Table 3. VLE data for the system n-heptane with n-hexane at 750 mmHg is reported by Tenn and Missen (1963) while Chen and Zwolinski (1974) report VLE data calculated from total pressure measure- ments at 298.15 K.

3.3. Data evaluation

Thermodynamic consistency of the measured data was checked by using the point-to-point method of Van Ness et al. (1973) as modified by Fredenslund et al. (1977). The calculations showed that the experimental data are thermodynamically consistent, satisfying the usually adopted consistency criterion of AAD (Ay) < 0.01 (Table 4).

262 P. Rice, A. EI-Nikheli / Fluid Phase Equilibria 107 (1995) 257-267

Table 3a Vapour- l iquid equilibrium data for the system n-pentane with n-hexane

T = 298.7 T = 303.7 T = 308.7

P (kPa) x y P (kPa) x y P (kPa) x y

20.69 0.0 0.0 25.61 0.0 0.0 31.70 0.0 0.0 25.80 0.0738 0.2469 30.90 0.0638 0.2011 37.96 0.0645 0.2250 28.80 0.1405 0.3606 33.20 0.1218 0.3054 42.56 0.1444 0.3632 32.50 0.2105 0.4678 35.80 0.1700 0.4141 48.40 0.2116 0.4585 36.06 0.2931 0.5821 38.80 0.2213 0.4678 52.16 0.2908 0.5677 42.40 0.4011 0.7080 45.80 0.3291 0.6166 58.36 0.3631 0.6568 47.40 0.4753 0.7592 54.90 0.4750 0.7480 60.96 0.3936 0.6878 52.60 0.5932 0.8256 59.20 0.5401 0.7808 67.70 0.4822 0.7433 59.30 0.7260 0.9006 64.30 0.6064 0.8409 74.80 0.5556 0.7994 63.21 0.8573 0.9543 69.00 0.6864 0.8825 85.96 0.6894 0.8823 68.20 0.9458 0.9947 72.30 0.7683 0.9232 94.66 0.8267 0.9315 69.96 1 1 75.40 0.7977 0.9355 100.63 1 1

78.70 0.8729 0.9511 83.82 1 1

The coefficients of the two-parameter UNIQUAC (Abrams and Prausnitz, 1975), NRTL (Renon and Prausnitz, 1968) and Wilson (1964) equations were evaluated using the method of maximum likelihood (Prausnitz et al., 1980). The activity coefficients ~/i for each data point were estimated by the relation

(YiPdPi) T, = v /L (p_ ps ) (5)

( xieist~ s ) exp (RT)

Table 3b Vapour- l iquid equilibrium data for the system n-pentane with n-octane

T = 303.7 T = 308.7 T = 313.7

P (kPa) x y P (kPa) x y P (kPa) x y

2.55 0 0 3.39 0 0 4.29 0 0 26.67 0.3034 0.9298 5.70 0.0220 0.3933 19.00 0.1154 0.8013 30.50 0.3409 0.9415 14.00 0.1503 0.8005 30.20 0.2209 0.8831 38.80 0.4488 0.9623 25.80 0.2528 0.9000 41.72 0.3142 0.9268 45.50 0.5185 0.9714 29.80 0.2885 0.9248 45.90 0.3614 0.9333 48.60 0.5524 0.9778 39.50 0.3737 0.9455 53.40 0.4253 0.9494 49.70 0.5773 0.9793 47.20 0.4544 0.9597 55.40 0.4379 0.9591 54.20 0.6220 0.9801 58.30 0.5657 0.9721 62.20 0.4903 0.9647 59.90 0.6813 0.9821 67.70 0.6547 0.9855 70.80 0.5712 0.9757 63.80 0.7252 0.9873 77.20 0.7394 0.9927 79.70 0.6353 0.9842 68.60 0.7718 0.9917 86.35 0.8424 0.9974 85.70 0.6919 0.9908 75.80 0.8673 0.9957 95.20 0.9267 0.9993 97.00 0.7770 0.9946 81.70 0.9481 0.9999 100.6 1 1 118.0 1 1

P. Rice, A. EI-Nikheli / Fluid Phase Equilibria 107 (1995) 257-267

Table 3c Vapour-liquid equilibrium data for the system n-pentane with n-decane

263

T = 317.7 T = 333.7

P (kPa) x y P (kPA) x y 0.65 0 0 1.57 0 0

48.18 0.3584 0.9882 49.60 0.2283 0.9591 51.99 0.3858 0.9902 61.17 0.2790 0.9695 60.18 0.4483 0.9918 75.50 0.3501 0.9842 70.70 0.5191 0.9951 88.53 0.3993 0.9874 81.30 0.5956 0.9958 103.35 0.4669 0.9885 95.70 0.6824 0.9990 114.06 0.5205 0.9900

105.30 0.7459 0.9998 124.10 0.5691 0.9935 112.06 0.8023 1 127.73 0.5855 0.9941 121.11 0.8631 1 135.70 0.6240 0.9950 135.39 1 1 146.41 0.6722 0.9965

218.27 a 1 1

a Value taken from API (1971).

where ~b is the fugac i ty coeff icient , P is the total pressure, V is vo lume , T is temperature , R is the

gas constant , x and y are the liquid and gas phase mole fractions, respect ively , and i, s and L refer to

c o m p o n e n t i, saturated condi t ions and liquid phase, respect ively.

Fugac i ty coeff ic ients were calcula ted f rom the second virial coeff ic ient using the correla t ion o f

H a y d e n and O ' C o n n e l l (1975).

The mo la r v o l u m e s were es t imated by the modi f ied Racket t equat ion o f Spencer and Danner

(1972) as stated above.

W e have used the m e t h o d o f m a x i m u m l ikel ihood and have a s sumed that all measu remen t errors

are independent ly no rma l ly distr ibuted with var iances o-2 in the properties, where M represents P , Mj

Table 4 Consistency test mean deviations in total pressure and vapour-phase mole fraction also 3-term Legendre coefficients and component liquid volumes used in the test (Fredenslund et al. (1977) computer program)

Temp. (K) A P (kPa) A y 3-term Legendre coeffts. Liquid Volume (cm 3 mol- l)

(1) (2)

n-Pentane(1)+n-hexane(2) 298.7 0.0042 0.0107 0.2277 303.7 0.0039 0.0076 0.1835 308.7 0.0042 0.0122 0.3044

n-Pentane(1)+ n-octane(2) 303.7 0.0019 0.0036 0.4658 308.7 0.0076 0.0113 -0.1325 313.7 0.0052 0.0043 0.2559

n-Pentane(1)+n-decane(2) 317.7 0.0055 0.0010 0.6920 333.7 0.0042 0.0035 0.0285

0.0937 0.0931 111.88 131.28 0.1222 0.1749 112.79 132.18 0.1805 0.3234 113.72 133.10

-0.2302 0.3734 112.79 170.05 0.2594 0.0008 113.72 170.99 0.0358 0.1713 114.69 131.95

- 0.4119 0.4474 115.49 198.27 0.01019 - 0.0333 118.90 201.44

264 P. Rice, A. EI-Nikheli / Fluid Phase Equilibria 107 (1995) 257-267

Table 5 Parameters estimated by Maximum Likelihood

System T-(K) Model A 12 a A 21 a A y RMSD b

A P (kPa)

n-Pentane + 298.7 UNIQUAC 241.46 - 158.88 0.0048 0.466 n-hexane NRTL 465.01 - 177.74 0.0048 0.471

WILSON - 347.25 798.33 0.0047 0.470

n-Pentane + 303.7 UNIQUAC 304.59 - 191.84 0.0062 0.404 n-hexane NRTL 606.75 - 229.57 0.0063 0.411

WILSON - 449.43 1117.17 0.0057 0.388

n-Pentane + 308.7 UNIQUAC 356.83 - 207.26 0.0053 0.591 n-hexane NRTL 773.26 - 203.56 0.0055 0.581

WILSON - 466.56 1472.29 0.0051 0.511

n-Pentane + 303.7 UNIQUAC 338.69 - 206.72 0.0029 0.407 n-octane NRTL 796.08 - 288.90 0.0030 0.440

WILSON - 417.75 1391.18 0.0029 0.351

n-Pentane + 308.7 UNIQUAC 357.01 - 216.94 0.0033 0.476 n-octane NRTL 825.15 - 306.04 0.0033 0.473

WILSON - 430.01 1352.19 0.0060 0.583

n-Pentane + 313.7 UNIQUAC 250.77 - 163.66 0.0048 0.335 n-octane NRTL 579.11 - 223.20 0.0048 0.365

WILSON - 301.78 899.27 0.0047 0.321

n-Pentane + 317.7 UNIQUAC 331.04 - 200.27 0.0012 0.284 n-decane NRTL 916.66 - 299.38 0.0011 0.332

WILSON - 327.01 1407.52 0.0012 0.243

n-Pentane + 333.7 UNIQUAC 78.10 - 50.34 0.0044 0.149 n-decane NRTL 386.92 - 196.35 0.0044 0.145

WILSON - 77.96 360.25 0.0044 0.149

a Note that for the three models AI2 and A21 represent the following:

UNIQUAC A12 = u12 - //22; A21 = U21 -- U l l ( J m ° l - I )

N R T L a l 2 = g12 -- g 2 2 ; A21 = g21 - g l l (J m°l-I) WILSON AI2 = A12 - A22; A21 = A21 -- All (J mol - I ) b RMSD = ((exp.value - ca lc .va lue)2 /n - 3) °'5.

T , x a n d y , a n d t h a t t h e v a r i a n c e s a r e i n d e p e n d e n t o f j f o r g i v e n M . T h e s e a r e m i n i m i z e d a c c o r d i n g

to t h e o b j e c t i v e f u n c t i o n

4 N (Mj,calc__Mj,exp) 2 s = E E 0 -2

g = l j = l Mj ( 6 )

W e h a v e e s t i m a t e d t h e s t a n d a r d d e v i a t i o n s o- to b e O-p = 0 . 1 3 3 k P a , o- r = 0 . 0 5 K, o- x = 0 . 0 0 1 a n d

try = 0 . 0 0 1 . T h e s e v a l u e s a r e w i t h i n t h e l i m i t s o f t h e e q u i p m e n t a c c u r a c y .

T h e r e s u l t s o f t h e f i t f o r t h e t h r e e m o d e l s a n d t h e R M S d e v i a t i o n s A p a n d A y a r e s h o w n in T a b l e

5. N o t e t h a t f o r t h e t h r e e m o d e l s A12 a n d A21 r e p r e s e n t t h e f o l l o w i n g :

U N I Q U A C A12 = u12 - u22; A21 = u21 - - Ul l ( J m o 1 - 1 )

P. Rice, A. EI-Nikheli / Fluid Phase Equilibria 107 (1995) 257-267

Table 6 Deviations in pressure and vapour-phase mole fractions using best fit parameters of liquid-phase models

265

System T (K) Model AAD (Ay) a %AAD ( A p )

n-Pentane + 298.7 UNIQUAC 0.14 0.73 n-hexane NRTL 0.02 0.81

WILSON 0.02 0.76

n-Pentane + 303.7 UNIQUAC 0.20 0.61 n-hexane NRTL 0.32 0.63

WILSON 0.01 0.55

n-Pentane + 308.7 UNIQUAC 0.12 0.42 n-hexane NRTL 0.14 0.44

WILSON 0.13 0.37

n-Pentane + 303.7 UNIQUAC 0.13 0.25 n-octane NRTL 0.14 0.28

WILSON 0.13 0.22

n-Pentane + 308.7 UNIQUAC 0.09 0.03 n-octane NRTL 0.09 0.07

WILSON 0.16 0.25

n-Pentane + 313.7 UNIQUAC 0.31 0.12 n-octane NRTL 0.06 0.14

WILSON 0.31 0.12

n-Pentane + 317.7 UNIQUAC 0.07 0.08 n-decane NRTL 0.06 0.10

WILSON 0.07 0.07

n-Pentane 333.7 UNIQUAC 0.16 0.00 n-decane NRTL 0.16 0.01

WILSON 0.16 0.03

a A A D = (1 / N ) ~'qN exp.value-calc.value/exp.value.

N R T L A12 = g l 2 -- g22; A21 = g21 - g11(J mo1-1) W I L S O N A12 = h i2 - A22; A21 = A21 - h l l ( J mo1-1)

Deviations in pressure and vapour-phase mole fraction using these best-fit liquid-phase model parameters are listed in Table 6.

For the NTRL equation a value of 0.47 for a was used as recommended by Bruin and Prausnitz (1971).

In general all equations correlated the data but with the Wilson equation being slightly better than the UNIQUAC equation for the n-pentane + n-hexane system and the reverse for the n-pentane + n- decane system. Both were slightly better than the NRTL. If a had been allowed to vary a greater accuracy might have been obtained. However, it would then be a three-parameter equation.

4. List of symbols

A,B,C Antoine equation constants M property representing P, T, x, y

266 P. Rice, A. EI-Nikheli / Fluid Phase Equilibria 107 (1995) 257-267

P R

RMSD T u

x

Y

pressure gas constant root-mean-square deviation temperature molar volume mole fraction of the component in the liquid phase mole fraction of the component in the vapour phase

4.1. Greek letters

a NRTL parameter "y activity coefficient o" variance ~b fugacity coefficient

4.2. Subscripts

G gas phase i component i data point L liquid phase s saturation

R e f e r e n c e s

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American Petroleum Institute, Project 44, 1977. Texas A & M University, College Station, Texas. Bruin, S. and Prausnitz, J.M., 1971. One parametric equation for Gibbs free energy of strongly non-ideal liquid mixtures.

Ind. Eng. Chem. Process. Des. Dev., 10:562-572. Chen, S.-S. and Zwolinski, B.J., Excess thermodynamic functions of binary mixtures of normal and isomeric alkanes (C 5

and C6). J. Chem. Soc. Faraday Trans. 2, 70:1133-1142. Ellis, J.A. and Chao, K.C., 1973. Vapour pressures and interaction constants of some nearly ideal solutions. J. Chem. Eng.

Data., 18:264-266. Fredenslund, A., Gmehling, J. and Rasmussen, P., 1977. Vapour-Liquid Equilibria Using UNIFAC. Elsevier, Amsterdam, p.

68. Griswold, J., Andres, D. and Klien, V.A., 1943. Determination of high pressure vapor-liquid equilibria. The vapor-liquid

equilibrium of benzene-toluene. Trans. Am. Inst. Chem. Eng., 39:223-240. Gutsche, B. and Knapp, H., 1982. Isothermal measurements of vapor-liquid equilibriums for three n-alkane-chloroalkane

mixtures. Fluid Phase Equilibria, 8:285-300. Hayden, J.G. and O'Connell, J.P., 1975. A generalised method for predicting second virial coefficients. Ind. Eng. Chem.

Process Des. Dev., 14:209-216. Majer, V. and Svoboda, V., 1985. Enthalpies Of Vaporization Of Organic Compounds. Blackwell Scientific Publications,

London. Prausnitz, J.M., Anderson, T.F., Grens, E.A., Eckert, C.A., Hsieh, R. and O'Connell, J.P., 1980. Computer Calculations For

Multicomponent Vapor-Liquid Equilibria. Prentice-Hall, Englewood Cliffs, NJ. Renon, H. and Prausnitz, J.M., 1968. Local compositions in thermodynamic excess functions. AIChE J., 14: 135-144.

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Rice, P., E1-Nikheli, A. and Teja, A.S., 1990. Isothermal vapor-liquid equilibrium data for the system n-pentane+ n- propanol. Fluid Phase Equilibria, 56: 303-312.

Riddick, J.A. and Bunger, E.B., 1970. Organic Solvents Physical Properties And Methods Of Purification, 3rd edn. Wiley-Interscience, NY.

Rossini, F.D., Pitzer, K.S., Arnett, R.L., Braun, R.M. and Pimentel, G.C., 1953. Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds. National Bureau of Standards, Pittsburg.

Soave, G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27: 1197-1203.

Spencer, C.F. and Danner, R.P., 1972. Improved equation for prediction of saturated liquid densities. J. Chem. Eng. Data., 7: 236-240.

Term, F.G. and Missen, R.W., 1963. A study of the condensation of binary vapors of miscible liquids. Can. J. Chem. Eng., 41:12.

Van Ness, H.C., Byer, S.M. and Gibbs, R.E., 1973. Vapor-liquid equilibrium. Part 1. An appraisal of data reduction methods. AIChE J., 19: 238-244.

Wilson, G.M., 1964. Vapour equilibrium XI. A new expression for the excess free energy of mixing. J. Am. Chem. Soc., 86:127-130.