DISQUAC and UNIFAC group interaction parameters for chloroalkanes

ELSEVIER

Fluid Phase Equilibria132 (1997) 15-20

DISQUAC and UNIFAC group interaction parameters for chloroalkanes O m a r D a h m a n i a,1, Ivan Wichterle a, *, A h m e d Ait-Kaci b a Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, 165 02 Prague 6, Czech Republic b U.S.T.H.B., lnstitut de Chimie, Laboratoire de Thermodynamique des Solutions, B.P. 32, EI-Alia, Bab-Ezzouar, Alger, Algeria Received 4 October 1996; accepted 23 December 1996

Abstract

DISQUAC and UNIFAC parameters for 1-chlorobutane, 2-chlorobutane and 2-chloro-2-methylpropane in binary systems with n-heptane, methylcyclohexane and toluene are reported. These parameters were evaluated by the fitting of P, T, x, and y new experimental data using the maximum likelihood method. © 1997 Elsevier Science B.V. Keywords: Vapour-liquid equilibria; Group contribution; Chloroalkanes

1. Introduction

In group contribution methods for the prediction of mixture properties such as DISQUAC [1] or UNIFAC [2], etc., greater accuracy can be achieved by taking into account some particular effects such as "proximity" and "steric" effects. The sensitivity of the group interaction parameters to "steric effects" is examined here in the DISQUAC and UNIFAC models. Group interaction parameters are evaluated for the three types of chlorine groups in 1-chlorobutane (primary butyl chloride), 2-chlorobutane (sec-butyl chloride) and 2-chloro-2-methylpropane (tert-butyl

* Corresponding author. n On leave from the U.S.T.H.B., Institut de Chimie, Laboratoire de Thermodynamique des Solutions, B.P. 32, El-Alia, Bab-Ezzouar, Alger, Algeria. 0378-3812/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0378-3812(97)00018-6

O. Dahmani et al. / Fluid Phase Equilibria 132 (1997) 15-20

16

chloride) for the DISQUAC model. Other group interaction parameters for the UNIFAC method are calculated for the segments CH2C1, CHC1 and CC1 based on data for the corresponding chloroalkanes.

2. DISQUAC and UNIFAC parameters Vapour-liquid equilibrium data for C 4 chloroalkanes with C 7 (paraffinic, naphthenic, aromatic) hydrocarbons were measured for this purpose. The 12 binary systems determined at constant temperature, 323.15 K [3], are listed below. 1-Chlorobutane + n-heptane 2-Chlorobutane + n-heptane 2-Chloro-2-methylpropane + n-heptane 1-Chlorobutane + methylcyclohexane 2-Chlorobutane + methylcyclohexane 2-Chloro-2-methylpropane + methylcyclohexane 1-Chlorobutane + toluene 2-Chlorobutane + toluene 2-Chloro-2-methylpropane + toluene 1-Chlorobutane + 2-chlorobutane 1-Chlorobutane + 2-chloro-2-methylpropane 2-Chlorobutane + 2-chloro-2-methylpropane The data on the above-mentioned systems have been used for the evaluation of the model parameters.

2.1. DISQUAC parameters The notation in this paragraph corresponds to the usage in the DISQUAC method. Chlorine in 1-chlorobutane, 2-chlorobutane, and 2-chloro-2-methylpropane is denoted d l, d 2, and d3, respectively. The parameters Cst,1 are evaluated from experimental vapour-liquid equilibrium data by means of the maximum likelihood method using a program similar to that published in Ref. [4]. The objective function S is defined as N s= L

--Pie) 2 /Or1; 4-(Tie - Tic ) 2 / 0 " T2 ( X i e - x i c ) /crx

q-

2 (Yie -- Yic ) /o~ ]

i=1

where N is the number of experimental points, Pie, Tie, Xie, and Yie are experimental data and Pic, Tic, Xic and yi~ are calculated values for the pressure, temperature, liquid and vapour compositions, respectively. The standard deviations of the pressure, temperature, liquid and vapour compositions were estimated and set at O-p = 0.1% of P, o"r ---0.02 K, o-x = 0.002 and ~ = 0.002, respectively. The DISQUAC parameters for the aliphatic-aromatic ring contact, ab, and for the aliphatic-naphthenic ring contact, ac, are required for the evaluation of the remaining parameters. These two non-polar contacts were treated as entirely dispersive, i.e. Cab.l(quac)= 0 and Cac,l(quac)= 0. The dispersive parameters Cab,l(dis p) and Cac,l(disp) determined at 25°C are available in the literature [5], and in the present work they have been recalculated at 50°C using the hab/RT and h a J R T values

O. Dahmani et al. / Fluid Phase Equilibria 132 (1997) 15-20

17

Table 1 Size parameters Component i

ri

qi

°tai

adl

ad2

°td3

°tci

°tbi

l-Chlorobutane

3.2699

2.7483

0.7742

0.2258

0,0

0.0

-

-

2-Chlorobutane 2-Chloro-2-methylpropane n-Heptane

3.3055 3.3049 4,5847

2.7517 2.8207 3.7891

0.7719 0.7775 1.0000

0.0 0.0 -

0.2281 0.0 -

0.0 0.2225 -

0.0

0.0

Methylcyclohexane

4.1828

3.2586

0.2243

-

-

-

0.7757

0.0

Toluene

3,4761

2.5690

0.2845

-

-

-

0.0

0.7155

-CH 2-

0.6744

0.540

.

.

.

.

.

.

-CCIH 2 -CCIH-CC1 =

1.4654 1.2380 1.0060

1.264 0.952 0,724

. . .

. . .

. . .

. . .

. . .

. . .

from the same source. The calculated values at 50°C are Cab,l(disp) = 0.216 and Qc,l(disp) = 0.039. Table 1 contains the size parameters of the components evaluated according to Ref. [6]. The evaluated quasi-chemical and dispersive parameters are summarized in Table 2, where the contact st is denoted as follows: ad i aliphatic-chlorine cd i naphthenic ring (in methylcyclohexane)-chlorine bd~ aromatic ring-chlorine did 2 chlorine (in 1-chlorobutane)-chlorine (in 2-chlorobutane), d 1d3 chlorine (in 1-chlorobutane)-chlorine (in 2-chloro-2-methylpropane), d2d 3 chlorine (in 2-chlorobutane)-chlorine (in 2-chloro-2-methylpropane), where i = 1 for 1-chlorobutane, i = 2 for 2-chlorobutane, and i = 3 for 2-chloro-2-methylpropane. Parameters Cst,1 are interchange parameters gst/RT. The ad~, cd i, did 2, did 3, and d2d 3 polar contacts are treated as entirely quasi-chemical (i.e. Cst,~(disp) = 0) while the bd i contacts are treated in the zero approximation, i.e. Cst,l(quac) = 0. Table 2 D I S Q U A C parameters st

Cst, l(quac)

Cst, l(dis p)

trp (kPa)

tr r (K)

trx

o~v

ad I ad z ad 3 cd I cd 2

2.071 1.970 1.872 1.909 1.896

0.0 0.0 0.0 0.0 0.0

0.01 0.02 0.03 0.03 0.02

0.00 0.01 0.01 0.01 0.01

0.0012 0.0030 0.0023 0.0026 0.0012

cd 3 bdj bd 2

1.885 _ 0,020 0.0 0.0

0,0 0.867 + 0.010 0.952 _ 0.036

0.03 0.01 0.06

0.01 0.01 0.02

0.0029 0.0017 0.0049

bd 3 d ld 2 d td 3 d 2d 3

0.0 0,012 _ 0.004 0.007 + 0,001 0.028 _ 0.007

1.234 ___0.030 0.0 0.0 0.0

0.05 0.04 0.10 0.08

0.01 0.01 0.02 0.01

0.0038 0.0015 0,0033 0,0021

0.0012 0.0011 0.0021 0.0030 0.0019 0.0036 0.0015 0.0043 0.0034 0,0018 0.0048 0.0032

+_0.011 _ 0.022 + 0,031 + 0.014 + 0.008

O. Dahmani et al. / Fluid Phase Equilibria 132 (1997) 15-20

18

200

2110.

GI

Gn

2O0

2GO,

!

180.

100

100.

80

50.

0

10C

0 0

i i 0.1 0 2

. 08

. . . . . . 0.4 G8 GII G7 0.8 G g

klcle t r g ~ 0 n of ~

1

0 0

~

B

G

m!

--

i * 0.1 0.2

-8G

. . , , . , . , , 0.1 0.2 0 8 0.4 0.6 GO 0.7 GO GO Mole frloUOn OI ONcroMkone

A

* i i | i G8 0.4 0.6 GO G7

A

, i GO Gg

k4o4e IlmoUcn of 0nlar0e.ume

Fig. 1. Excess Gibbs free energy (J tool-n) at 323.15 K for hydrocarbon with (1) 1-chlorobutane, (2) 2-chlorobutane, (3) 2-chloro-2-methylpropane. Hydrocarbons: (a) n-heptane; (b) methylcyclohexane; (c) toluene. Lines, DISQUAC; points, experiment [3]. The procedure for parameter evaluation was as follows. First, the adi contacts were evaluated from the vapour-liquid equilibrium data on the chloroalkane + n-heptane systems. Then, the parameters for the cd i contacts were calculated using the adjusted ad i, the ac parameter from the literature, and the chloroalkane + methylcyclohexane data. Analogously, the bdi parameters were evaluated from the adi, from the known ab parameter, and from the data on the chloroalkane + toluene systems. Finally, the d;d i parameters were obtained with use of the adi, and the chloroalkane + chloroalkane vapour-liquid equilibrium data. Thus, every row in Table 2 corresponds to one relevant system of the 12 binaries. Standard deviations of the parameters and the corresponding standard deviations for P, T, x and y are also reported there.

Devlllkln In ~

~l~on

In ohm

[

~

In

A 8G

o.gg

~

~26

O,N

I '° °

\\ \ \ \~ \\ \\ ~\

°1C

-

\

I

"

- 6 0 - - 4 0 %q0-20 -10

0

10

I 20

~10 40

\

\\

J\\ \'.,.

i

\

\\

_2°

1j

\×\\

,0

r..\

60

-40

-GO

-20

-10

0

' 10

20

t

~K)

-T6

40

-,®

I

-128

!

-leo -40

i ~

-20

J -10

\ 0

T

10

20

~10

40

0¢Mellon In emn

Fig. 2. Confidence ellipses of UNIFAC parameters for the systems n-heptane with (a) 1-chlorobutane, (b) 2-chlorobutane, (c) 2-chloro-2-methylpropane.

O. Dahmani et al. / Fluid Phase Equilibria 132 (1997) 15-20

19

Table 3 UNIFAC parameters n

m

amn

anm

ire (kPa)

trr (K)

~x

try

CH 2 CH 2 CH 2

CICH 2 CICH CIC

130.74 + 9.50 250.90 + 5.82 379.23 + 9.50

99.45 _ 15.44 92.92 _ 9.53 87.23 ± 36.01

0.04 0.02 0.03

0.01 0.01 0.01

0.0010 0.0029 0.0024

0.0011 0.0012 0.0019

Therefore, the experimental excess Gibbs energies for 1-chlorobutane, 2-chlorobutane and 2chloro-2-methylpropane with n-heptane, methylcyclohexane and toluene are shown in Fig. 1 together with the results of the evaluation (not prediction) of the DISQUAC model. Excess Gibbs energies for 1-chlorobutane + 2-chlorobutane, 1-chlorobutane + 2-chloro-2-methylpropane and 2-chlorobutane + 2-chloro-2-methylpropane are not presented since those binary systems exhibit ideal behaviour; the excess Gibbs energy is less than 10 J mol-1. 2.2. UNIFAC parameters

In the UNIFAC group contribution model we have defined three types of chlorine groups: C1CH 2 (such as in 1-chlorobutane), C1CH (such as in 2-chlorobutane) and C1C (such as in 2-chloro-2-methylpropane). Interaction parameters for the chlorine groups + CH 2 have only been evaluated in this work by the correlation of vapour-liquid equilibrium data on the chloroalkane + n-heptane systems using the maximum likelihood method. The estimated standard deviations for the computation were the same as for the DISQUAC procedure. The size parameters for the UNIFAC model are summarized in Table 1. The evaluated parameters a m, anm, their standard deviations and the standard deviations for P, T, x, and y are reported in Table 3. As for the DISQUAC results, the data presented in three rows represent the results of the correlation of the n-heptane systems containing 1-chlorobutane, 2-chlorobutane, and 2-chloro-2-methylpropane, respectively. In Fig. 2, confidence ellipses [7,8] are presented for different combinations of the a m and a m parameters. The regions shown represent the areas in which the parameter values are expected within the indicated confidence level, namely 0.80 and 0.99.

3. Discussion

It should be pointed out that only the evaluation of new parameters for both methods have been carded out in this work. The prediction ability could be subsequently proved with use of relevant data (if available). For adi and cdi, we have found that Cadl, 1 > Cad2,1 > Cad3, l and Ccdl,1 > Ccd2,1 > Ccd3,1 hold. However, for the experimental dipole moments [9] of the C 4 chloroalkanes, /z(primary) (2.05 D _+2%) ~/.~(secondary) (2.04 D +_5%)
20

O. Dahmani et aL / Fluid Phase Equilibria 132 (1997) 15-20

dipole moments of the C 4 chloroalkanes are in inverse order compared with the quasi-chemical group interaction parameters; this may be due to the fact that the dipolar orientations are somewhat sterically hindered. In the bd; contacts, there is only a dispersive contribution. We have observed that the dispersive parameters increase from 1-chlorobutane to 2-chloro-2-methylpropane. These parameters increase when the steric effect "increases". The parameters Calla2,1, Cdld3,1 , and Cd2d3,1 are approximately equal to zero. There are no significant interactions between chlorine groups d 1, d 2 and d 3. For the UNIFAC method the interaction parameters am. increase and anm decrease from 1-chlorobutane to 2-chloro-2-methylpropane.

Acknowledgements The authors would like to acknowledge the partial support of the grant agency of the Czech Republic; this study has been carried out under grant no. 104/96/0571. O.D. would like to thank the Ministere de l'Enseignement Sup6rieur et de la Recherche Scientifique Algerien, Algeria, for enabling this work.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

H.V. Kehiaian, B. Marongiu, Fluid Phase Equilibria, 40 (1988) 23-78. Aa. Fredenslund, J. Gmehling, P. Rasmussen, Vapor-Liquid Equilibria Using UNIFAC, Elsevier, Amsterdam, 1977. O. Dahmani, I. Wichterle, A. Ait-Kaci, Fluid Phase Equilibria, 124 (1996) 135-146. J.M. Prausnitz, C.A. Eckert, R.V. Orye, J.P. O'Connell, Computer Calculations for Multicomponent Vapor-Liquid Equilibria. Prentice-Hail, Englewood Cliffs NJ, 1965. H.V. Kehiaian, J.P.E. Grolier, G.C. Benson, J. Chim. Phys., 75 (1978) 1031-1048. A. Bondi, Physical Properties of Molecular Crystal, Liquids and Glasses, Wiley, NY, 1968. J.V. Beck, K.J. Arnold, Parameter Estimation in Engineering and Science, John Wiley, New York, 1977. T.F. Anderson, D.S. Abrams, E.A. Grens, AIChE J., 24 (1978) 20-29. R.D. Nelson, D.R. Lide, A.A. Maryott, Natl. Stand. Ref. Data Ser. Natl. Bur. Stand., 10 (1967). M.J.S. Dewar, W. Thiel, J. Am. Chem. Soc., 99 (1977) 4899-4907. M.J.S. Dewar, J. Phys. Chem., 89 (1985) 2145-2150. M.J.S. Dewar, J.J.P. Stewart, Chem. Phys. Lett., 111 (1984)416-420. J.J.P. Stewart, MOPAC a Semi-Empirical Molecular Orbital Program, Quantum Chemistry Program Exchange, 455 (1983).