Calculation of vapour-liquid and liquid-liquid equilibrium by an equation of state

121

Fluid Phase EquzYibria, 13 (1983) 121-132 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands Calculation

Vapour-Liquid

of

and

an G. Instrtut

of

R.A.S.

Kolasinska,

fuer

Liquid-Liquid

Equation

Technische

Equrlibrium

Moorwood,

Chemie

by

State.

II,

H.

Wenzel

Egerlandstr.3,

852

Erlangen,

FRG ABSTRACT The

equation-of-state

method

pour-lrqurd

and

parameters.

Essentially,

parameter ted

is

form

used

systems

The

well

as

a

both

srngle

“a-

set

of

temperature-dependent

system.

Ternary one

systems

or

perfluorocarbon

furfural,

nitroethane,

tonitrrle,

describe

adjustable,

involved a

substances:

methane,

to using

are

predic-

alone.

considered as

associated

brnary

data

applred

equilibria one

per

binary

components

is

liquid-liquid

formic

nitrobenzene,

acrd,

or

non-associating

one

methyl

phenot

1,2-ethanediol,

two

or

of

the

following

acetic

acid,

formate,

nitro-

aniline,

diethytene

ace-

glycol.

INTRODUCTION

in of

a

VLE

prevrous

paper

oatcutatrons

gen-bonding

and

such

in

some

some

resu1

wrth

systems

one

using

equa-

a

result

Included

these

method

ts

hydro-

the as

calculations

cases,

the

others,

reported

association

the

In

we systems

assuming

Occasionally,

separations.

while

duced,

al,lg82) ternary

treated

method

bonding.

phase

et and

We

(EoS)

hydrogen

quid

Wenzel

brnary

substance.

tron-of-state of

(

cn

were

Ii-

welt

obvrousty

repro-

requrred

im-

provement. The

purpose

of

the

whether

matically models

is

-liquid

able

to

MIXTURES In

to

pure

We from

VLE and

where

a

this

in 105

we

have

To aniline, found ciated

at

the

liquid

had

29

Include to for VLE substances

0378-3812/83/$X13.00

binary

had

We

already to

different LLE, make

work, on We

the

substance associated hydrooar-

certain

halo-

an

we aqueous

and

calculated their with

I

methaetre-

all

relevant

(lQ79,1Q80),

ternary

substance

a

mode

excluded systems

Arlt

the

associated

and

inert

association

considered

Sdrensen

them

and

an

reported

calculated

estimate

a

form

containing

this

in

also

of of

saturated

found

1979)

an

is

to

sub-

inert.

LLE

of

pure

mixtures

alkenes

already

collection

a

properties

inert

able

practice,

be

to

al.,

systems. involving

in an

nor rn

already

et

able

We,=

systems

and

for the

equilibria

however, we

water:

collection

else

syste-

association

(VLE)

model

benzene,

the we

calculations;

provided

more with

consider

context,

found

studied

altogether

this

extent,

which

data

phase itself

are

for

to

substance;

lesser

(Baumgaertner

binary

also In

another to

therefore

t ante

investigate

vapour-liquid

only

associated

hydrocarbons

subs

to

conjunction

association

not

inerts.

with and

genated

both

adequate

but

neither

species bans,

an

necessary

with is

nol

find is

substance

substance that

for

in

(LLE).

i t

the

is

method

STUDIED

order

stance,

paper

EoS

account

equilibria

THE

present

the

and

constituent

in

systems two

inerts,

binaries

sufficient

or

accuracy

(17

temperatures). we slight

found it necessary, modifications

calculations. considered

to

Column

1

in

present

the

of

with the

the models

Table

0 1983 Elsevier Science Publishers B.V.

1 study.

lists

except ton previously the

asso-

of

122

METHOD

OF

Our

CALCULATION

method

described state p

=

to

combine

elsewhere of

the

association

(Wenzel

van

der

et

Waals

RT/(V-b)-a(T)/(V2

+

with

al.

, 1982).

the We

EoS used

model an

has

been

equatton

of

type:

(1+3w)bV

-3wb2)

(1)

the acentric factor w is introduced into the equation of Here, state in such a way that the form of the attraction term becomes substance dependent. We used a single interaction parameter defined as usual in the mixing rule for parameter a :

‘i

=

z:I:

while

xi

(I

xj

the

mixing

-

ei

(aiaj)1’2 ,

, j)

rule

for

(2)

b,

b =

Z x.b. does not &ontain an adjustable unlike-pair ties h and g are the corresponding mixture be used in eq.(l).

TABLE

1

Association

compound

models

model

furfural

of

pure

association factor at Tr=0.6

parameter. values of

The quantia and b to

substances

oligomer

- AS kJ/mol/K

-AH kJ/mol

l-2-3

1.72

dimer trimer

83.96 169.70

18.89 38.14

formic

acid

l-2-3-5

3.79

dimer trimer pentamer

143.33 240.26 434.57

60.57 94.07 160.73

acetic

acid

l-2-3-8

2.19

dimer trimer octamer

144.48 244.28 741.45

59.98 93.65 260.36

nitromethane

l-2-3

2.51

dimer trimer

100.58 176.24

17.38 44.72

nitroethane

l-2

1.74

dimer

85.88

20.39

nitrobenzene

l-2

1.66

dimer

81.84

19.49

methyl

l-2

1.65

dimer

104.14

22.46

aniline

l-2

1.31

dimer

86.37

25.51

acetonitrile

l-2

1.98

dimer

80.44

21.36

1,2-ethanediol

1-2

1.22

dimer

128.38

40.80

phenol

l-2

1.66

dimer

110.12

26.63

l-2-3

2.09

dimer trimer

83.18 248.49

23.26 85.92

formate

diethylene

glycol

123

We discovered that there is some freedom in the choice of the association model for a particular pure component and were able to use this freedom to achieve a better description of LLE. Originally, in the routine that determines the parameters of our the objective functions comprised deviapure-component models, liquid and vapour density of the pure tions in vapour pressure, component under consideration as well as deviations in binary VLE calculations. To improve LLE calculations, we included here the deviations in binary LLE as objective functions. Apart from a of adjustments to improve convergence behaviour, no furnumber ther modifications were applied to the method, In all LLE calculations the interaction parameters 6 were made temperature dependent, following a linear relationship, since the calculation of LLE was found to be more sensitive to the choice of interaction parameter than that of VLE. RESULTS OF CALCULATION Pure-comaonent models The new models found are aiven in Table 1: for instance. furfural is described by a l-2:3 model, i.e. its model comprises monomeric, dimeric and trimeric species: its association factor at a reduced temperature T = 0.6 is 1.72: this means that the average number of monomers fn a molecular species is 1.72: in the case of complete dimerixation, Its value would be equal to 2. AS and AH are the entropies and enthalpies of association, reap. As an example, the critical data of the individual constituents of furfural are given in Table 2. TABLE 2

Critical data T P and acentric factor for the asaociation model oE'furfura1.

Tc/K

pc/HPa

acentric factor

values

670.0

5.89

0.383

monomer dimer trimer calculated value of furfural

649.1 722.8 930.7

6.122 2.746 2.153

0,398 0.531 0.666

670.0

5.89

-

Substance experimental

The representation of pure-component properties is comparable to that of the previous models: the vapour pressure still can not be described with the desired accuracy over a wide temperature range. Table 3 compares experimental and calculated vapour pressures of furfural. TABLE 3: Experimental pcalc of furfural T/K /kPa P pEzyc/kPa

329.1 1.76 1.75

and calculated vapour pressures pexp 358.1 7.25 7.29

376.5 1.571 1.564

394.0 29.74 29.84

409.1 48.94 49.36

and 424.9 77.25 79.81

124 liquid molar volumes at T = 0.7 While the calculated are etfianediol car rect to within 2% for formic acid, furfural, and diethelene glycol, this property exceeds the experimental values to the order of 20% for acetic acid, nitromethane, methyl formate nitrobenzene and the deviation approaches 50 % for and acetonitrile and nitro-ethane: the value for phenol is 13% . Liauid-liauid eauilibrium test the adequacy of the mixing rule eq.(2) for LLE calcuTo lations, we started with systems where association could be excluded. Suitable examples are systems of perfluorocarbons with hydrocarbons or inert halogenated hydrocarbons. Fig. 1 shows the results for the system perfluorocyclohexane - tetrachloromethane. Using experimental critical data for perfluorocyclohexane, Fig.1 Suspecting that these might be due to reveals some deviations. inaccurate experimental critical data, we also estimated critical data using a method described earlier(Schmidt,Wenfor Z&a btained deviations of the opposite ze1,1981) sign (dashed Since the differences in critical data were small line in Fig.1 we concluded that they are probably within experimental error and we therefore decided to retain the mixing rule eq.(2).

Fig.2LL.E

Fig.3

perlluorohnmc

-

hcxane

125 our calculations to all systems available to us We extended involving a perfluorocarbon and an inert. The system perfluoroThe remaining results are sumhexane-hexane is shown in Fig.2 . marized in the appendix in Table 4. Fig. 3 compares experimental. and calculated values for a ternary system: throughout this work, we predict ternary data from binary data alone. Proceeding now to associated substances we first chose furfural. An attempt to predict liquid phase separation in the system furfural - heptane without association results in the dashed line is in Fig. 4: the full line shows the result when association included. In Fig.5, the system furfural - cyclohexane is given as a further example. Fig. 6 shows both LLE and VLE of the system furfural - 2,2,4_trimethylpentane at atmospheric pressure, using our interaction parameter 0 varies here between a uniform model: 8 = 0.085 at 300 K and 0.05 at 400 K. The result obtained by the Wilson equation is also shown. The experimental VLE data and the Wilson parameters were taken from the data collection of Gmehling et a1.(1979). Fig.7 reveals that the characteristic shape of an equilibrium with a substance of higher molecular weight is also well reproduced. However, the low concentrations show deviations: the calculated mole fraction of docosane (C whereas the ex$ZZ$~lnt~l'"v'~YC' Si e.g. T =353 K is 0.0026, 0.0067. the Fig. 8 shows a ternary system involving furfural; circles represent binary data extrapolated from the experimental ternary data.

*

a . *

.

fi

Fig.8

126 Further results for binary LLE calculations are given in Table Some more graphical representations are given of systems that 4. in the system aniline - hexane, are relevant to ternary systems: between the full and the dashed line shows that Fig.9, comparison our model reproduces the data by Keyes and Hildebrand better than those by Drucker. The differences between experiment and calculation in the system aniline - methylcyclohexane (Fig.101 are prowithin experimental uncertainty. The ternary system mebably thylcyclopentane-hexane-aniline (Fig.ll)is only in fair agreement with experiment because extrapolation of ternary data (circles) suggests a relatively wide immiscibility gap for the system aniline - methylcyclopentane at 307.5 K while the present method predicts a smaller gap; however, according to the binary data by Pennigton and Marwil (1953) this binary system should be completely miscible at 307.5 K. Another example is acetonitrile: the binary system acetonitrilehexane is well represented (Fig.121, but the ternary heptane benzene - acetonitrile (Fig.131 shows strong deviations: the binodals with full and dashed lines use different 6 - values for the binary system acetonitrile - heptane.

0

Fig.9 0

LLC

.2 MINILINI

- kyer.

.4 -

.6

ttcw

Hlldrbrand ,917 x - Drvckcr ,923 -,----calcul.trd by ms

.B

1.0

127

Our VLE calculations for the binary system acetonitrile-benzene This might indicate that we did not yield good results either. have not yet found an appropriate model for acetonitrile or that salvation occurs between acetonitrile and benzene. also appears to be a problem in conjunction with diBenzene Several authors have provided measurements for ethylene glycol. but the data are not in good agreement, Fig. this binary system, 14 shows two attempts to fit these data: neither of them gives the system diethylene glycol -heptane (Fig.151, good agreement: however, is well reproduced. The ternary system diethylene glycol - heptane - benzene (Fig.16) at T = 398 K shows strong deviations in the slopes of the tie-lines.The interaction parameter used for the system diethylene glycol - benzene is the one that produces it appears that a correct representathe full line in Fig.14 : solution tion of the ternary (Fig.161 would require a critical leading to an immiscibility higher than T = 398 K , temperature gap in the binary diethylene glycol - benzene as indicated by the however; this would be in contrast to- the circles in Fig.i6: binary data shown in Fig.14.

d

Johnson.

Fran&s

1954

~'Skinner

1955

Fig.16

128

Vavour-liauid eauilibrium we applied the new models developed for LLE to calculate When Only in VLE we obtained in general comparable or better results. a feu cases the data was less well reproduced. From the fairly large number of systems calculated we arbitrarily selected the results with furfural: they are shown in a conform in the appendix in Table 5: the Table reveals that densed several systems are described better by EoS than by the RedlichKister equation, despite the lower number of adjustable parameters used in the EoS method. DISCUSSION There are some trends noticeable in Table 4: the interaction 8 tend to assume the highest values for alkanes and parameters decreasing for i-alkanes, alkenes, halogenated hydronaphthenes, In some cases, e.g. phenol with alkanes, carbons and aromatics. these values are nearly constant, thereby allowing the prediction of similar systems. However, there are a number of exceptions to thiophene and possibly in this rule: obviously, carbon disulfide, some cases benzene may not be treated as an inert. The scattering of S and especially of u indicates the presence Some of the LLE data are quite old experimental errors. and of results of different authors are often inconsistent. These the experimental errors make it difficult to assess the adequacy of the pure-component data to which we fit our our models. Moreover, model parameters may be unreliable: it happened on several occasions that a first association model for a substance yielded poor and then a second one, results, based on a different set of vapour pressure data for this substance, led to a good description of LLE data. We therefore tend to assume that the EoS method is basically able to treat liquid-liquid equilibrium between an associated compound and an inert, and that the observed deviations- are primarily due to experimental errors of either the data to which we fitted the model parameters or the data uith which we compared the results of LLE calculations. The prediction of ternary systems from binary data mainly depends on how well the corresponding binary systems are reproconsistent with the duced and on whether the binary data are ternary data. Where the temperature of a ternary system is only a few degrees higher than the critical solution temperature of one of its binary systems. a correct reproduction of this latter is important. The next step in developing the EoS method to LLE is Its apto mixtures containing more than one associated plication substance. In this area, we have so far only treated VLE - systems Wenzel 1982) and found that allouing alcohol - esters (Skrzecz, for solvation in these systems yielded satisfactory results. LITERATURE Baumgaertner M.. Iioorwood. and H. Wenzel, 1979. Phase R.A.S. by Equation of State for Aqueous Equilibrium Calculation Systems with Low Mutual Solubility. Thermodynamics of AqueACS ous Systems with Ind.Appl., Stephen A. Newman, Ed. D.C. 1980. Symp.Ser. 133, Washington Vapor-Liquid Equilibrium Gmehling J., U. Onken, W. Arlt 1979. Data Collection. Chemistry Data Series Vol.1, Parts 3+4.

Maczynski A., 2. Haczynska, T. Treszczanowicz, K.Duna]ska. Verified Vapor-Liquid Equilibrium Data. Vol.4 . PWN-Polish Scientific Publishers, Warsaw 1979. Schmidt G., H.Wenzel, 1981. Estimation of Critical Data by Equa. tion of State. Can. S. Chem. Eng. 59: 527-531 Skzrecz A., Wenzel H. 1982, unpublished results. Serensen J.M., W.Arlt 1979. Liquid-Liquid Equilibrium Data Collection. Dechema Chemistry Ser., VOl.V, Part 1.2 and 3, Frankfurt 1979/1980 Wenzel H., R.A.S. Moorwood, and M.Baumgaertner, 1982. Calculation Equilibrium of Associated Systems by an of Vapour-Liquid Equation of State. Fluid Phase Equil. 9: 225-266 Wingard R.E., Durant U.S., Tubbs H.E., Brown W.O., 1955. Ind. 47: 1757 Eng. Chem.

ACKNOWLEDGEHENT The authors wish to thank DEUTSCHE financial support.

FORSCHUNGSGEMEINSCHAFT

for

APPENDIX TABLE 4 : Results of binary LLE calculations. ( Lit.: page number in data collection by Serensen and Arlt.1979: N: number of data pairs compared smoothed values taken if available; o : average shortest distance in mm betueen calculated curve and experimental data in a quadratic diagram of 100 mm side length: if two values are given, the first excludes the CST region, 9 : average value of interaction parameter in the grven temperature range) Substances

cvclohexane.methvl.oerfluoro + methane,tetrachloro methane,trichloro benzene,chloro benzene toluene

Lit. temper. range K

1 3:; 338 437

298-318 363-393 333-353 338-358

1:; 341 437 440

298-323 323-343 298 373-383 298-318 291-295

hexane.oerfluorQ + carbon disulfide hexane benzene tetradecane

102 315 315 317

298 278-293 303 298

o

1 4 1 1

e 3 xl0

2"*: 3:6

101 109 132 135 132

:*: 0:04 1.4 0.55 0.70

81 82 129 96 129 110

0.11 1.1 0.27 1.4

231 129 159 144

2.4 0.50

278-298

heotane.Derfluoro + methane,tetrachloro methane,trichloro carbon disulfide benzene heptane pentane,2,2,4-trimethyl

4

N

130 Table

4. cont.

Substances furfural+ cyclopentane cyclohexane cyclopentane,methyl butane,2,2_dimethyl butane,2,3_dimethyl hexane pentane,2-methyl cyclohexane,methyl heptane pentane,2,4_dimethyl octane pentane,2,2,4_trimethyl hexane,2,2,5-trimethyl decane docosane formic acid + methane,tetrachloro methane,tetrabromo carbon disulfide benzene toluene acetic acid + carbon disulfide cyclohexane octane nonane decane hendecane dodecane methane.nitro t carbon disulfide butane,2_methyl cyclohexane 2-pentene,2_methyl butane,2,2-dimethyl .butane,2,3_dimethyl hexane pentane,2-methyl pentane,3-methyl heptane pentane,2,4_dimethyl 2-heptene,2-methyl 1-octene octane pentane,2,2,4_trimethyl ,pentane,2,3,4_trimethyl 1-nonene hexane,2,2,5_trimethyl nonane

decane hendecane dodecane

Lit.

temper. range K

257 258 258 261 261 262 262 264 264 267 268 268 268 270 270

293-308 293-323 293-333 293-313 293-313 293-343 293-323 293-343 293-363 293-333 293 298-363 293-373 293 333-393

: 19 22 24 97 123 125 125 125 129 129 24 30 33 35 35 38 38 41 41 45 48 48 51 59 59

62 62 71 71 76 76 79

298 298 193-E 298 274-276 274-276 290-291 296-301 298-311 308-323 318-333

N

o

:

2.1 1.9 1.3

91 96

1.0

7': 81 85

6 5 5 7 : 9 6 : 10 1 4

: 1 7 1 3 3 3 : 4 4

1.4 2.1

63 xl0

to" a.: 95 2:o 86 1.4 103 1.3 81 2.1 1.2/2.3 84 110 1.7 81 0.50 2. 6 2.0 EO

182 151 164 240

3:s

171

15.0 13.9 0.70 1.2 1.2 0.40 0.50

71 109 115 115 121 121 118

.298-333 5 5.518. 144 4 355-367 134 3.1 288-363 10 0.60 166 318-333 4 0.50 128 353-368 4 141 4.8 358-368 3 139 5.1 365-373 3 3.4 143 358-368 3 144 4.2 353-368 4 149 4.7 323-373 4 162 1.5 358-373 4 308-353 6 0.93;:.6 ::: 328-348 5 1.3 128 323-383 7 l-312.4 166 367-377 4 3.5 129 367-375 3 3.9 139 343-358 4 2.2 124 368-383 4 3.5 135 298-283 10 0.711.3 172 393 I 2.8 132 393-398 2 2.7 134 398-403 2 2.5 130

131

TABLE 4, cont. Substances

Lit. temper. range K

N

0

e3 xl0

ethane.nitro + hexane pentane,2-methyl octane pentane,2,2,4_trimethyl decane

138 140 142 144 146

278-303 278-298 278-313 278-298 283-323

8 5 6

:*:9 1:s 1.4 1.8

::: 119 109 117

benzene.nitro hexane

327

273-288

4

0.25

59

ester t 132 134 134 134

259-273 268-283 278 285-287

5 4 1 2

0.40 0.50 2.4 3.0

124 119 116 112

:

+

formic acid.methyl heptane cyclooctane octane nonane

aniline+ 2-butene,2-methyl cyclohexane cyclopentane,methyl butane,2,2-dimethyl hexane cyclohexane,methyl heptane pentane,2,2,4_trimethyl docosane

279 365 367 367 367 370 370 371 371

277-285 298-303 288-303 288-298 298-333 298 298-323 313-343 298

: 5 4'1 6 4 1:1 2 1.1 5 1.8/4.0 1 2.4. 4 2.4 4 0.30 1 0.55

55 73 70 67 71 76 51 46

acetic acid.nitrile carbon disulfide hexane heptane tridecane pentadecane

97 110 110 115 115

288-323 293-313 298 303-333 298-303

6 5.5/12. 1.3 1.3 0.50 0.16

116 173 185 194 184

157 154

296-353 298-353

phenol + butane,Z-methyl nentane hexane pentane,2-methyl heptane octane

299 302 351 353 353 356

298-333 313-328 318-323 308-328 308-323 293-318

+ diethylene benzene heptane styrene benzene,l,2_dimethyl benzene,ethyl

249 252 252 252 255

293-353 323-433 298 313-393 298

1.2-ethanediol benzene thiophene

+

t

67 0:90 :': 2.5

63 60 58

1.8 1.5

6":

1.8

0.25 3.4 2.3 0.90

28 131 40 67 51

132 TABLE

5:

Results with

an

of binary Inert.

VLE

oalou

ations

for

turfural

colLection of Maczynskl et data-set number In the data for W = data by W ngard et al., 1955 ; N =except data palrs avantable; ti = interaction parameter, eq.C2) =average shortest distance between experimental points and

( ref. : 1979, al _ number of

:

Q

calculated equilibrium curve using our' equation of state, as in Tab.4 . d = deviation as defined in the data collection by Nacusing the Redlich-Kister equation (R.Ki.1 or zynski et a1.,1979, our equation of state (EoS) 1 Inert

Temp/press

EoS

EoS

R.Ki

EoS

R.Ki

ullq

=vap

dllq

dliq

dvap

dvap

6+x 3

ref

K /kPa

cyclohexane

1

p=lOl.3

IO

0.7

2.1

1.6

2.1

3.7

4.0

86

hexane

1

p=lOl.3

12

1.2

1.3

1.6

6.7

1.6

2.9

80

methylcyclohexane

0.9 3' 0.5

0.9

f

0.8 0.1

0.4

0.9

0.7

p=lOl.3 p=lOl.3

heptane

N

EoS

13 9 3

lo

8": 2.4 1.9

::5"

3.9 1.5

80 80 85

octane

1

p=lOl.3

13

4.2

3.2

3.4

2.7

5.4

4.4

77

i-octane

2 1

T=298.2 p=lOl.3

4 10

4.8 1.4

2.5

0.9 0.7

0.0 2.8

2.5

4.3

107 54

1

p=lOl.S

11

1.9

3.6

1.0

2.4

3.1

5.4

77

p= 26.7 p= 40.0 p= 53.3 p= 80.0 p=lOl.3

35 35 35

0.5 0.5 0.5

i-8 0:8

::: 0.5

1.9 1.6 1.8

1.7 1.2

3.5 3.2 4.4

18 15 13

decane toluene

2"; 0":: II 9 A::

0"*5" ::: 2:9 ::: 1.3

04:;

A.: 0:s ::7" 5.3 10.9 2.5 0.6

1':

0.5

I.5

32

::6"

:A

ethylbenzene

1

p= 96.4

I6

I.6

2.4

0.7

p-xylene

1

p= 96.4

20

1.5

1.8

0.6

tetralin

1 2

p= 3.6 p= 13.3

95::

08 4:6

::6'

5.3 3.9

9.8 1.5

-16 33

2 1

T=298.2 p=lOl.3

1:

::6'

2.1

0.1 1.9

0.2 6.7

3.5

10.0

';

w

p=IOl.3

9

I.5

1.0

1.9

5.4

1.4

1.4

79

benzene

CCL4

6 1.7 5 10.3

2.5

35

1.0