Determination of ternary vlle by p(x1,x2) measurements

195

Fluid Phase Equilibria, 42 (1988) 195-207 Elaevier Science Publishers B.V., Amsterdam -Printed

DETERMINATION

L. KARRER Institut

OF TERNARY

in The Netherlands

VLLE BY P(X,,X2)

MEASUREMENTS

and J. GAUBE fur Chemische

Technischen

Technologie

Hochschule

PetersenstraRe

der

Darmstadt

20

6100 Darmstadt Federal

Republic

Germany

ABSTRACT For determination misciblity constant similar

gap

temperature

excess added

out for the system

Gibbs energy term.

entire fore,

regions. could

Thus,

The apparatus

method

by a NRTL-equation

this mixture

behaves

is

out separately

good representation

be achieved.

0378-3812/88/$03.500 1988Elaevier Science Publiiera B.V.

at The

with an

strongly

non-

for the

with one set of parameters.

had to be carried

a fairly

used

a

at

has been chosen.

of the data was not possible

range of composition data reduction

showing

ethanol/water/cyclohexane

Barker's

is represented Because

ideal a representation

systems

measurements

by Gibbs and Van Ness. Measurements

K. For data reduction ternary

of p(x,,x2)

has been applied.

to that described

have been carried 303.15

of VLE and LLE of ternary

the static method

Therefor limited

of both VLE and LLE

196 INTRODUCTION For the separation nents

or showing

altering

the activity

separated. benzene

of mixtures

azeotropic

Examples

coefficients as entrainer.

characterized

by low boiling

The condensed

vapor

liquid

which

phases

upper

plates

tically

allows

of the distillation

rectification

Despite

the fact that

carried

out in industrial

of mixtures The reason

with

the co-existence with

ternary

heterogeneous

are

azeotropes. into two

the entrainer.

two

liquid

column.

of the mixture

phases

Fig.

exist on the

shows

schema-

diagram

for the

1

ethanol/water/benzene.

rectifications

scale ternary

analysis

lack of knowledge a liquid

are frequently

VLLE data for this type

splits

the application

of liquid

is that the vapor which

of composition

curve frequently

Therefore

and compositions

and condensed

of both phases

must

in the vicinity

into two phases

of the recirculation vapor

is difficult.

be determined.

Ethanol

i342.3K

water Fig.1

with

mixtures

splits

line in a triangular

azeotropic

to be

are rare. for this

in equilibrium condensed.

These

compo-

is added for

are ethanol/water

composition

to recycle

rectifications

the distillation

azeotropic

ternary

of azeotropic

close-boiling

a component

of the components

of such mixtures

or cyclohexane

In such azeotropic

containing

behaviour

Benzene

Distillation line of the ternar) mixture ethanol(l)/waterIZ)/benrene(3) at P i lOSPa

is

of

when method Ratio

197 For

purpose

this

recirculation is collected both

in order

liquid

approach

phases.

and colleagues

librium

Palmer

cell,

to measure

However,

(1972)

analysis

using

task.

static

ternary

Because

vapor

VLLE data.

phase

ratio system.

a static

have carried

containing

of these

problems

measurements

As example

equiliquid

out How-

water

the

is a very

discussed

above we are

for the evaluation

the system

because

of

for the

acetonitrile/benzene/heptane. mixtures

a

vapor

and of both

by gas chromatography

pressure

has been chosen

hexane

have preferred

The authors

for the mixture

of the gas phase

difficult

volume

the

is required

of the vapor

in the case of ternary

ever,

analysis

accurately

of condensed

state of the recirculation

by gas chromatography.

measurements

have constructed

amount

a long time

and Smith

with

(1962)

a sufficient

of the stationary

Therefore, phases

Schmidt

still where

of

ethanol/water/cyclo-

of 'its industrial

importance.

EXPERIMENTAL The apparatus Ness

(1972).

ments

is similar

Their

of several

systems

apparatus

completely

nol/water

(Chaudry

(Balcazar-Ortiz

excess

Gibbs energies

method

of data reduction

authors.

Non-ideal

account

The improved (1987). reached

in about

transfer

along

30 minutes.

must

dosing

by these

the second

into

term.

by Gaube et al.

equilibrium

in the region

by a third

is usually close to the

is necessary.

by the relatively

into the other.

liquid

phase

Using

are moved

the rim of the bottom

Barker's

This

(1985).

phase

be dissolved.

to evaluate

has been extended

is caused

of the second

droplets

et al.,1975),

has been taken

after

in detail

However

by Van Ness

a homogeneous

these

the heavy

truncated

Vapor-liquid

in equilibration

during

droplets

coefficients

of the gas phase

is described

from one liquid

equilibrium

In order

gap a longer time up to 4 hours

was also observed This delay

(Abbott

1953) has been applied

study the apparatus unit.

measure-

non-ideal

1980) and dioxane/etha-

1979).

(Barker,

equation

and dosing

miscibiliby

et al.,

et al.,

behaviour

apparatus

For this

degassing

stirrer

but strongly

and so activity

by the virial

by Gibbs and Van

has been used for p(x,,x2) miscible

such as acetone/chloroform/methanol

acetone/ethanol/water

formed

to that described

results,

(or third) a simple

one or on the surface

droplets

component.

magnetically

like in a merry-go-round

when the second of the

slow mass

Even if in

or third

are These driven either

component

is

liquid when this component

198 is the light necessary

one.

Usually

in order

zone of high turbulence. the long time which overcome

this

Measurements

that

is required

problem

a new stirrer

are

in a and

In order

to

is in construction.

K. Following

ethanoI/-

the procedure

data were taken

is shown

as

moving

the slow masstransfer

out for the mixture

at T - 303.15

in the way which

droplets

for equilibration.

et al. (1975) experimental

proceded

is not as vigorous

these

This explains

have been carried

water/cyclohexane Abbott

stirring

to cause

of

in runs that

in Fig. 2.

Ethanol

Water /

Fig.2

Cyclohexane

Compositions for which total p~e~swe

data have been

taken for the mixture ethanol~I~/water[2l/cyclahexane(3) at T i 303.15 K.

RESULTS

AND DISCUSSION

The results as isobars slopes

of the vapor

pressure

in Fig. 3. This diagram

but also very flat regions

pressure

curve.

the slopes

The straight

of the tie

lines.

measurements is characterized

lines represent

of cyclohexane.

lines represent

The dashed

with good

In Fig. 4 the vapor

are plotted

interpolated

from measurements

by very steep

of the three-dimensional

runs a,b and c (see Fig.21 were

are presented

versus

precision

pressure

of the

the mole fraction

vapor

in the region

pressures

which

of two liquid

199 Ethanol

1104 41

tytlohexane 11622)

Fig.3

lsobsrr

in

10’ Pa

qclmexane(3)

for the mixture ethanDl(i)/water(21/-

at T z 303.15 K Obtained by interpolation

of experimental vapor pressure data.

I

250

P W’Pa 2w

150

100 90 0

0.01 0.02

r

0.03

1

0.04

0.05 x3 -

Fig.4

Vapor pressure for compositions along the PUnS a,b,c (given in Fig.2) versus the mole fraction of Cyclokexkne .A. -we

experimental data interpolated vapor rve~su~e in the two liauld region

200 phases.

The intersections

lines give

of the pressure

approximately

For accurate

and thermodynamically

the co-existence

curve

curve

the co-existence

consistent

the isoactivity

with these

dashed

curve. determination

condition

of

has to be

satisfied. As shown

by Abbott

reduction activity

coefficients

All other equation

,2

+

gE..

g

more

to that

E

gE= gE

+

g

,3

+

are the fitted a=

- C2x2)

has been

In order

the experimental

Since

the excess

is rather

Therefore,

limited

region

Fig. 2. In tables

reduction to obtain Omitting

a fairly

binaries. and

term

good

were

corner

in

of the pure parameters iS

iS absolutely

necessary

of the experimental

in a root mean

of

For this data

of ~~~~~~~~~~~~~~~~~

term results

out for a

as indicated

and the fitted

good representation

it

of

of this ternary

pressures

term

as

slopes

curve

is capable

set 1) are given. ternary

handled

steep

pressure

which

of

of

data.

has been carried

ethanol

square

parameters

show similar

a gE function

coefficients

The additional

representation

parameter

and ternary

1,2 and 3 the vapor

the ternary

ternary

range of miscibility

to-the

the root mean

RMS = 0.0981.

(1)

x2 x3

(Gmehling

both the binary

functions

(see parameter

a fairly

x,

for the constituent NRTL equation

a data reduction

the virial

RMS = 0.0129.

et al. used an (1953)

as the three-dimensional

to find

close

the gE function

to obtain pressures

the entire

system.

components,

functions

Gibbs energy

hopeless

representing

Abbott

and so

measurements.

by numerical

R T (Co - C,x, - C2x2)

for both binary

and very flat regions

pressure

by Wohl

and the added ternary

parameters

of data

gE values

x, x2 x3

vapor

the NRTL equation

method

reduction

0.3 and the added

R T (Co - C,x,

fitting

complex.

study the ternary

1977) with

used.

vapor

of data

proposed

E 23

In the piisented Onken,

methods

are vastly similar

Barker's

way to obtain

from ternary

alternative

techniques

where

et al. (1975)

is the only useful

square

of

data.

TABLE 1 Summary of the properties

physical

of the components

T/K

ethanol(l)

water(2)

cyclohexane(3)

property

pi Sat/102Pa

a)

303.15

104.4

42.4

162.2

Pig

b,

293.15

0.7893

0.99823

0.7785

b)

_

46.07

18.01528

84.16

cms3

M/g mol-'

a) Values determined b, Values given

in the given measurement

in the CRC Handbook

(1986)

TABLE 2 Virial coefficients

used in the Barker Algorithm

Bij/cm3mol-'

ethanol(l)

water(2)

cyclohexane(3)

ethanol(l)

-2594 a)

-1544

-1615

water(2)

-1544 b,

-1080 a)

-1370

cyclohexane(3)

-1615 c,

-1370 c'

-1700 a)

a)

Dymond and Smith (1980)

L); Noppe et al. (1981) Calculated

by the correlations

of Tsonopoulos

(1974)

202

TABLE

3

Values

of the parameters

Barker

Algorithm

hexane(3)

for the GE function

for the mixture

at 303.15

Different

Set

-1 mol-l

A21'ca1

mol-l

A13'ca*

mol-l

A31'ca1

mol-l

A23'ca* A32/cal

mol-l

mol

Set 3

657.502

1191.247

1129.781

915.271

27.892

208.315

44.146

1288.877

Set 4

1554.572

1317.139

226.689

-117.388

219.179

1720.836

3763.641

3458.627

3283.591

1274.704

1643.641

2259.205

2308.771

1020.390

0.300

0.300

0.300

0.300

0.300

0.300

0.300

0.300

0.300

0.300

0.300

0.300

43

u2

Set 2

1

745.774

a13

Cl

Sets

892.444

a12

CO

by the

K

Parameters

A12'ca1

obtained

Ethanol(l)/Water(2)/Cyclo-

1766.824

251.613

113.907

-2171.633

-305.054

-137.020

-689.393

-180.888

240.726

-81.349

159.712

Aij = gij - gii

(Renon and Prausnitz,

745.799

1968)

Fig. 5 shows regions of negative ( <-0.01 ) and positive values ( >O.Ol) of the relative deviation (p,,p- pcalc)/p,xp. It is obvious that the function is not flexible enough to describe

the steep

ethanol/water co-existence

as

slope of the pressure

well

curve.

as the flat

This

region

is demonstrated

curve

towards

the binary

in the proximity by a pressure

of the

curve

for

203

Ethanol

0.50 Cyclohexane

Flg.5

Devlatlons

~~,,P-P,,~~)/P,~~

d.e,f,g

(given

in

= APIPexp 21 and the

Fig.

for

the

binaries

Puns

containing

ethanol -

APIPexp

>

m

APIPexp

c -0.01

-

-0.01

constant

<

0.01

AP/P,,,

0.01

ratio of the mole fractions

in Fig. 6. However, cients

5

in order

on the co-existence

pressure

data

in the

to evaluate

properly

proximity

in detail

as indicated

the activity

curve we must

immediate

This has been discussed

ethanol/water

coeffi-

fit the

of the miscibility

for binary

mixtures

gap.

by Gaube et

al. (1987). The slopes

of the tie lines could

by pressure

measurements

the end points

added

ternary

be determined

using expressions term)

pressure

which curve

were obtained in the

curve

are shown

in Fig. 7. The activities are plotted

Fig. 8. The isoactivity

versus

by fitting

immediate

see table

3, sets 2-4).

along

the tie

is well

with

the three-

proximity

the mole fraction

condition

of all components

(NRTL-equation

for gE

existence extensions

(parameters

very accurately

(see Fig. 3). In order to evaluate

of the tie lines the activities

were evaluated dimensional

only

of the coThese

regions

line and its

of cyclohexane

satisfied,

in

for example

204

al ’

x,' = 0.552

’ = 0.400 x2 ’ = 0.048 ’ = 0.500 ’ = 0.460 x2

a3' = 0.91

With a few tie

Comparison

U = 0.91

al

’ = 0.040

Fig.6

' = 0.92

’ = 0.78 ’ = 0.72 a2

x1

sufficiently

al U = 0.74

a3

x3

x3

= 0.75 ’ = 0.65 a2

a2 a3 al

U = 0.65

H = 0.77 H = 0.68

a2 a3 N = 0.91

lines the location

the calculated

pressure cum

and

the

experimental data v?rsus the mole fraction of cyclohexane (run dl

x2 x3 x1

’ = 0.060 N = 0.740 H = 0.130

' = 0.056 x2 x3 ' = 0.814

of the co-existence

determined.

of

x1 U = 0.200

curve

is

205

Ethanol

Cytlohexanc

water

Fig.7

Coexistence curve of the mixture ethanol(l)/water(2)/cyclohexane(31 evaluated by vepor pressure measurements and the isoactivity condition

I

I

255-

‘\

P 10'Pa 245-

235-1

I

1.0 a3

a, 0.5

0 1

Fig.8

Interpolated vapor

pressures

vater(Zl and cyclohexane(3)

end activities of ethanol(l). versus the mole fraction of

cyclohexane along the upper line given in Flg. 7

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at

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Austral.

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second

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virial

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Co;C@2 g

molar

excess

M

molar

mass

P pi

sat

pressure vapor

coefficient

of added Gibbs

ternary energy

(cm3 mol -') term (J mol-')

(g mol -I)

(Pa)

pressure

universal

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gas constant

;

density

T

temperature

(g cme3)

X

mole

fraction

(K)

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parameters

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