Prediction of Isobaric Vapor-Liquid Equilibrium Data for Mixtures of

6 Prediction of Isobaric Vapor-Liquid Equilibrium Data for Mixtures of Water and Simple Alcohols

Downloaded by HARVARD UNIV on May 31, 2014 | http://pubs.acs.org Publication Date: August 1, 1974 | doi: 10.1021/ba-1972-0115.ch006

A. ANDIAPPAN and A. Y. McLEAN Annamalainagas University, Tamifnedu, India and Nova Scotia Technical College, Halifax, Nova Scotia

The Non-Random, Two Liquid Equation was used in an attempt to develop a method for predicting isobaric vapor– liquid equilibrium data for multicomponent systems of water and simple alcohols—i.e., ethanol, 1-propanol, 2-methyl-1propanol (2-butanol), and 3-methyl-1-butanol (isoamyl alcohol). Methods were developed to obtain binary equilibrium data indirectly from boiling point measurements. The binary data were used in the Non-Random, Two Liquid Equation to predict vapor-liquid equilibrium data for the ternary mixtures, water-ethanol-1-propanol, water—ethanol-2-methyl1-propanol, and water-ethanol-3-methyl-1-butanol. Equilibrium data for these systems are reported.

/

T p h e d e s i g n of a z e o t r o p i c o r extractive d i s t i l l a t i o n c o l u m n s , as w i t h c o n A

v e n t i o n a l c o l u m n s , d e m a n d s a k n o w l e d g e of the v a p o r - l i q u i d e q u i l i b -

r i u m p r o p e r t i e s o f the system to b e d i s t i l l e d . S u c h k n o w l e d g e is o b t a i n e d e x p e r i m e n t a l l y o r c a l c u l a t e d f r o m o t h e r properties of the c o m p o n e n t s o f the system.

S i n c e the systems i n a z e o t r o p i c o r e x t r a c t i v e d i s t i l l a t i o n

processes h a v e at least three c o m p o n e n t s , d i r e c t m e a s u r e m e n t

of t h e

e q u i l i b r i u m p r o p e r t i e s is l a b o r i o u s a n d , therefore, expensive, so m e t h o d s of c a l c u l a t i o n o f these d a t a are d e s i r a b l e . F o r a z e o t r o p i c d i s t i l l a t i o n e s p e c i a l l y the systems are n o n - i d e a l w h i c h makes c a l c u l a t i n g v a p o r - l i q u i d e q u i l i b r i u m p r o p e r t i e s m o r e difficult t h a n , for e x a m p l e , i n d i s t i l l a t i o n of m i x t u r e s of s i m p l e h y d r o c a r b o n s . W o r k p r e d i c t i n g the v a p o r - l i q u i d e q u i l i b r i u m properties of t e r n a r y m i x t u r e s o f 93 In Extractive and Azeotropic Distillation; Tassios, D.; Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

94

E X T R A C T I V E

A N D

A Z E O T R O P I C

DISTILLATION

water, e t h a n o l , a n d o n e of the s i m p l e alcohols—i.e., 1-propanol, 2 - m e t h y l 1-propanol, 3 - m e t h y l - l - b u t a n o l , ( a l l f o r m b i n a r y azeotropes w i t h w a t e r ) — i s p r e s e n t e d here. A q u e o u s solutions of these alcohols o c c u r w h e n sugar solutions are fermented

a n d m a y b e separated b y d i s t i l l i n g t h e m i x t u r e s .

It is a

c o m m o n , e c o n o m i c a l l y v a l u a b l e process for m a n u f a c t u r i n g p o t a b l e l i q u o r s a n d for p r o d u c i n g i n d u s t r i a l a l c o h o l f r o m f e r m e n t e d molasses solutions o r p u l p m i l l wastes.

O n e of the authors ( A . Y . M . ) reports t h a t d e s i g n

a n d o p e r a t i o n of these c o l u m n s is h a m p e r e d b y l a c k of v a p o r - l i q u i d e q u i l i b r i u m d a t a , e s p e c i a l l y for m a k i n g p o t a b l e l i q u o r s , w h e r e

small


a m o u n t s of t h e alcohols other t h a n e t h a n o l greatly affect the flavor a n d , therefore, the p r o d u c t ' s m a r k e t a b i l i t y . Prediction of Vapor—Liquid Equilibrium

Data

A system c o n s i s t i n g of a l i q u i d m i x t u r e a n d v a p o r is i n e q u i l i b r i u m if, for a n y c o m p o n e n t i, the fugacities i n the v a p o r a n d l i q u i d phases, fi

Y

a n d /i

L

are e q u a l .

/i = /, V

(1)

L

A s the fugacities are not i n themselves q u a n t i t i e s w h i c h are easily estab l i s h e d e x p e r i m e n t a l l y , i t is necessary to relate t h e m to easily d e t e r m i n a b l e quantities—e.g., t e m p e r a t u r e , pressure, a n d c o m p o s i t i o n .

T h i s is d o n e

b y i n t r o d u c i n g the f u g a c i t y a n d a c t i v i t y coefficients Φ* a n d y ι w h i c h are defined as f o l l o w s ,

w h e r e y is t h e c o m p o s i t i o n o f c o m p o n e n t f i n t h e v a p o r phase, Ρ is the {

t o t a l pressure of t h e system, x is t h e c o m p o s i t i o n of c o m p o n e n t i i n the {

l i q u i d phase, a n d

fi

0L

is the f u g a c i t y of c o m p o n e n t i i n the l i q u i d at a

reference state. T h i s reference state is the f u g a c i t y of p u r e l i q u i d i at the t e m p e r a t u r e a n d pressure of t h e system. E q u a t i o n 1 t h e n becomes Φ-ϊ^Ρ

=

JiXiU

(3)

0lj

A t c o n d i t i o n s w h e n it is safe to assume t h a t t h e gas p h a s e w i l l b e h a v e i n a n ideal manner—i.e.,

at l o w

pressure w i t h a l l c o m p o n e n t s

con

densable—

«^land/^^P, Pi

s

8

is t h e v a p o r pressure of p u r e l i q u i d i at t h e t e m p e r a t u r e o f t h e system,

a n d e q u i l i b r i u m is d e s c r i b e d b y the e q u a t i o n , yP

— ytiPi*

In Extractive and Azeotropic Distillation; Tassios, D.; Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

(4)

6.

ANDiAPPAN

A N D M C L E A N

Isobaric Vapor-Liquid

Equilibrium

95

A t c o n d i t i o n s w h e r e i t is i n c o r r e c t t o assume i d e a l b e h a v i o r f o r t h e gas a n d /i

phase, et al.

are calculated b y procedures described b y Prausnitz

0L

(1).

T h e calculation of y

i9

t h e a c t i v i t y coefficient, establishes γ* as a f u n c

t i o n of c o m p o s i t i o n , as w e l l as t e m p e r a t u r e a n d pressure. T h i s is d o n e b y r e l a t i n g γ* t o t h e excess G i b b s energy G , — L e . , b y t h e e q u a t i o n E

a n d expressing G

E

o r g , t h e m o l a r excess G i b b s energy, i n terms of E


composition. T h e p r o b l e m o f expressing t h e excess G i b b s energy as a f u n c t i o n o f c o m p o s i t i o n has b e e n researched extensively, a n d m a n y m e t h o d s of v a r y i n g a c c u r a c y a n d usefulness h a v e b e e n p r o p o s e d . A n extensive d i s c u s s i o n of these m e t h o d s is g i v e n b y H a l a et al. (2), m o n expressions—e.g.,

w h o s h o w that m a n y c o m

those o f v a n L a a r a n d M a r g u l e s — a r e

f r o m t h e g e n e r a l expression of W o h l C u k o r a n d P r a u s n i t z (4),

deduced

(3).

h o w e v e r , p o i n t o u t that W o h l ' s

expression p r e c l u d e s other expressions f o r t h e c o m p o s i t i o n

general

dependence

of t h e excess free energy, i n c l u d i n g that o f W i l s o n ( 5 ) , w h i c h has b e e n u s e d b y several authors t o p r e d i c t a n d correlate v a p o r - l i q u i d e q u i l i b r i u m W i l s o n s equation and the modification proposed b y Renon and

(1,6,7).

P r a u s n i t z (8)

u s e t h e l o c a l m o l e f r a c t i o n concept, p r o d u c e d

because

molecules i n s o l u t i o n aggregate as a result o f t h e v a r i a t i o n i n i n t e r m o l e c u l a r forces.

T h e l o c a l m o l e f r a c t i o n c o n c e p t results i n a m o r e u s e f u l

d e s c r i p t i o n o f t h e b e h a v i o r of m o l e c u l e s i n a n o n - i d e a l m i x t u r e . The Wilson Equation and the Two-Liquid

(NRTL)

Non-Random

Equation

T h e W i l s o n e q u a t i o n , u s e d b y P r a u s n i t z et al. (1) (6,7),

a n d other w o r k e r s

equals or surpasses earlier t w o - p a r a m e t e r equations i n c o r r e l a t i n g

v a p o r - l i q u i d e q u i l i b r i u m d a t a f o r a large n u m b e r of n o n - i d e a l systems. T h e e q u a t i o n w h i c h is sufficiently d i s c u s s e d elsewhere

( J ) contains t w o

adjustable parameters p e r b i n a r y a n d p r e d i c t s m u l t i c o m p o n e n t e q u i l i b r i u m d a t a u s i n g t h e b i n a r y parameters only. N o m u l t i c o m p o n e n t e x p e r i m e n t a l d a t a are necessary as f o r t h e v a n L a a r t y p e e q u a t i o n s o f t h i r d o r d e r a n d above. O n e l i m i t a t i o n of t h e W i l s o n e q u a t i o n has b e e n that i t c a n n o t b e a p p l i e d t o systems w h e r e t h e n o n - i d e a l i t y is s u c h that t w o l i q u i d phases are

formed—e.g.,

water-2-methyl-l-propanol

and

water-3-methyl-l-

butanol.


96

E X T R A C T I V E

A N D A Z E O T R O P I C

DISTILLATION

R e n o n a n d P r a u s n i t z ( 8 ) p r o p o s e d a n o t h e r e q u a t i o n , b a s e d also o n the l o c a l m o l e f r a c t i o n c o n c e p t , w h i c h w o u l d a v o i d this l i m i t a t i o n a n d c o u l d b e a p p l i e d to partially miscible mixtures. T h e relationship between a c t i v i t y coefficient a n d l i q u i d p h a s e c o m p o s i t i o n is g i v e n b y t h e e q u a t i o n Ν

/

i n y ^ i f ^ 2

+ t ^ ^ K - i ^ M ^

Gx ki

'

k

k-\


where Ν =

(ëa

Ν

=

2 Gx

1

kj

k

k=l

I

2

\

k=l

1

)

)

(5

GjcjXk

number of components

~~ ëu) is t h e adjustable p a r a m e t e r ( t w o p e r b i n a r y ) s i m i l a r t o that

contained i n the W i l s o n equation.

is a n e m p i r i c a l non-randomness

parameter. R e n o n a n d P r a u s n i t z ( 8 ) r e c o m m e n d values o f

f o r v a r i o u s classes

of m i x t u r e s . I f these v a l u e s a r e v a l i d t h e n E q u a t i o n 5 has o n l y t w o a d justable p a r a m e t e r s p e r b i n a r y .

T h e N R T L e q u a t i o n w a s u s e d i n this

work. Experimental T o test t h e N R T L

equation for predicting V L E data for ternary

mixtures, experimental data for the ternary mixtures a n d for the binary c o m p o n e n t s o f t h e m i x t u r e s a r e necessary.

A literature survey

showed

t h a t d a t a w e r e n o t r e a d i l y a v a i l a b l e f o r a n y o f t h e ternaries o r f o r t h e two binaries ethanol-3-methyl-l-propanol a n d 3-methyl-l-butanol-water, a n d i t w a s therefore necessary to o b t a i n these d a t a e x p e r i m e n t a l l y . T h e direct measurement of v a p o r - l i q u i d e q u i l i b r i u m data for part i a l l y m i s c i b l e m i x t u r e s s u c h as 3 - m e t h y l - l - b u t a n o l - w a t e r is difficult, a n d a l t h o u g h stills h a v e b e e n d e s i g n e d f o r this p u r p o s e (9, 10), t h e d a t a w a s i n d i r e c t l y o b t a i n e d f r o m measurements

o f pressure, P , t e m p e r a t u r e , t,

a n d l i q u i d c o m p o s i t i o n , x. I t w a s also felt that a test o f t h e v a l i d i t y o f the N R T L

equation i n predicting the V L E data for the ternary mix-

tures w o u l d b e t h e successful p r e d i c t i o n o f t h e b o i l i n g p o i n t . T h i s e l i m inates

the complicated

analytical procedures

necessary

i n the direct

measurement of ternary V L E data. A modified version of the M-100 b o i l i n g point apparatus, made b y the James F . S c a n l o n C o . , W h i t t i e r , C a l i f , w a s u s e d ; t e m p e r a t u r e w a s measured b y a H e w l e t t - P a c k a r d m o d e l 2801A quartz thermometer. A l l measurements w e r e m a d e at a t m o s p h e r i c pressure w i t h t h e t e m p e r a t u r e c o r r e c t e d t h e n t o 760 m m H g .


6.

ANDiAPPAN

A N D


M C L E A N

T a b l e I.

97

F u g a c i t y Coefficients

Component


Equilibrium

Temperature,

°C

Φ,

Water

80 90 130 100

0.9925 0.9960 1.0150 1.0000

Ethanol

80 90 100

1.0015 1.0119 1.0240

1-Propanol

80 90 100

0.9898 0.9954 1.0018

2-Methyl-l-propanol

80 90 100

0.9726 0.9809 0.9904

3-Methyl-l-butanol

80 90 100 130

0.9535 0.9608 0.9686 C.9991

T o extract y f r o m P, t, x, d a t a o b t a i n e d for the b i n a r y system, a c o m p u t e r p r o g r a m u s i n g the N R T L e q u a t i o n w a s p r e p a r e d . U p o n re c e i v i n g the i n p u t data—i.e., P, x 1 a n d a v a l u e of a, u s u a l l y a r o u n d 0.475 — v a l u e s of the adjustable parameters (gi2-g22) a n d ( g 2 i - g n ) w e r e as s u m e d . T h e a c t i v i t y coefficients w e r e c a l c u l a t e d u s i n g E q u a t i o n 5 a n d values of y w e r e c a l c u l a t e d u s i n g E q u a t i o n 4. T o justify u s i n g E q u a t i o n 4, values of the f u g a c i t y coefficients w e r e c a l c u l a t e d . T h e s e values ( T a b l e I ) are b e l i e v e d sufficiently near u n i t y to p e r m i t that the effects of gas p h a s e n o n i d e a l i t y c a n b e i g n o r e d . T h e s u m of t/i a n d y w a s c o m p a r e d w i t h u n i t y , a n d the p r o c e d u r e w a s r e p e a t e d u n t i l s u m y w a s w i t h i n a g r e e d l i m i t s of u n i t y . T h i s p r o g r a m also a l l o w e d the c a l c u l a t i n g of b i n a r y energy parameters u s e d i n p r e d i c t i n g properties of the t e r n a r y systems. 9

2

A n a d d i t i o n a l p r o g r a m took the energy parameters of the b i n a r y systems m a k i n g u p ternary m i x t u r e s a n d c a l c u l a t e d t h e b o i l i n g p o i n t of the t e r n a r y a n d the e q u i l i b r i u m c o m p o s i t i o n of the v a p o r phase. C o m p a r i s o n of the m e a s u r e d b o i l i n g p o i n t w i t h the p r e d i c t e d b o i l i n g p o i n t for the same c o m p o s i t i o n a n d pressure was u s e d as a c r i t e r i o n of successful p e r f o r m a n c e of the N R T L e q u a t i o n . T o illustrate the consistency b e t w e e n the t w o programs, d a t a for the e t h a n o l - w a t e r system r e p o r t e d b y R i e d e r a n d T h o m p s o n ( 11 ) w e r e u s e d . T h e first p r o g r a m estimated the values of the energy parameters a n d c a l c u l a t e d the vapor-phase c o m p o s i t i o n , y, w i t h a root m e a n square d e v i a t i o n ( R M S D ) of 0.00847. T h e m e a n a r i t h m e t i c d e v i a t i o n b e t w e e n the


98

E X T R A C T I V E

A N D

A Z E O T R O P I C

DISTILLATION

s u m y a n d u n i t y w a s 0.0064. T h e e s t i m a t e d parameters w e r e u s e d i n the s e c o n d p r o g r a m w h i c h p r e d i c t e d t h e same values of y a n d also p r e d i c t e d the t e m p e r a t u r e of the b o i l i n g m i x t u r e . T h e p r e d i c t e d a n d e x p e r i m e n t a l t e m p e r a t u r e a g r e e d w i t h a R M S D v a l u e of 0.22°C. T h e p r o c e d u r e e s t a b l i s h i n g the v a p o r - l i q u i d e q u i l i b r i u m d a t a for t h e b i n a r y system was tested u s i n g the homogeneous water, a n d the heterogeneous

system,

1-propanol-

system, 2 - m e t h y l - l - p r o p a n o l - w a t e r , u s i n g

the d a t a of M u r t i a n d V a n W i n k l e (12)

and Ellis and Garbett

(9).

T h e R M S D v a l u e b e t w e e n the e x p e r i m e n t a l a n d t h e c a l c u l a t e d values of y w e r e 0.011 a n d 0.0155, respectively, T h e c o m p a r i s o n b e t w e e n

ex


p e r i m e n t a l a n d c a l c u l a t e d V L E d a t a is s h o w n i n F i g u r e 1 a n d F i g -

Figure

1. Comparison of calculated librium data at 760 mm Hg.

•

Indirectly

Ο

Directly

measured, Gadwa

ψ

Directly

measured, Murti and Van

and experimental vapor-liquid 1-Propanol (1)-Water (2).

measured, present work (15) Winkle

(12)


equi


6.

ANDiAPPAN

Figure 2. librium

A N D

M C L E A N


Equilibrium

99

Comparison of calculated and experimental vapor-liquid equi data at 760 mm Hg. 2-Methyl-l-Propanol (1)-Water (2).

ψ Indirectly measured, present work Ο Directly measured, Ellis and Garbett

(9)

u r e 2, a n d they agree w e l l e n o u g h to justify u s i n g t h e i n d i r e c t m e t h o d of e s t a b l i s h i n g t h e V L E d a t a o n t h e system, e t h a n o l - 2 - m e t h y l - l - p r o p a n o l and 3-methyl-l-butanol-water. D i r e c t m e a s u r e m e n t of t h e V L E d a t a for t h e e t h a n o l - 2 - m e t h y l - l p r o p a n o l system w e r e also m a d e , u s i n g a M E S 1 0 0 m o d e l e q u i l i b r i u m s u p p l i e d b y the James F . S c a n l o n C o . Results and Discussion Binary System.

T h e e t h a n o l - 2 - m e t h y l - p r o p a n o l system was

to b e h a v e i n a n e x p e c t e d i d e a l w a y .

T h e x-y

found

d a t a , that was d i r e c t l y


100

E X T R A C T I V E AND

Table II.

AZEOTROPIC DISTILLATION

Vapor—Liquid Equilibrium Data at 760 mm. H g Ethanol ( l ) - M e t h y l - l - P r o p a n o l (2)


t°c 104.15 101.88 101.55 101.03 98.07 94.67 94.08 90.96 89.34 87.56 86.75 86.11 85.24 84.18 83.67 82.54 81.45 81.11 80.06

Table III.

0.050 0.080 0.085 0.090 0.155 0.220 0.243 0.330 0.382 0.465 0.490 0.510 0.560 0.610 0.635 0.705 0.770 0.800 0.870

0.126 0.200 0.215 0.235 0.332 0.460 0.479 0.595 0.658 0.712 0.742 0.770 0.790 0.817 0.845 0.875 0.915 0.920 0.950

Vapor—Liquid Equilibrium Data at 760 mm. H g 3-Methyl-1-Butanol ( l ) - W a t e r (2) t

°c

99.17 97.99 97.82

XJ

Yi

0.0009 0.0024

0.0386

0.0155

0.0031

0.0482

96.60

0.0051

96.27

0.0072

0.0725 0.0932

96.14

0.0073

0.0942

95.90

0.0205

95.26

0.0616

0.1603 0.1694

97.32

0.5766

0.1810

104.03

0.6536

0.2323

109.86

0.7698

0.3495

119.65

0.8873

125.76 126.96

0.9347 0.9427

0.5710 0.7158

128.54

0.9696

0.7449 0.8512

129.84

0.9884

0.9394


ANDiAPPAN


6.

A N D

M C L E A N


0

Figure

Equilibrium

5

3.

Vapor-liquid

101

1

equilibrium data at 760 mm Hg. 2-Methyl-l-Propanol (2).

Ethanol

(1)-

Ο Directly measured y Indirectly measured — Ideal behavior m e a s u r e d , are p r e s e n t e d i n T a b l e II.

F i g u r e 3 shows t h e c o m p a r i s o n

w i t h the d i r e c t l y m e a s u r e d d a t a , the i n d i r e c t l y m e a s u r e d d a t a , a n d the data calculated from Raoult's L a w . T h e v a p o r - l i q u i d e q u i l i b r i u m d a t a for t h e 3 - m e t h y l - l - b u t a n o l - w a t e r system are s h o w n i n T a b l e I I I a n d F i g u r e 4. T h e b o i l i n g p o i n t measure ments a g r e e d w i t h those r e p o r t e d i n T i m m e r m a n s (13).

T h e v a l u e of

a =

alcohol-water

0.45 as suggested b y R e n o n a n d P r a u s n i t z ( 8 )

for

systems w a s not suitable. V a r i o u s other values of a w e r e t r i e d , a n d a v a l u e of

a

=

0.3 w a s f o u n d to agree best. T h i s fit c a n b e e s t a b l i s h e d b y u s i n g

the m e t h o d d e s c r i b e d to test t h e consistency of t h e equations—i.e.,


the


102

E X T R A C T I V E

0

Figure

A N D AZEOTROPIC

DISTILLATION

5

4.

Vapor-liquid

Table IV.

1

equilibrium data at 760 mm Hg. Butanol (1)-Water ( 2 ) .

3-Methyl-l-

N R T L Parameters for the Binary Systems Isobaric Systems at 1 A t m . Reference

E t h a n o l U ) - W a t e r (2) 1 - P r o p a n o l ( i ) - W a t e r (2) 2 - M e t h y l - l - P r o p a n o l (1)-Water (2) 3 - M e t h y l - l - B u t a n o l U ) - W a t e r (2) E t h a n o l (1 ) - l - P r o p a n o l (2) Ethanol (i)-3-Methyl-lB u t a n o l (2) Ethanol (J)-2-Methyl-lP r o p a n o l [2)

( gia-fW

a

cal./gram mole

(

gai-gu) cal./gram mole

16

0.475 0.500 0.475 0.300 0.500

121.0 438.4 611.5 -386.9 465.5

1161.5 1762.9 2475.7 3483.8 -324.5

16

0.475

20.8

7.4

11 15,12 9 —

—

—

0


0

6.

ANDiAPPAN

A N D

Table V .


Xj

103

Equilibrium

Vapor—Liquid Equilibrium Data at 760 mm H g Water ( l ) - E t h a n o l (2)-l-Propanol (3)

, χ*

0.1763 0.3742 0.5397 0.7271 0.1642 0.3216 0.4759 0.6350 0.1293 0.2707 0.4214 0.5519 0.1201 0.2421 0 3764 0.4812 0.1246 0.2046 0.3030 0.4071 0.0962 0.1896 0.3096 0.0853 0.1911 0.1125 0.1524 0.0851


M C L E A N

0.0905 0.0992 0.0944 0.0987 0.1920 0.1949 0.1966 0.1984 0.2698 0.2956 0.3123 0.3076 0.4024 0.3935 0.3777 0.3934 0.4861 0.4837 0.4944 0.4939 0.6059 0.6054 0.5907 0.7030 0.7026 0.7007 0.7319 0.8319

y/ 0.3133 0.4527 0.5143 0.5345 0.2720 0.3909 0.4526 0.4768 0.2152 0.3297 0.3932 0.4217 0.1793 0.2852 0.3566 0.3797 0.1702 0.2388 0.2936 0.3312 0.1248 0.2045 0.2731 0.1036 0.1889 0.1264 0.1579 0.0920

0.1353 0.1426 0.1503 0.2100 0.2730 0.2649 0.2828 0.3395 0.3752 0.3822 0.4123 0.4510 0.5203 0.4857 0.4750 0.5214 0.5966 0.5744 0.5797 0.5994 0.7064 0.6785 0.6652 0.7814 0.7518 0.7691 0.7792 0.8648

t°C

t

89.13 86.70 86.14 85.75 87.57 85.55 84.63 84.04 86.89 84.47 83.12 82.54 84.85 83.30 82.43 81.60 83.47 82.42 81.35 80.63 82.14 80.92 80.03 80.94 79.65 80.59 79.69 79.24

89.07 86.40 85.60 85.46 87.65 85.47 84.57 83.94 87.19 84.59 83.12 82.51 85.12 83.45 82.47 81.52 83.79 82.65 81.47 80.67 82.39 81.03 80.01 81.11 79.68 80.01 79.30 79.07

°C

"Predicted using N R T L equation. Measured. 5

c a l c u l a t i o n of the parameters w i t h the first p r o g r a m a n d the use of the p a r a m e t e r s to c a l c u l a t e t h e i n i t i a l t e m p e r a t u r e . Ternary System. T h e values of a l l b i n a r y parameters u s e d i n p r e d i c t i n g t h e t e r n a r y d a t a are s h o w n i n T a b l e I V . T h e p r e d i c t e d values of the v a p o r - l i q u i d e q u i l i b r i u m data—i.e., the b o i l i n g p o i n t , a n d t h e c o m p o s i t i o n of the v a p o r phase, y, f o r g i v e n values of t h e l i q u i d c o m p o s i t i o n , x, are p r e s e n t e d i n T a b l e s V , V I , a n d V I I .

A l s o s h o w n are t h e m e a s u r e d

b o i l i n g p o i n t s for the g i v e n values of the l i q u i d c o m p o s i t i o n . T h e R M S D v a l u e b e t w e e n t h e p r e d i c t e d a n d m e a s u r e d b o i l i n g p o i n t s for the sys tems w a t e r - e t h a n o l - l - p r o p a n o l , w a t e r - e t h a n o l - 2 - m e t h y l - l - p r o p a n o l , a n d w a t e r - e t h a n o l - 2 - m e t h y l - l - b u t a n o l are 0.23°C, 0.69°C, a n d 2.14°C.

It

seems therefore that since t h e N R T L e q u a t i o n successfully p r e d i c t s t e m p e r a t u r e , t h e p r e d i c t e d values of y c a n b e a c c e p t e d confidently.


104

E X T R A C T I V E

A N D

A Z E O T R O P I C

DISTILLATION

T o test the m e t h o d of p r e d i c t i n g some d i r e c t l y m e a s u r e d t e r n a r y d a t a , t h e p r e d i c t e d results for the system w a t e r - e t h a n o l - l - p r o p a n o l w e r e u s e d to c a l c u l a t e r e l a t i v e v o l a t i l i t i e s w h i c h w e r e c o m p a r e d w i t h t h e ex p e r i m e n t a l l y d e t e r m i n e d v a l u e s of C a r l s o n et al. (14).

This comparison

is s h o w n o n F i g u r e 5. T h e c o m p a r i s o n seems to i n d i c a t e that the m e t h o d of p r e d i c t i n g is satisfactory a n d gives less scatter t h a n t h e e x p e r i m e n t a l l y d e t e r m i n e d values of r e l a t i v e v o l a t i l i t y .


Table VI. Vapor—Liquid Equilibrium Data at 760 mm H g Water ( l ) - E t h a n o l (2)-2-Methyl-l-Propanol (3) x»

y."

t°C

t°C

0.1937

0.0999

0.4203

0.1632

93.28

93.0

0.3582

0.1062

0.5294

0.1574

90.13

89.25

0.5377

0.1003

0.5945

0.1548

88.78

87.67

0.7115

0.1014

0.6098

0.1912

88.09

86.93

0.1589

0.2002

0.3300

0.3163

91.78

0.3156

0.1996

0.4521

0.2854

88.68

91.46 87.72

0.5570

0.1820

0.5377

0.2813

86.88

85.92

0.6352

0.2066

0.5208

0.3492

85.71

84.87

0.1264

0.3072

0.2468

0.4635

90.05

89.89

0.3006

0.2943

0.3947

0.4012

86.86

86.09

0.4103

0.3056

0.4323

0.4161

85.33

84.59 85.1 87.76

0.5562

0.2981

0.4572

0.4474

84.09

0.1255

0.3990

0.2158

0.5602

0.2611

0.3974

0.3274

87.85 85.24

0.3722

0.3897

0.3791

0.5145 0.5041

0.4789

0.3993

0.3930

0.5414

82.53

82.23

0.0959

0.4984

0.1556

0.6666

86.29

86.38

0.1934

0.5010

0.2470

0.6228

84.18

83.96

0.3099

0.4949

0.3135

0.4991

0.3385

82.55 81.32

82.28

0.4006

0.6009 0.6149

0.0954

0.6042

0.7448

83.97

84.08

0.1347

83.95

85.09 83.46

81.10

0.2124

0.5908

0.2339

0.6877

82.05

81.93

0.4614

0.4118

0.3870

0.5465

80.23

0.1021

0.6959

0.1266

0.7982

82.46 81.94

0.1952

0.1955 0.0865

0.7680 0.8764

80.14

0.0757

0.7051 0.8162

80.15

80.11 80.25

0.1805

0.7530

0.1768

0.7997

79.49

79.49

0.0526

0.8987

0.0577

0.9264

79.09

79.19

Predicted using N R T L equation. * Measured.

β


81.99

6.

ANDiAPPAN


A N D M C L E A N

105

Equilibrium

Table VII. V a p o r - L i q u i d Equilibrium Data at 760 mm H g Water ( l ) - E t h a n o l ( 2 ) - 3 - M e t h y l - l - B u t a n o l (3) Xi

XJ

y/

t°C

t °C

0.7422

0.0101

0.8790

0.0198

95.08

94.37

0.4982

0.0127

0.8318

0.0266

97.93

94.67

0.3477

0.0120

0.7503

0.0311

103.20

99.58

0.8455

0.0589

94.46

93.57 100.44

0.7248


y/

0.0303

0.6809 0.8464

0.0729

104.88

0.0565

93.78

0.8412

0.0277

94.56 95.22

0.0241

0.8492

0.0456

95.14

94.13

0.0384

0.7685

0.0826

98.26

95.68

0.6338

0.1773

0.6234

0.3225

89.45

89.41

0.5055

0.2112

05744

0.3604

89.97

89.71

96.20

92.15

0.2944

0.0263

0.7784 0.8878

0.0269 0.0094

0.0344 0.4465

95.40

0.2774

0.1984

0.4574

0.4082

0.2087

0.1867

0.3944

0.4306

99.46

93.92

0.3781

0.3232

0.4331

0.5084

88.31

88.31 86.25

0.6071

0.2999

0.4801

0.4971

84.75

0.1377

0.3002

0.2369

0.6182

96.57

91.73

0.1984

0.3953

0.2684

0.6495

90.32

88.62

0.2802

0.4149

0.3265

0.6180

87.35

87.39

0.4460

0.3727

0.4225

0.5431

85.22

86.62

0.1335

0.4835

0.1774

0.7491

89.05

87.69

0.1857

0.5114

0.2212

0.7262

86.56

86.65

0.3912

0.5172

0.3319

0.6538

81.75

84.07

0.1047

0.6257

0.1248

0.8307

85.20

85.37

0.1939

0.6103

0.2054

0.7648

83.33

84.63

0.2963

0.5946

0.2709

0.7134

81.50

83.62

0.1112

0.6845

0.1247

0.8441

83.31

84.20

0.1353

0.7158

0.1428

0.8359

81.85

83.40

0.2135

0.6820

0.2050

0.7806

83.94

82.97

0.0453

0.8104

0.0511

0.9280

81.67

82.76

0.1022

0.8118

0.1059

0.8824

80.21

82.00

0.1547

0.7925

0.1498

0.8434

79.49

81.51

0.9551

80.02

80.09

0.0312

0.8920

0.0499

0.8998

0.0532

0.9402

79.38

79.45

0.0680

0.8989

0.0706

0.9252

78.96

78.99

α 6

0.0343

Predicted using N R T L equation. Measured.



106

E X T R A C T I V E

A N D

A Z E O T R O P I C

DISTILLATION

Ο >

•

> < L—OOfCpCBDO

MOLE Figure

5.

FRACTION

OF WATER IN

LIQUID

Comparison of calculated and experimental volatilities panol relative to ethanol in presence of water

of 1-pro-

Ο Indirectly measured, present work ψ Directly measured, Carbon et al. (14) Conclusion T h e n o n - r a n d o m , t w o - l i q u i d (NRTL) a n d P r a u s n i t z (8)

equation proposed b y Renon

seems to p r e d i c t successfully m u l t i c o m p o n e n t ( t e r n a r y )

m i x t u r e s of a l c o h o l s a n d w a t e r .

T h e alcohols s t u d i e d i n t h i s w o r k etha

n o l , 1 - p r o p a n o l , 2 - m e t h y l - l - p r o p a n o l , a n d 3 - m e t h y l - l - b u t a n o l , w h i c h oc c u r f r o m the f e r m e n t a t i o n

of

sugar solutions, s h o w h i g h l y n o n - i d e a l

b e h a v i o r i n a q u e o u s solutions a n d present a severe test of t h e effectiveness of a n y p r e d i c t i o n m e t h o d . T h e success of the N R T L e q u a t i o n i n u n d e r g o i n g this test w o u l d suggest that i t w i l l b e a p o w e r f u l t o o l i n t h e d e s i g n of processes i n v o l v i n g a z e o t r o p i c or extractive d i s t i l l a t i o n . T h e effect of the a d d i t i o n of a t h i r d


6.

ANDiAPPAN

A N D

M C L E A N


Equilibrium

107

c o m p o n e n t t o a difficult to separate b i n a r y m i x t u r e c a n b e p r e d i c t e d w i t h a d e g r e e of confidence, c e r t a i n l y f o r a l c o h o l - w a t e r mixtures. O n l y e q u i l i b r i u m d a t a f o r t h e b i n a r y c o m p o n e n t s of t h e system are necessary, a n d this w o r k shows that e v e n f o r systems of l i m i t e d l i q u i d - p h a s e m i s c i b i l i t y , t h e N R T L e q u a t i o n c a n b e u s e d to extract t h e necessary i n f o r m a t i o n

from


measurements of b o i l i n g p o i n t , l i q u i d c o m p o s i t i o n , a n d pressure alone.

Literature Cited 1. Prausnitz, J. M., Eckert, C. Α., Orye, R. V., O'Connell, J. P., "Computer Calculations for Multicomponent Vapor-Liquid Equilibria," p. 14, Prentice Hall, New Jersey, 1967. 2. Hala, E., Pick, J., Fried, V., Vilim, O., "Vapor-Liquid Equilibrium," p. 33, Pergamon, London, 1967. 3. Wohl, K., Trans. Amer. Inst. Chem. Eng. (1946) 42, 215. 4. Cukor, P. M., Prausnitz, J. M., Int. Symp. "Distillation," p. 73, Inst. Chem. Eng., London (Sept. 9, 1969). 5. Wilson, G. M.,J.Amer. Chem. Soc. (1964) 86, 127. 6. Garrett, G. R., VanWinkle, Matthew,J.Chem. Eng. Data (1969) 14, 302. 7. Gurukul, S. Μ. Κ. Α., Raju, Β. N.,J.Chem. Eng. Data (1966) 11, 501. 8. Renon, H., Prausnitz, J. M., A.I.Ch.E. J. (1968) 14, 135. 9. Ellis, S. R. M., Garbett, R. D., Ind. Eng. Chem. (1960) 52, 385. 10. Othmer, D. F., Gilmont, R., Conti, J. J., Ind. Eng. Chem. (1960) 52, 625. 11. Rieder, R. M., Thompson, A. R., Ind. Eng. Chem. (1949) 41, 2905. 12. Murti, P. S., VanWinkle, Matthew, Ind. Eng. Chem., J. Chem. Eng. Data (1958) 3, 72. 13. Timmermans, J., "The Physico Chemical Constants of Binary Systems," Vol. 4, p. 237, Interscience, New York (1960). 14. Carlson, C. S., Smith, P. V., Jr., Morrell, C. E., Ind. Eng. Chem. (1954) 46, 350. 15. Gadwa, T. W., Chemical Engineering Thesis, M.I.T., 1936. 16. Gay, L., Chim. et Ind. (1927) 18, 187.


Prediction of Isobaric Vapor-Liquid Equilibrium Data for Mixtures of

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