Supercritical Fluids - American Chemical Society

Chapter 10

High-Pressure Phase Equilibria in Ternary Fluid Mixtures with a Supercritical Component A. Z. Panagiotopoulos and R. C. Reid

Downloaded by PENNSYLVANIA STATE UNIV on August 26, 2013 | http://pubs.acs.org Publication Date: December 16, 1987 | doi: 10.1021/bk-1987-0329.ch010

Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, M A 02139

Experimental results are presented for high pressure phase equilibria in the binary systems carbon dioxide - acetone and carbon dioxide - ethanol and the ternary system carbon dioxide - acetone - water at 313 and 333 Κ and pressures between 20 and 150 bar. A high pressure optical cell with external recirculation and sampling of all phases was used for the experimental measurements. The ternary system exhibits an extensive three-phase equilibrium region with an upper and lower critical solution pressure at both temperatures. A modified cubic equation of a state with a non-quadratic mixing rule was successfully used to model the experimental data. The phase equilibrium behavior of the system is favorable for extraction of acetone from dilute aqueous solutions using supercritical carbon dioxide. The potential of supercritical extraction, a separation process in which a gas above its critical temperature is used as a solvent, has been widely recognized in the recent years. The first proposed applications have involved mainly compounds of low volatility, and processes that utilize supercritical fluids for the separation of solids from natural matrices (such as caffeine from coffee beans) are already in industrial operation. The use of supercritical fluids for separation of liquid mixtures, although of wider applicability, has been less well studied as the minimum number of components for any such separation is three (the solvent, and a binary mixture of compo nents to be separated). The experimental study of phase equilibrium in ternary mixtures at high pressures is complicated and theoretical methods to correlate the observed phase behavior are lacking. One important potential application of supercritical extraction is the recovery of polar organic compounds from aqueous solutions. Such mixtures arise frequently as products of biochemical syntheses. In many cases, the costs of the energy-intensive separations are high and there is substantial incentive for the development of more efficient processes. Previous work in the area of high-pressure phase equilibrium of aqueous solutions of organic compounds with supercritical fluids 0097-6156/87/0329-0115$06.00/0 © 1987 American Chemical Society

In Supercritical Fluids; Squires, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

116

SUPERCRITICAL FLUIDS

i n c l u d e s the p i o n e e r i n g work o f E l g i n and W e i n s t o c k (1) c a r r i e d out i n t h e 1950's. F r a n c i s (9) p r e s e n t e d a l a r g e number o f q u a l i t a t i v e r e s u l t s f o r t e r n a r y systems o f l i q u i d c a r b o n d i o x i d e a t 298 K. In the more r e c e n t y e a r s , P a u l a i t i s e t a l . ( 2 , 3 ) , Kuk and Montagna ( 4 ) , McHugh e t a l . (5) and Radosz (6) have r e p o r t e d measurements i n systems w i t h some o f the f i r s t a l c o h o l s , water and s u p e r c r i t i c a l f l u i d s .

Experimental The e x p e r i m e n t a l s e t u p u s e d i s shown i n F i g u r e 1. The main element o f the equipment i s a h i g h p r e s s u r e o p t i c a l c e l l ( J e r g u s o n gage model 19-TCH-40) w i t h an i n t e r n a l volume o f about 50 cm , t h a t s e r v e s as a m i x i n g and s e p a r a t i n g v e s s e l , as w e l l as f o r the v i s u a l o b s e r v a t i o n o f t h e number and q u a l i t y o f t h e c o e x i s t i n g p h a s e s . Connections at the bottom, top and s i d e o f the v e s s e l p e r m i t w i t h d r a w a l o f the lower, u p p e r and m i d d l e phases, any two o f which c a n be r e c i r c u l a t e d e x t e r n a l l y w i t h a d u a l h i g h p r e s s u r e M i l t o n - R o y M i n i Pump. An o n - l i n e M e t t l e r Paar v i b r a t i n g tube d e n s i t y meter (DMA 60 w i t h a DMA 512 c e l l ) i s u s e d t o measure the d e n s i t y o f one o f the r e c i r c u l a t i n g p h a s e s . The d e n s i t y meter c a n be s w i t c h e d t o sample any o f the r e c i r c u l a t i n g streams.


3

The J e r g u s o n gage i s immersed i n a c o n s t a n t temperature b a t h w i t h s i l i c o n f l u i d as the h e a t - t r a n s f e r medium, t h a t a l s o t h e r m o s t a t s the d e n s i t y meter. The b a t h temperature i s c o n t r o l l e d t o ± .01 Κ w i t h a Thermomix 1460 temperature r e g u l a t o r and temperature i s measured w i t h a c a l i b r a t e d m e r c u r y - i n - g l a s s thermometer t o w i t h i n .01 K. The l i n e s e x t e r n a l t o the b a t h a r e m a i n t a i n e d a t the b a t h temperature w i t h the h e l p o f h e a t i n g t a p e s and temperature a t s e v e r a l p o i n t s i s m o n i t o r e d w i t h thermocouples. P r e s s u r e i s measured w i t h two c a l i b r a t e d H e i s e p r e s s u r e i n d i c a t o r s t o w i t h i n ±.16 b a r f o r p r e s s u r e s up t o 160 b a r and t o w i t h i n ±.4 b a r f o r p r e s s u r e s up t o 350 b a r . Sampling i s p e r f o r m e d w i t h two h i g h p r e s s u r e s w i t c h i n g v a l v e s w i t h i n t e r n a l volume .5 μΐ ( f o r the upper phase) and .2 μΐ f o r the lower or middle phases. The samples a r e d i r e c t l y d e p r e s s u r i z e d i n t o a He c a r r i e r gas stream and a n a l y z e d w i t h a P e r k i n Elmer Sigma 2 Gas Chromatograph, u s i n g a Porapak Q column s u p p l i e d by S u p e l c o . The r e s p o n s e f a c t o r s f o r the m a t e r i a l s u s e d were found t o be c l o s e t o t h o s e r e p o r t e d by D i e t z ( 7 ) . T y p i c a l r e p r o d u c i b i l i t y o f the a n a l y s i s i s ±.003 i n mole f r a c t i o n , w i t h somewhat l a r g e r d e v i a t i o n s f o r the gas-phase c o m p o s i t i o n s a t low p r e s s u r e s . A f t e r p u r g i n g and e v a c u a t i o n o f the equipment, t h e c e l l i s c h a r g e d w i t h a l i q u i d m i x t u r e o f known c o m p o s i t i o n and the supercritical component up t o the d e s i r e d p r e s s u r e . The r e c i r c u l a t i o n pumps a r e s t a r t e d , and a p p r o a c h t o e q u i l i b r i u m m o n i t o r e d by the s t a b i l i t y o f p r e s s u r e , d e n s i t y and c o m p o s i t i o n measurements w i t h t i m e . F o r the m i x t u r e s s t u d i e d , a t y p i c a l e q u i l i b r a t i o n time i s 15 min, b u t a t l e a s t 30 min a r e a l l o w e d b e f o r e the f i n a l s a m p l i n g . At l e a s t two samples a r e t a k e n from each phase a t e q u i l i b r i u m . A new pressure p o i n t c a n be e s t a b l i s h e d i m m e d i a t e l y by i n t r o d u c i n g o r removing s u p e r c r i t i c a l f l u i d o r l i q u i d , so t h a t the l e v e l o f the i n t e r f a c e s i n the c e l l a t the new d e s i r e d p r e s s u r e i s a p p r o p r i a t e f o r sampling t h r o u g h the a v a i l a b l e p o r t s . E n t r a i n m e n t o f the phases i s n o t n o r m a l l y a problem, e x c e p t n e a r a c r i t i c a l p o i n t . Selective flashing and a d s o r p t i o n on t h e s w i t c h i n g v a l v e s i s sometimes a d i f f i c u l t y f o r the u p p e r ( g a s ) phase s a m p l i n g l o o p , b u t i s p r e v e n t e d by h e a t i n g t h e v a l v e .


In Supercritical Fluids; Squires, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987. F i g u r e 1.

CARRIER GAS

PUMP

Schematic drawing o f t h e equipment.

CARRIER GAS

CONSTANT ' TEMPERATURE ENCLOSURE

LIQUID I FEED

SCF

N2

h O PI

A A K > i



118


Results B i n a r y Systems. As a t e s t o f t h e v a l i d i t y o f t h e equipment d e s i g n and e x p e r i m e n t a l p r o c e d u r e s , we f i r s t i n v e s t i g a t e d a b i n a r y system f o r which r e s u l t s have been p r e v i o u s l y published. Knowledge o f the b e h a v i o r o f the b i n a r y systems i s i n i t s e l f i m p o r t a n t , s i n c e the d a t a p r o v i d e the a p p r o p r i a t e l i m i t s f o r the c o r r e s p o n d i n g t e r n a r y systems. In F i g u r e 2, we p r e s e n t e x p e r i m e n t a l r e s u l t s and l i t e r a t u r e d a t a f o r the system c a r b o n d i o x i d e - acetone a t 313 and 333 Κ ( l i t e r a t u r e r e s u l t s a r e o n l y a v a i l a b l e f o r the lower t e m p e r a t u r e ) . The agreement between the two s e t s o f r e s u l t s i s e x c e l l e n t . A l s o shown on the same f i g u r e as c o n t i n u o u s l i n e s a r e the r e s u l t s o f f i t t i n g the e x p e r i m e n t a l d a t a u s i n g a m o d i f i e d Peng-Robinson e q u a t i o n o f s t a t e d e s c r i b e d i n the Appendix. The agreement between e x p e r i m e n t a l and p r e d i c t e d phase compositions i s w i t h i n the e x p e r i m e n t a l u n c e r t a i n t y o f the d a t a , e x c e p t i n the c r i t i c a l r e g i o n . S e v e r a l o f the f e a t u r e s o f t h e phase b e h a v i o r shown on F i g u r e 2 a r e quite general. I n p a r t i c u l a r , i t can be seen t h a t the s o l u b i l i t y o f c a r b o n d i o x i d e i n the l i q u i d phase i s h i g h even a t moderate p r e s s u r e s . The system c r i t i c a l p r e s s u r e i s comparable t o t h e c r i t i c a l p r e s s u r e o f c a r b o n d i o x i d e and i n c r e a s e s w i t h temperature a t the temperature range s t u d i e d . A l t h o u g h the s o l u b i l i t y o f a c e t o n e i n the gas phase i s low i n the two-phase r e g i o n , t h e r e i s complete m i s c i b i l i t y between C0 and a c e t o n e a t r e l a t i v e l y moderate p r e s s u r e s . Carbon d i o x i d e a t l i q u i d - l i k e d e n s i t i e s i s an e x c e l l e n t s o l v e n t f o r a wide range o f o r g a n i c compounds, as was f i r s t o b s e r v e d by F r a n c i s (9) f o r near c r i t i c a l l i q u i d C0 . One a d d i t i o n a l example o f the same g e n e r a l type o f b e h a v i o r i s d e m o n s t r a t e d by the c a r b o n d i o x i d e - e t h a n o l system. T h r e e measured i s o t h e r m s f o r t h i s system a r e p r e s e n t e d i n F i g u r e 3. No comparable set o f e x p e r i m e n t a l r e s u l t s appears t o be a v a i l a b l e i n the open literature. A g a i n , agreement between e x p e r i m e n t a l r e s u l t s and model p r e d i c t i o n s i s good. 2

2

T e r n a r y Systems. As one o f a s e r i e s o f model systems, we s t u d i e d the c a r b o n d i o x i d e - acetone - water t e r n a r y system a t 313 and 333 K. The most i n t e r e s t i n g f e a t u r e o f the system b e h a v i o r i s an e x t e n s i v e three-phase r e g i o n a t both temperatures. The t h r e e - p h a s e r e g i o n i s f i r s t observed a t a p r e s s u r e o f l e s s t h a n 30 b a r a t 313 Κ and a p p r o x i m a t e l y 35 b a r a t 333 K, e x t e n d i n g up t o a p p r o x i m a t e l y the c r i t i c a l p r e s s u r e o f the b i n a r y c a r b o n d i o x i d e - a c e t o n e system. T a b l e I summarizes our e x p e r i m e n t a l r e s u l t s f o r the c o m p o s i t i o n o f the t h r e e phases a t e q u i l i b r i u m as a f u n c t i o n o f p r e s s u r e and temperature. The p h y s i c a l p i c t u r e t h a t u n d e r l i e s t h i s b e h a v i o r , as p o i n t e d out f i r s t by E l g i n and W e i n s t o c k ( 1 ) , i s the ' s a l t i n g o u t ' e f f e c t by a s u p e r c r i t i c a l f l u i d on an aqueous s o l u t i o n o f an o r g a n i c compound. As p r e s s u r e i s i n c r e a s e d , the tendency o f the s u p e r c r i t i c a l f l u i d t o s o l u b i l i z e i n the o r g a n i c l i q u i d r e s u l t s i n a phase s p l i t i n the aqueous phase a t a lower c r i t i c a l s o l u t i o n p r e s s u r e (which v a r i e s w i t h temperature). As p r e s s u r e i s f u r t h e r i n c r e a s e d , t h e second l i q u i d phase and the s u p e r c r i t i c a l phase become more and more s i m i l a r to e a c h o t h e r and merge a t an upper c r i t i c a l s o l u t i o n p r e s s u r e . Above t h i s p r e s s u r e o n l y two phases c a n c o e x i s t a t e q u i l i b r i u m . T h i s p a t t e r n o f b e h a v i o r was a l s o o b s e r v e d by E l g i n and W e i n s t o c k f o r the system e t h y l e n e - a c e t o n e - water a t 288 K. I n a d d i t i o n , the same type o f


In Supercritical Fluids; Squires, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987. C02

F i g u r e 2. Phase e q u i l i b r i u m b e h a v i o r f o r the b i n a r y system c a r b o n d i o x i d e - acetone. E x p e r i m e n t a l , 313 Κ ( Δ ) ; e x p e r i m e n t a l , 333 Κ (•) ; l i t e r a t u r e , 313 Κ (χ) ; m o d i f i e d Peng-Robinson e q u a t i o n o f s t a t e (—). L i t e r a t u r e d a t a a r e from r e f e r e n c e (10).

Mole Fraction


ο

120



120

0

0.2

0.4 Mole F r a c t i o n

0.6

0.8

C02

F i g u r e 3. Phase e q u i l i b r i u m b e h a v i o r f o r the system c a r b o n d i o x i d e - ethanol. E x p e r i m e n t a l , 308.1 Κ (+) ; 323.1 Κ ( 0 ) ; 338.1 Κ ( Δ ) ; m o d i f i e d Peng-Robinson e q u a t i o n o f s t a t e ( — ) .


1

10.

PANAGIOTOPOULOS AND REID

121

High-Pressure Phase Equilibria

: Three phase e q u i l i b r i u m c o m p o s i t i o n s f o r the system Water (1) - A c e t o n e (2) · CO (3)

TABLE I


2

upper

lower phase X

X

l

X

2

3

yi

m i d d l e ph ase

phase y

y

2

Z 3

Z

l

Z

2

3

Τ - 313 Κ 29 35 43 55 61 65 75 79

3 9 2 9 1 8 .2 .6

0 0 0 0 0 0 0 0

810 864 904 920 942 944 959 966

0 0 0 0 0 0 0 0

153 106 075 052 037 032 017 011

0. 037 0. 030 0. 021 0 028 0 021 0 024 0 024 0 023

0.005 0.006 0.003 0.002 0.004 0.002 0.002 0.002

0.025 0.019 0.017 0.015 0.015 0.015 0.014 0.015

0. 970 0 975 0 980 0 983 0 981 0 983 0 984 0 983

454 427 360 230 191 148 069 035

0. 294 0. 197 0. 153 0. 119 0 114 0 130 0 020 0 049

0 0 0 0 0 0 0 0

0 0 0 0 0 0

0 .398 0 .418 0 .359 0 .300 0 .234 0 .127

0 0 0 0 0 0 0 0

252 376 487 651 695 722 911 916

Γ - 333 Κ 39 .4 51 .1 59 .4 70 .3 79 .2 92 .6

1

0 0 0 0 0 0

795 880 906 925 939 946

0 0 0 0 0 0

We were n o t a b l e

163 091 068 049 039 029

0 0 0 0 0 0

042 029 026 026 022 025

1 1

0.006 0.008 0.006 0.010

0.030 0.035 0.032 0.046

0 0 0 0

964 957 962 944

to obtain r e s u l t s f o r these s t a t e

400 182 173 117 089 084

0 202 0 400 0.468 0 583 0 677 0 789

conditions.




122

b e h a v i o r , b u t a t q u i t e d i f f e r e n t p r e s s u r e s r e l a t i v e t o the pure s o l v e n t c r i t i c a l p r e s s u r e was r e p o r t e d by P a u l a i t i s e t a l . (3.) f o r t h e system c a r b o n d i o x i d e - i s o p r o p a n o l - water, by McHugh e t a l . (5) f o r t h e system ethane - e t h a n o l - water and by P a u l a i t i s e t a l . (2) f o r the c a r b o n d i o x i d e - e t h a n o l - water system. T h i s b e h a v i o r appears then to be q u i t e common. A more complete p i c t u r e o f the phase e q u i l i b r i u m b e h a v i o r i s g i v e n i n F i g u r e 4 f o r t h e system under s t u d y a t 333 K. A t t h i s temperature, we measured t i e l i n e s i n t h e two-phase r e g i o n i n a d d i t i o n t o t h e three-phase compositions. The d a r k e r l i n e s and s q u a r e s on F i g u r e 4 r e p r e s e n t t h e s e e x p e r i m e n t a l measurements. The l i g h t l i n e s a r e model p r e d i c t i o n s , u s i n g values o f i n t e r a c t i o n parameters determined s o l e l y from r e g r e s s i o n o f b i n a r y d a t a (see A p p e n d i x ) . The two s e t s o f r e s u l t s a r e i n good agreement w i t h each o t h e r . The a b i l i t y t o p r e d i c t t e r n a r y d a t a from b i n a r y d a t a o n l y i s o f g r e a t p r a c t i c a l importance, s i n c e i t p e r m i t s t h e e v a l u a t i o n o f a l a r g e range o f p r o c e s s a l t e r n a t i v e s from l i m i t e d experimental information. An i n t e r e s t i n g f e a t u r e o f t h e phase e q u i l i b r i u m b e h a v i o r i s t h e r e l a t i v e i n s e n s i t i v i t y o f the phase e n v e l o p e and p o s i t i o n s o f the t i e l i n e s t o v a r i a t i o n s i n p r e s s u r e i n t h e two-phase r e g i o n , as e v i d e n c e d by c o m p a r i s o n o f t h e diagrams a t 100 and 150 b a r i n F i g u r e 4. This w o u l d seem t o imply t h a t s i m i l a r s e p a r a t i o n s c a n be a c h i e v e d by o p e r a t i o n a t a range o f p r e s s u r e s above t h e upper c r i t i c a l s o l u t i o n p r e s s u r e o f -95 b a r . From an e n g i n e e r i n g p o i n t o f view, t h e most i m p o r t a n t q u a n t i t i e s i n t h e e v a l u a t i o n o f a s e p a r a t i o n scheme b a s e d o n a phase b e h a v i o r p a t t e r n such as t h e one shown, a r e t h e s e l e c t i v i t y o f t h e s e p a r a t i o n w i t h r e s p e c t t o t h e d e s i r e d component, as w e l l as t h e l o a d i n g o f the d e s i r e d component i n t h e e x t r a c t a n t phase. I t i s w e l l known t h a t t h o s e two f a c t o r s u s u a l l y i n c r e a s e i n d i f f e r e n t d i r e c t i o n s . Figures 5 and 6 p r e s e n t e x p e r i m e n t a l d a t a and model p r e d i c t i o n s f o r t h e d i s t r i b u t i o n c o e f f i c i e n t o f a c e t o n e and the s e l e c t i v i t y r a t i o a o f acetone o v e r w a t e r ( d e f i n e d as t h e r a t i o o f d i s t r i b u t i o n c o e f f i c i e n t s o f a c e t o n e and water i n t h e l i q u i d and f l u i d p h a s e s ) . The d i s t r i b u t i o n c o e f f i c i e n t shows a maximum a t b o t h t e m p e r a t u r e s , w i t h a h i g h e r v a l u e at t h e h i g h e r temperature, whereas t h e s e l e c t i v i t y d e c r e a s e s smoothly from t h e l i m i t i n g v a l u e o f -300 a t low a c e t o n e c o n c e n t r a t i o n s t o 1 as the p l a i t p o i n t i s approached. The e x p e r i m e n t a l d a t a show t h e same t r e n d s , a l t h o u g h t h e r e i s some s c a t t e r due t o t h e f a c t t h a t s m a l l absolute e r r o r s i n t h e low s u p e r c r i t i c a l phase c o n c e n t r a t i o n s o f a c e t o n e and water r e s u l t i n l a r g e r e l a t i v e e r r o r s f o r t h e d i s t r i b u t i o n c o e f f i c i e n t and s e l e c t i v i t y f a c t o r s . S e l e c t i v i t i e s are generally h i g h e r f o r t h e lower t e m p e r a t u r e , b u t l o a d i n g s a r e l o w e r . I n F i g u r e 7, we p r e s e n t t h e w/w c o n c e n t r a t i o n o f a c e t o n e i n t h e s u p e r c r i t i c a l phase on a C 0 - f r e e b a s i s v e r s u s t h e c o r r e s p o n d i n g c o n c e n t r a t i o n o f acetone i n t h e l i q u i d phase. The c u r v e shows a b r o a d maximum a t a range o f c o n c e n t r a t i o n s o f a c e t o n e i n t h e aqueous phase between 2% and 15% w/w. The maximum c o n c e n t r a t i o n o f acetone i n t h e s u p e r c r i t i c a l phase i s c l o s e t o 95% w/w. We can, t h e r e f o r e , o b t a i n almost pure a c e t o n e from a d i l u t e aqueous s o l u t i o n u s i n g a s i n g l e - s t e p e x t r a c t i o n with s u p e r c r i t i c a l carbon d i o x i d e . 2


10.




Acgtong (2)

Acetong (2)

Water (1) ;

333 Κ . Ρ = 27. 6 bar

123

C02 (3) Τ = 333 Κ . Ρ = 40. 0 bar

Acgtong (2)

C02 (3)

Figure 4. Phase equilibrium behavior f o r the system water (1)acetone (2) - carbon dioxide (3) at 333 Κ : experimental phase compositions (•) and t i e - l i n e s (—) ; predicted t i e - l i n e s (—) ; predicted three-phase equilibrium compositions (Δ).



124


0.55

0.65

0.75 x1/

(x1

0.85 +

0.95

x2)

F i g u r e 5. D i s t r i b u t i o n c o e f f i c i e n t o f a c e t o n e f o r t h e system water (1) - a c e t o n e (2) - c a r b o n d i o x i d e (3) a t 150 b a r , as a f u n c t i o n o f the water concentration i n the lower phase. E x p e r i m e n t a l , 333 Κ (•); p r e d i c t e d , 333 Κ and 313 Κ ( — ) .



10.


0.55

0.65

125


0.75 x1/

(x1

0.85 +

0.95

x2)

F i g u r e 6. S e l e c t i v i t y f a c t o r f o r a c e t o n e o v e r water f o r t h e system water (1) - a c e t o n e (2) - c a r b o n d i o x i d e (3) system a t 150 b a r , as a f u n c t i o n o f t h e water c o n c e n t r a t i o n i n t h e lower phase. E x p e r i m e n t a l , 333 Κ ( 0 ) ; p r e d i c t e d , 333 Κ and 313 Κ ( — ) .


In Supercritical Fluids; Squires, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987. 4

8

16

20

Acetone in aqueous phase (% w/w)

12

24

2

F i g u r e 7. Concentration o f acetone i n the s u p e r c r i t i c a l f l u i d phase as a f u n c t i o n o f the c o n c e n t r a t i o n o f a c e t o n e i n t h e l i q u i d phase ( c o n c e n t r a t i o n u n i t s : % w/w on a C 0 - f r e e b a s i s ) . E x p e r i m e n t a l , 333 Κ (•); p r e d i c t e d , 333 Κ and 313 Κ ( — ) .

Ο


28

^

C/5

Η ο ^ pE3 G D

m Π

10.

127



APPENDIX

Equation of State

used

F o r the c o r r e l a t i o n o f the e x p e r i m e n t a l r e s u l t s , we u s e d a m o d i f i c a t i o n o f the Peng-Robinson e q u a t i o n o f s t a t e d e v e l o p e d by the a u t h o r s . The e s s e n c e o f the method, w h i c h i s p r e s e n t e d i n d e t a i l i n (8.) i s the use o f a n o n - q u a d r a t i c m i x i n g r u l e f o r the a t t r a c t i v e p a r a m e t e r a . The m i x i n g r u l e i n v o l v e s two b i n a r y i n t e r a c t i o n p a r a m e t e r s t o be d e t e r m i n e d from r e g r e s s i o n o f e x p e r i m e n t a l d a t a . The e q u a t i o n s f o r the p r e s s u r e , the m i x i n g r u l e u s e d and the r e s u l t i n g e x p r e s s i o n f o r the c h e m i c a l p o t e n t i a l o f a component i n a m i x t u r e a r e g i v e n below f o r the case o f a g e n e r a l c u b i c e q u a t i o n o f s t a t e ( f o r the Peng-Robinson e q u a t i o n o f s t a t e , u = 2 and w = - 1 ) .


m

RT

a

ρ V - b

a

m

=

b

a.. -

OA

ο =

Yx

(a

r i

n

Υ Υ . . ι J « -

f

T

k F

+

— wb m m

(1)

x

b

i

(2)

( 3 )

i

[1-k..+(k..-k..)x.]

b

-

= + uVb

χ. χ. a.. ι ι ij

?

a. a.

2

k ~b

/ PV RT

Ί

x

„ "

i

(4)

P(V-b ) RT m

n

+

) - yyx χ (k -k )7a a + χ Tx k -k )Ja a b i j ij ji i j i ki ik k i k ij ι _ a ' b m m a 2V + b (u-7u -4w) in = (5) - 4w b R T 2V + b (u+7u -4w) +a

ik

I

i

7

V

m

-

k i

;

/

V

2

2

Ju

2

m

m

To e s t i m a t e the pure component p a r a m e t e r s , we u s e d the t e c h n i q u e o f P a n a g i o t o p o u l o s and Kumar ( 1 1 ) . The t e c h n i q u e p r o v i d e s p a r a m e t e r s t h a t e x a c t l y r e p r o d u c e the v a p o r p r e s s u r e and l i q u i d d e n s i t y o f a s u b c r i t i c a l component. T a b l e I I p r e s e n t s the pure component p a r a m e t e r s t h a t were used. F o r the s u p e r c r i t i c a l components, the u s u a l a c e n t r i c f a c t o r c o r r e l a t i o n was u t i l i z e d . I t i s i m p o r t a n t t o n o t e , t h a t the i n t e r a c t i o n p a r a m e t e r s between the components (two p e r b i n a r y ) were e s t i m a t e d s o l e l y from b i n a r y phase e q u i l i b r i u m d a t a , i n c l u d i n g l o w - p r e s s u r e VLE d a t a f o r the b i n a r y a c e t o n e - water; no t e r n a r y d a t a were u s e d i n the f i t t i n g . The v a l u e s o f the i n t e r a c t i o n p a r a m e t e r s o b t a i n e d a r e shown i n T a b l e I I I .


128


TABLE I I

: Pure component p a r a m e t e r s


Component

T(K)

3

a

(Jxm /mol)

10

6

Acetone

313.15 333.15

2.1772 2.1165

62.35 62.65

Ethanol

308.15 323.15 338.15

2.0292 1.9679 1.9069

48.23 48.44 48.61

Water

313.15 333.15

.81614 .79123

16.07 15.99

TABLE I I I

System

:

b

3

(m /mol)

I n t e r a c t i o n parameters

Τ (Κ)

^12

^2 1

C0 (1) - acetone(2)

313 15 333 15

C0 (1) - ethanol(2)

308 15 323 15 338 15

0.072 0.093 0.089

0.069 0.077 0.061

C 0 ( 1 ) - water(2)

313 15 333 15

-0.205 -0.185

0.162 0.160

acetone(1) - water(2)

313 15 333 15

-0.310 -0.293

-0.150 -0.132

2

2

2

-0.02 -0.02

0.00 0.00


10.

PANAGIOTOPOULOS A N D REID


129


Conclusions A r e c i r c u l a t i o n apparatus f o r the d e t e r m i n a t i o n o f h i g h pressure phase e q u i l i b r i u m d a t a f o r m i x t u r e s o f water, p o l a r o r g a n i c l i q u i d s and s u p e r c r i t i c a l f l u i d s was c o n s t r u c t e d and o p e r a t e d f o r b i n a r y and t e r n a r y systems w i t h s u p e r c r i t i c a l c a r b o n d i o x i d e . The system c a r b o n d i o x i d e - a c e t o n e - w a t e r was i n v e s t i g a t e d a t 313 and 333 K. The system d e m o n s t r a t e s s e v e r a l o f t h e g e n e r a l c h a r a c t e r i s t i c s o f phase e q u i l i b r i u m b e h a v i o r f o r t e r n a r y aqueous systems with a s u p e r c r i t i c a l f l u i d . These i n c l u d e an e x t e n s i v e LLV r e g i o n t h a t a p p e a r s a t r e l a t i v e l y low p r e s s u r e s . Carbon d i o x i d e e x h i b i t s a h i g h s e l e c t i v i t y f o r a c e t o n e o v e r w a t e r and c a n be u s e d t o e x t r a c t a c e t o n e from d i l u t e aqueous s o l u t i o n s . A model b a s e d on a m o d i f i e d m i x i n g r u l e f o r t h e Peng-Robinson e q u a t i o n o f s t a t e was a b l e t o r e p r o d u c e q u a n t i t a t i v e l y a l l f e a t u r e s o f t h e o b s e r v e d phase e q u i l i b r i u m b e h a v i o r , w i t h model p a r a m e t e r s determined from b i n a r y data only. The use o f s u c h models may s u b s t a n t i a l l y f a c i l i t a t e t h e t a s k o f p r o c e s s d e s i g n and o p t i m i z a t i o n for separations that u t i l i z e s u p e r c r i t i c a l f l u i d s .

Acknowledgments F i n a n c i a l s u p p o r t f o r t h i s r e s e a r c h was p r o v i d e d b y a g r a n t from t h e National Science Foundation. One o f t h e a u t h o r s (AZP) was a l s o s u p p o r t e d by a H a l c o n I n c . F e l l o w s h i p . We g r a t e f u l l y acknowledge both sponsors.

Literature Cited 1. Elgin, J.C.; Weinstock, J.J. J. Chem. Eng. Data 1959, 4(1), 3-12. 2. Paulaitis, M.E.; Gilbert, M.L.; Nash, C.A. "Separation of Ethanol - Water Mixtures with Supercritical Fluids", paper presented at the 2nd World Congress of Chemical Engineering, Montreal, Canada, Oct. 5, 1981. 3. Paulaitis, M.E.; Kander, R.G.; DiAndreth, J.R. Ber. Bunsenges. Phys. Chem. 1984, 88, 869-875. 4. Kuk, M.S.; Montagna, J.C. Ch. 4 in Paulaitis. M.E. et al. (ed), "Chemical Engineering at Supercritical Fluid Conditions", Ann Arbor Science Publishers, Ann Arbor, Mich., 1983 pp. 101-111. 5. McHugh, M.A.; Mallett, M.W.; Kohn, J.P. "High Pressure Fluid Phase Equilibria of Alcohol - Water - Supercritical Solvent Mixtures", paper presented at the 1981 annual AIChE meeting, New Orleans, Louisiana, Nov. 9, 1981. 6. Radosz, M. Ber. Bunsenges. Phys. Chem. 1984, 88, 859-862. 7. Dietz, W.A. J. Gas Chrom. 1967, 5(2) 68-71. 8. Panagiotopoulos, A.Z.; Reid, R.C., in "Equations of StateTheories and Applications", Robinson, R.L; Chao, K.C. (ed.), ACS Symposium Series No. 300, American Chemical Society, Washington, D.C., 1986; pp. 571-582. 9. Francis, A.W. J. Phys. Chem. 1954, 58, 1099-1114 10. Katayama, T.; Oghaki, K.; Maekawa, G.; Goto, M.; Nagano, T. J. Chem. Eng. Jpn. 1975, 8(2) , 89-92. 11. Panagiotopoulos, A.Z.; Kumar, S. Fluid Phase Equil. 1985, 22, 77-88. RECEIVED

June 24, 1986


Supercritical Fluids - American Chemical Society

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