8
Second Virial Cross-Coefficients: Correlation and Prediction of kij CONSTANTINE TSONOPOULOS
Downloaded by CORNELL UNIV on December 6, 2012 | http://pubs.acs.org Publication Date: December 1, 1979 | doi: 10.1021/ba-1979-0182.ch008
Exxon Research and Engineering Company, Florham Park, NJ 07932
The prediction of the second virial cross-coefficient Bij depends most sensitively on the mixing rule for the charac teristic critical constantT (Equation 5). The characteristic binary constant, k , can be determined by fitting B and other data. The prediction of B , therefore, requires knowl edge of k The k values are available for binaries of inorganic gases and hydrocarbons with up to 8 carbon atoms. Extensions in the data base and correlations for k 's are presented here in two areas. First, recent B data for binaries involving C -C hydrocarbons are reduced to k 's, which are shown to be both meaningful and satisfactory in the calculation of B over the entire carbon-number range. A similar approach is taken in the second area investigated, binaries involving polar compounds. New k data are used to establish trends and develop preliminary k correlations so that B and, more importantly, fugacity coefficients can be predicted reliably. cij
ij
ij
ij
ij.
ij
ij
ij
10
30
ij
ij
ij
ij
ij
I
n t h e analysis a n d c o r r e l a t i o n of v a p o r - l i q u i d e q u i l i b r i u m ( V L E ) d a t a i t is essential, e s p e c i a l l y at s u p e r a t m o s p h e r i c
a c c o u n t t h e effect of v a p o r - p h a s e
nonideality.
pressures, to t a k e i n t o
T h i s is expressed b y t h e
f u g a c i t y coefficient w h i c h , as l o n g as t h e d e n s i t y of t h e m i x t u r e is n o t greater t h a n o n e f o u r t h of its c r i t i c a l v a l u e , c a n b e c a l c u l a t e d r e l i a b l y w i t h the following equation (for a binary m i x t u r e ) :
In φι = where φ, y {
iy
2 -ψ- (yi B * m
u
+ yj
— In z
(1)
m
a n d Bu are t h e f u g a c i t y coefficient, v a p o r m o l e f r a c t i o n , a n d
s e c o n d v i r i a l coefficient of C o m p o n e n t i, w h i l e v
m
and z
m
are the molar
0-8412-0500-0/79/33-182-143$05.00/l © 1979 American Chemical Society
In Equations of State in Engineering and Research; Chao, K., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979.
144
EQUATIONS
OF STATE
v o l u m e a n d c o m p r e s s i b i l i t y factor of the v a p o r m i x t u r e . I t is t h e p r e d i c t i o n of By, t h e s e c o n d v i r i a l cross-coefficient,
that w i l l p r i m a r i l y con-
c e r n us. Bu w i l l b e p r e d i c t e d w i t h a n e m p i r i c a l c o r r e l a t i o n that w a s p r o p o s e d in
1974 ( J ) .
T h e original correlation was developed
oxygenated polar compounds,
primarily for
b u t i t has b e e n e x t e n d e d to haloalkanes
( 2 ) a n d w a t e r p o l l u t a n t s ( 3 ) . Refs. 1, 2, a n d 3 c a n b e c o n s u l t e d f o r details o n t h e d e v e l o p m e n t of t h e c o r r e l a t i o n a n d t h e results. Nonpolar
Mixtures
Downloaded by CORNELL UNIV on December 6, 2012 | http://pubs.acs.org Publication Date: December 1, 1979 | doi: 10.1021/ba-1979-0182.ch008
F o r n o n p o l a r c o m p o u n d s a n d m i x t u r e s , t h e c o r r e l a t i o n is a m o d i f i e d f o r m of t h e P i t z e r - C u r l r e l a t i o n s h i p (see Réf. I ) : BP* RT„
_
f
(
0
(
)
f ( r ) = 0.1445 -
Γ ε )
+
e
f
0.330/r
n
0.0121/7V Ε
T h e same equations are u s e d f o r B T , and ω Cij
ί;
-
)
( ) 2
0.1385/7V
-
0.423/7V -
0.008/r
R
8
(4)
b u t w i t h characteristic p a r a m
ij9
Cij
R
( Γ β
O.00O6O7/7V
f
