Chapter 9
Van der Waals Mixing Rules for Cubic Equations of State Ε. H. Benmekki, T. Y. Kwak, and G. A. Mansoori
Downloaded by UNIV OF MICHIGAN ANN ARBOR on June 15, 2013 | http://pubs.acs.org Publication Date: December 16, 1987 | doi: 10.1021/bk-1987-0329.ch009
Department of Chemical Engineering, University of Illinois, Box 4348, Chicago, IL 60680
A new concept for the development of mixing rules for cubic equations of state consistent with statistical mechanical theory of the van der Waals mixing rules is introduced. Utility of this concept is illustrated by its application to the Redlich-Kwong (RK) and the Peng-Robinson (PR) equations of state. The resulting mixing rules for the Red1ich-Kwong and the PengRobinson equations of state are tested through prediction of solubility of heavy solids in supercritical fluids and prediction of phase behavior of binary mixtures of hydrocarbons and nonhydrocarbons. There has been extensive progress made in recent years in research towards the development of analytic statistical mechanical equations of state applicable for process design calculations 0,2). However, cubic equations of state are still widely used in chemical engineering practice for calculation and prediction of properties of fluids and fluid mixtures Q). These equations of state are generally modifications of the van der Waals equation of state (4.5). RT (1) ν-b v2 which was proposed by van der Waals (k) in 1873· According to van der Waals, for the extension of this equation to mixtures, it is necessary to replace a and b with the following compositiondependent expressions: η η a = Σ Σ xj Xj . ajj ' J 0097-6156/87/0329-0101 $06.00/0 © 1987 American Chemical Society
In Supercritical Fluids; Squires, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.
(2)
102
SUPERCRITICAL FLUIDS η
η
b = Σ
Σ
'
J
xj
X
(3)
bjj
j
Downloaded by UNIV OF MICHIGAN ANN ARBOR on June 15, 2013 | http://pubs.acs.org Publication Date: December 16, 1987 | doi: 10.1021/bk-1987-0329.ch009
E q u a t i o n s 2 and 3 a r e c a l l e d t h e v a n d e r Waals m i x i n g rules. In these e q u a t i o n s , a;: and b j : (i=j) a r e parameters corresponding t o pure component \\) w h i l e a | : a n d b j : ( i * j ) arecalled the u n i i k e - i n t e r a c t i o n parameters. I t i s customary t o r e l a t e t h e uni i k e interaction parameters t o t h e pure-component parameters by t h e following expressions: ajj
=
(1 - k , j )
bij
=
(b
M
(·,, a j j ) 1 / 2
