Page 91 - Separation process principles 2

56 Chapter 2 Thermodynamics of Separation Operations

liquid-liquid, and vapor-liquid-liquid systems. For multi- UNIQUAC Model
component vapor-liquid systems, only binary-pair constants
In an attempt to place calculations of liquid-phase activity
from the corresponding binary-pair experimental data are re-
coefficients on a simple, yet more theoretical basis, Abrarns
quired. For a multicomponent system, the NRTL expression
and Prausnitz [43] used statistical mechanics to derive
for the activity coefficient is
an expression for excess free energy. Their model, called
UNIQUAC (universal quasichemical), generalizes a previ-
ous analysis by Guggenheim and extends it to mixtures of
molecules that differ appreciably in size and shape. As in the
Wilson and NRTL equations, local concentrations are used.
However, rather than local volume fractions or local mole
fractions, UNIQUAC uses the local area fraction Oij as the
where primary concentration variable.
The local area fraction is determined by representing a
molecule by a set of bonded segments. Each molecule is
The coefficients 7 are given by characterized by two structural parameters that are deter-
mined relative to a standard segment taken as an equivalent
sphere of a unit of a linear, infinite-length, polymethylene
molecule. The two structural parameters are the relative
number of segments per molecule, r (volume parameter),
and the relative surface area of the molecule, q (surface
where gij, gjj, and so on are energies of interaction between parameter). Values of these parameters computed from bond
molecule pairs. In the above equations, Gji # Gij, ~i, # rji, angles and bond distances are given by Abrams and
Gii = Gjj = 1, and 7ii = T,, = 0. Often (g.. - g..) and Prausnitz [43] and Gmehling and Onken [39] for a number
J JJ
other constants are linear in temperature. For ideal solutions, of species. For other compounds, values can be estimated by
7ji = 0. the group-contribution method of Fredenslund et al. [46].
The parameter aji characterizes the tendency of species j For a multicomponent liquid mixture, the UNIQUAC
and species i to be distributed in a nonrandom fashion. When model gives the excess free energy as
aji = 0, local mole fractions are equal to overall solution
mole fractions. Generally oiji is independent of temperature
and depends on molecule properties in a manner similar to
the classifications in Tables 2.7 and 2.8. Values of aji usually
lie between 0.2 and 0.47. When orji < 0.426, phase immisci-
bility is predicted. Although aji can be treated as an ad-
justable parameter, to be determined from experimental
binary-pair data, more commonly aji is set according to the The first two terms on the right-hand side account for com-
following rules, which are occasionally ambiguous: binatorial effects due to differences in molecule size and
shape; the last term provides a residual contribution due to
1. all = 0.20 for mixtures of saturated hydrocarbons and differences in intermolecular forces, where
polar, nonassociated species (e.g., n-heptanelacetone).
Xi r,
-
2. a,, = 0.30 for mixtures of nonpolar compounds (e.g., qJ. - -
I- rr - segment fraction (2-94)
benzeneln-heptane), except fluorocarbons and paraf-
fins; mixtures of nonpolar and polar, nonassociated
species (e.g., benzenelacetone); mixtures of polar
species that exhibit negative deviations from Raoult's e=- = area fraction (2-95)
C
law (e.g., acetonelchloroform) and moderate positive C xiqi
deviations (e.g., ethanollwater); mixtures of water and i=l
polar nonassociated species (e.g., waterlacetone). where 2 = lattice coordination number set equal to 10, and
3. a,, = 0.40 for mixtures of saturated hydrocarbons and u.. - u..
homolog perfluorocarbons (e.g., n-hexanelperfluoro- qi = exp ( )
n-hexane).
4. a,, = 0.47 for mixtures of an alcohol or other strongly Equation (2-93) contains only two adjustable parameters
self-associated species with nonpolar species (e.g., for each binary pair, (uji - uii) and (uij - ujj). Abrams
ethanolhenzene); mixtures of carbon tetrachloride and Prausnitz show that u,i = uij and Ti = Tjj = 1. In gen-
with either acetonitrile or nitromethane; mixtures of eral, (uji - uii) and (uij - u,,) are linear functions of
water with either butyl glycol or pyridine. temperature.