Thermodynamics of the separation
Thermodynamic properties play an important role in separation operations with respect to
energy requirements, phase equilibria, biological activity, and equipment sizing [1]. In
distillation, since liquid activity coefficient and excess properties of equilibrium state can
give predictions for K-value or property changes of mixing, analyzing phase equilibrium state
can be significant [2]. There are several models for the prediction of vapor-liquid equilibrium
(VLE). Here, we will deal with the underlying principles of VLE and the models for VLE for
binary system, and show them as diagrams of ethanol-water system comparing with
experimental data.
Underlying principles
The definition of activity coefficient is
species i,
where
is the fugacity of species i in solution,
is the activity coefficient of
is the fugacity of pure species i , and
is liquid mole fraction of i in solution. By Lewis/Randall rule, this equation converts into
where
is the fugacity of species i in ideal solution [2].
At VLE, the Gibbs free energy of the two phases should be equal, which means the fugacity
of the two phases also should be the same.
By the definition,
. VLE measurements are very often made at pressure low
enough that the vapor phase may be assumed an ideal gas. In this case,
equation to
=, leads the
[2].
With these principles and assumptions, the activity coefficient is re-defined as
, and this is modified Raoult’s law allowing calculation of activity coefficients
from experimental low-pressure VLE data [2].
Activity coefficient
is
also
(for
partial
molar
binary
property of
system).
By
solution,
which
summability
gives
relation,
. With this equation, the models show a little bit different relation
between liquid composition and activity coefficient, which gives the liquid activity
coefficient of the system. Vapor composition, pressure, and temperature also can be derived
from the activity coefficient and modified Raoult’s law [2].
Furthermore, the definition of K-value for modified Raoult’s law,
, can give
predictions for K-value from the derived activity coefficient [1].
Models – Margules, Van Laar, Wilson, NRTL, UNIFAC
[1] Seader J.D., Henley E.J., and Roper D.K., “Separation Process Principles”. John Wiley &
Sons, 3rd Edition, 2011.
[2] Smith J.M., Van Ness H.C., and Abbott M.M., “Introduction to Chemical Engineering
Thermodynamics”. McGrawHill, 7th edition, 2005.