Page 67 - Separation process principles 2

32 Chapter 2 Thermodynamics of Separation Operations

Table 2.2 Thermodynamic Quantities for Phase Equilibria
Limiting Value
for Ideal Gas and
Thermodynamic Quantity Definition Physical Significance Ideal Solution

Chemical potential Partial molar free energy, gi
8 = c exp (s)
Partial fugacity Thermodynamic pressure

fi
bE-
Fugacity coefficient of a pure species Deviation to fugacity due hv = 1.0
P
to pressure P;
hL =.p
&v = 1.0
Partial fugacity coefficient of a v - Deviations to fugacity due to &L = ,
species in a mixture pressure and composition Pi"

Activity Relative thermodynamic pressure aiv = Yi
aiL = xi

Activity coefficient Deviation to fugacity due yiv = 1.0
to composition yi~ = 1.0

K-Values To form an equilibrium ratio, these partial fugacities are
commonly replaced by expressions involving mole fractions
A phase-equilibrium ratio is the ratio of mole fractions of
as derived from the definitions in Table 2.2:
a species present in two phases at equilibrium. For the
vapor-liquid case, the constant is referred to as the K-value
(vapor-liquid equilibrium ratio or K-factor):
Yi
K. = - fir. = &xi P (2-24)
I - (2- 19)
Xi
and
For the liquid-liquid case, the ratio is referred to as the dis-
tribution coefficient or liquid-liquid equilibrium ratio:
If (2-24) and (2-25) are used with (2-19), a so-called
equation-of-state form of the K-value is obtained:
For equilibrium-stage calculations involving the separation
of two or more components, separation factors, like (1-4),
are defined by forming ratios of equilibrium ratios. For the
vapor-liquid case, relative volatility is defined by
This expression has received considerable attention, with
applications of importance being the Starling modification
of the Benedict, Webb, and Rubin (B-W-R-S) equation of
For the liquid-liquid case, the relative selectivity is state [5], the Soave modification of the Redlich-Kwong
(S-R-K or R-K-S) equation of state [6], the Peng-
Robinson (P-R) equation of state [7], and the Plocker et al.
modification of the Lee-Kesler (L-K-P) equation of state [8].
Equilibrium ratios can be expressed by the quantities in
If (2-23) and (2-25) are used, a so-called activity coefJi-
Table 2.2 in a variety of rigorous formulations. However, the
only ones of practical interest are developed as follows. For cient form of the K-value is obtained:
vapor-liquid equilibrium, (2-9) becomes, for each component,

fiv = fiL