Environmental Engineering Reference
In-Depth Information
Use of activity coefficients (
γ
i
)
Most systems cannot be described by
y
i
=
K
i
x
i
for a wide range of
x
i
values. This equation
only characterizes linear systems and is called an ideal relationship. For non-ideal systems
this relationship is modified by an activity coefficient,
γ
i
, for each component.
At low pressures (up to a few atmospheres):
p
i
y
i
x
i
=
γ
i
P
,
(3.4)
[note: fugacity coefficients are assumed to cancel each other (or nearly) and Poynting
corrections are assumed to be unity (or close)]
where
y
i
=
vapor mole fraction of component
i
x
i
=
liquid mole fraction of component
i
γ
i
=
activity coefficient of component
i
p
i
0
=
vapor pressure of component
i
P
=
total pressure.
Vapor pressure is typically predicted by an Antoine equation:
log
10
p
i
=
A
−
B
+
C
,
(3.5)
T
where
A
,
B
,
C
=
constants
temperature,
◦
C.
T
=
Activity coefficients are generally predicted by one of the Wilson, UNIQUAC, NRTL,
or van Laar methods. The Wilson and UNIQUAC methods are presented briefly here.
Most chemical engineering thermodynamics textbooks have a section on phase equilibria
that can provide more detailed descriptions. The Wilson equation [1] is only used with
miscible fluids. For highly non-ideal fluids and for systems in which liquid-liquid splitting
occurs, the NRTL method is applicable [2]. When no experimental data are available, the
UNIQUAC method can be used [3, 4].
Wilson equation
ln
m
m
x
k
ki
m
ln
γ
i
=−
x
j
ij
+
1
−
x
j
kj
,
(3.6)
j
=
1
j
=
1
k
=
1
where
exp
;
V
j
V
i
−
λ
ij
−
λ
ii
RT
ij
=
(3.7)
and
ii
=
jj
=
1
.
(3.8)
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