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In-Depth Information
Vapor, V, v
i
Flash3
Feed, F, f
i
Second Liquid, L
2
, l
2
i
Heat, Q
First Liquid, L
1
, l
1
i
Figure 7.7
Flash3 model.
of the second liquid phase, in moles/time; and
I
i
the flow of component
i
in the liquid,
in moles/time. Including the flash temperature
T
f
and pressure
P
f
results in 3
n
+
2
independent variables, where
n
is the number of components given the feed state. The
variables consist of the equilibrium temperature, the flash pressure, and the three total
flows (i.e., and
L
1
,L
2
,
and
V
), and 3
(n
−
1
)
componential flows or, alternatively, 3
n
componential flows, excluding the total flows. Mole fractions are calculated from the
independent variables by an equation such as equation (7.1).
The applicable material balances are
n
componential equations, such as
f
i
−
v
i
−
l
i
−
l
i
=
0
(7.7)
or alternatively,
n
−
1 equations such as equation (7.7) and one overall material bal-
ance, given by
F
−
V
−
L
1
−
L
2
=
0
(7.8)
Additionally, 3
n
equilibrium equations which describe the equality of the fugacities
of components in each phase can be written, but only 2
n
are independent. The vapor-
phase fugacity is represented by an equation of state where the
i
are the fugacity
coefficients of component
i
in the vapor phase, and the liquid phases are represented
by an activity coefficient equation where
γ
1
i
2
i
are the activity coefficients of
component
i
and
p
i
is the vapor pressure of component
i
. Then any two of
and
γ
i
x
i
1
2
i
x
i
γ
− γ
=
0
(7.9a)
V
i
P
− γ
i
,x
i
p
i
1
y
i
φ
=
0
(7.9b)
V
i
P
− γ
i
,x
i
p
i
2
y
i
φ
=
0
(7.9c)
apply. For the sake of simplicity the Poynting correction (see Poling et al., 2000), which
has a contribution only for very light components, has been omitted from equations
(7.9b) and (7.9c). The overall energy balance given by equation (7.5) completes a set
of 3
n
+
1 equations:
