Information Technology Reference
In-Depth Information
L
j-1
, l
j-1
i
V
j
, v
j
i
F
J
f
j
i
S
j
, s
j
i
Q
j
V
J+i
, v
i
j+1
L
j
, l
j
i
Stage j at T
j
and P
j
Figure 11.1
Theoretical stage.
K
i
depends on the stage temperature, pressure, and liquid and vapor mole fractions,
x
i
and
y
i
. Mole fractions can be expressed in terms of componential molar flows; for
example, a liquid mole fraction can be calculated by
l
i
k
=
1
,m
l
k
x
i
=
(11.1)
where
m
is the number of components.
V
j
and
L
j
are auxiliary variables which refer
to the total molar vapor and liquid leaving stage
j
and are calculated by summing the
componential flows in the vapor and liquid, leaving a stage as shown in
=
k
v
k
V
j
=
1
,m
(11.2)
l
k
L
j
=
k
=
1
,m
H
j
and
h
j
are the molar enthalpies of the vapor and liquid leaving stage
j
,which
depend on composition, temperature, and pressure.
The material balance for component
i
,onstage
j
,isgivenby
f
i
v
j
−
1
i
l
j
+
1
i
v
i
l
i
s
i
+
+
−
−
−
=
0
(11.3)
where
s
i
refers to the molar flow of component
i
in a sidestream, if it exists. There are
nm
material balances, where
n
is the number of theoretical stages and
m
is the number
of components. The introduction of a sidestream adds one degree of freedom since
the state of a sidestream is equal to the state of its source (i.e., the phase of the stage
from which it is removed), but its flow rate is unknown; however, the composition,
temperature, and pressure of the sidestream are known. A specification for a liquid
sidestream, such as the ratio of the sidestream to the liquid, removes the extra degree of
freedom and permits the added calculation of the componential flows of the sidestream.
