Environmental Engineering Reference
In-Depth Information
3.7.1
Allowance for stage efficiencies
There are two common approaches to include the influence of non-equilibrium on the
quality of separation achieved for a given number of stages or on the number of actual
stages required for a given separation requirement. The first of these involves the use of
an
overall efficiency E
o
defined as
number of equilibrium stages
number of actual stages
E
o
=
.
(3.60)
In order to use the overall efficiency in a design problem, one carries out an equilibrium-
stage analysis and then determines the number of actual stages as the number of equilibrium
stages divided by
E
o
. Thus the overall efficiency concept is simple to use once
E
o
is known,
but it is often not easy to predict reliable values of
E
o
.
The other commonly used approach involves the concept of the
Murphree vapor effi-
ciency E
MV
defined as:
y
1
−
y
N
+
1
E
MV
=
(3.61)
y
N
−
y
N
+
1
where
y
N
is the vapor composition which would be in equilibrium with the actual value
of
x
N
. There is more theoretical basis for correlating and predicting values of
E
MV
than
is the case for
E
o
.
For the case of a constant Murphree efficiency, the Kremser equation, Equation (3.49),
can be modified to calculate the actual number of stages:
ln
[1
L
)]
y
N
+
1
−
y
1
y
1
−
y
1
+
L
)
−
(
mV
/
(
m
v/
N
=
.
(3.62)
ln
{
1
+
E
MV
[(
mV
/
L
)
−
1]
}
If the value of
E
MV
is known for each stage in a binary separation (or is taken at a
single known constant value for the whole sequence of stages), it may be readily used in
the McCabe-Thiele graphical construction. Chapter 4, on distillation, has a section which
illustrates this approach.
3.8
Rate-limited processes
Analysis of rate-limited processes usually begins with a
differential mass balance
. One
description of this balance for our stationary control volume for a component
A
is:
+
=
+
.
In
Generation
Out
Accumulation
(3.63)
Rearranging,
Accumulation
=
(In
−
Out)
+
Generation
.
(3.64)
In mathematical notation, this is written as:
∂
C
A
∂
=−∇·
N
A
+
R
A
,
(3.65)
t
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