Environmental Engineering Reference
In-Depth Information
rates of mass transfer for a rate-based process:
x
i
,
1
/
x
j
,
1
α
ij
=
x
j
,
2
,
(2.8)
x
i
,
2
/
where
x
i
,
1
=
fraction of component
i
in stream 1
x
j
,
1
=
fraction of component
j
in stream 1
x
i
,
2
=
fraction of component
i
in stream 2
x
j
,
2
=
fraction of component
j
in stream 2.
Various terms will be used to represent these quantities depending on the process. A
target for the composition of one or more product streams usually dictates the separation
requirement for a particular process.
There are two types of separation factors commonly used; the ideal and the actual
separation factors. The ideal separation factor is based on the equilibrium concentrations
or transport rates due to the fundamental physical and/or chemical phenomena that dictate
the separation. This is the separation factor that would be obtained without regard to the
effects of the configuration, flow characteristics, or efficiency of the separation device.
This value can be calculated from basic thermodynamic or transport data, if available, or
obtained from small-scale laboratory experiments. For an equilibrium-based separation,
the ideal separation factor would be calculated based on composition values for complete
equilibrium between phases. For a rate-based separation, this factor is calculated as the ratio
of transport coefficients, such as diffusion coefficients, without accounting for competing
or interactive effects. Each component is assumed to move independently through the
separation device.
2.7.1
Equilibrium-based process
α
ij
, is the ratio of the concentration of components
i
and
j
(mole
fractions, for example) in product stream (1) divided by the ratio in product stream (2).
For example, in distillation
The separation factor,
α
ij
is defined in terms of vapor and liquid mole fractions
(Figure 2.4):
x
i
,
1
/
x
j
,
1
y
a
/
y
b
α
ij
=
x
j
,
2
=
x
b
,
(2.9)
x
i
,
2
/
x
a
/
(1)
y
a
,
y
b
Vapor
Liquid
(2)
x
a
,
x
b
Figure 2.4
Distillation product streams.
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