Environmental Engineering Reference
In-Depth Information
the reactor for an indefinite amount of time. The distribution of the time that the mole-
cules spend in the reactor is called the exit age distribution
E
or the RTD of the fluid.
E
has the units of time
−1
. It is common to work with a normalized
E
function so that
the area under the
E
-
t curve is unity:
∞
E
dt = 1
ð
Eq
:
6
:
43
Þ
0
E
can be easily determined by introducing a tracer into the reactor and measuring
its concentration at the exit flow of the reactor at different times. The tracer is typically
a nonreactive component whose concentration can be easily determined, e.g., by
measuring the (liquid
s) color or the conductivity of the exit flow.
There are several common ways of introducing the tracer into the reactor, namely,
as a pulse, step, periodic, or random function. Here, the pulse experiment will be
detailed; for information of other methods, the reader is referred to Westerterp
et al. (1988) and Rawlings and Ekerdt (2002).
Suppose we want to obtain the
E
curve of a reactor with volume V (m
3
) by using a
pulse experiment. The reactor has a continuous inlet flow of
'
s
−1
. Suddenly, an
amount m (kg or moles) of tracer is injected at once (pulse) in the inlet flow right
before it enters the reactor. Then, the concentration of tracer is measured at the outlet
of the reactor at different times. The observed curve of the tracer concentration versus
time has the following properties:
φ
V
0
m
3
Area =
∞
X
t
i
=
m
φ
V
0
m
−3
Area under the c
pulse
curve
cdt
c
i
Δ
kg
s
i
0
ð
Eq
:
6
:
44
Þ
∞
X
tcdt
t
i
c
i
Δ
t
i
=
V
φ
V
0
t=
0
i
X
Mean of the c
pulse
curve
½ ð
s
Eq
:
6
:
45
Þ
∞
c
i
Δ
t
i
cdt
i
0
To obtain the
E
curve, simply normalize the c
pulse
curve dividing by m/
φ
V
0
:
c
pulse
m
E
=
ð
Eq
:
6
:
46
Þ
=φ
V
0
=
t.
θ
Sometimes, it is useful to also normalize the time dividing by the average time
=t
To keep the area under the curve unity,
E
must be multiplied by
t:
E
=
V
c
pulse
m
=
V
E
θ
=
t
φ
V
0
m
c
pulse
ð
Eq
:
6
:
47
Þ
=φ
V
0
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