Page 113 - The engineering of chemical reactions

Comparison between Batch, CSTR, and PFTR 97

Example 3-5 Compare the reactor volumes necessary to attain the conversions in the
previous examples for first and second order irreversible reactions in a CSTR with a CSTR.
For a first-order irreversible reaction

VC~TR = 72 liters
and
Vpm~ = 18.4 liters
For a second-order irreversible reaction

VC~TR = 360 liters
and
Vpm~ = 36 liters
The PFTR is the clear “winner” in this comparison if reactor volume is the only
criterion. The choice is not that simple because of the costs of the reactors and
pumping costs.

COMPARISON BETWEEN BATCH, CSTR, AND PFTR

We have now developed mass balance equations for the three simple reactors in which
we can easily calculate conversion versus time &,r&, residence time t, or position L for
specified kinetics. For a first-order irreversible reaction with constant density we have solved
the mass balance equations to yield
1 %CA 1
TPFl’R = thatch = - - ~ = - - ln$=+iln$
k s CA k
CAo
and
CAo - CA
@sTR =
kCA
Obviously, batch and PFTR will give the same conversion, but the CSTR gives a lower
conversion for the same reaction time (batch) or residence time (continuous).
We can immediately see major reactor design considerations between batch, CSTR,
and PFTR. Table 3-l shows the first of many situations where we are interested in the
design of a reactor. We may be interested in choosing minimum volume or many other
process variables in designing the best reactor for a given process.
In spite of the simplicity and continuous operation of the CSTR, it usually requires a
longer residence time for a given conversion. For first-order kinetics at identical conversions
and volumetric flow rates, this ratio is

X
TCSTR VCSTR CAo - CA CAoICA - 1

CA ln(C~~/c~) = ln(C&CJ = (1 - X) ln[l/(l- X)]
TPFTR VPFTR
We indicate this ratio for different values of fractional conversion in Table 3-2.