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Reactor Design 381

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Substitute x (A = 0, x 2A = 0.37, V v = 5600 ft /h, m, A = 738.7 Ibmol/h and k =
3.766/h"1 into these equations. Then, solve the equations using POLYMATH [22].
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The reaction volume is 873.3 ft 3 (24.7 m ), which is the maximum reaction vol-
ume.
The minimum reaction volume will be for a plug flow reactor, which, for a
first order reaction is
1 5600 1
V v
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V r = — In ——— = ——— hi ———— = 687.0 ft (19.5 m )
k l-x 2A 3.766 1-0.37
For two CSTRs, generate a set of equations for n = 1 and n = 2. For the first
CSTR, when n = 1, the equations are the same as written above. For the second
CSTR, n = 2 in Equations 7.4.1 and 7.4.3 to 7.4.5.

m 2A = m 3A + (x 3A - x 2A ) m 2A

-r 3AV r = (x 3A -x 2A )m 2A

r 3A = - k c 3A

c 3A =m 3A /V v
With x 3A = 0.37, and using the same values of XIA , V v , m 1A, and k as for
one CSTR, the eight equations are solved simultaneously using POLYMATH
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[22]. For two CSTRs, the total reaction volume is 772.9 ft (21.9 m ) , which is in
between the reaction volumes of a single CSTR (873.3 ft3) (24.7 m3) and the plug
flow reactor (687.0 ft3) (19.5 m3). The difference in reaction volume between one
and two CSTRs is only 1 1.5 %, which is not substantial. Select a single CSTR.
The next step is to select a standard CSTR. For the calculated reaction vol-
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ume of 873.3 ft 3 (6533 gal, 24.7 m ), select a standard reaction volume from Table
7.3 of 8000 gal (30.3 m3). Also, from Table 7.3 the reactor volume is 8765 gal
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(33.2 m ) to allow for headspace. Now, we have a number of options available.
One option is not to fill the standard reactor up to the rated volume but only up to
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the calculated reaction volume of 6533 gal (24.7 m ) and maintain the volumetric
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flow rate at 5600 ft /h (21.2 m /h). This means that the conversion will be 0.37 as
specified. CSTRs have a minimum operating reaction volume to avoid imperfect
mixing. Mixing depends on the properties of the reaction mixture, the impeller
design and speed, and the internal design of the CSTR. The minimum operating
reaction volume for good mixing should be determined by consulting with the
manufacturer of the CSTR. A second option is to fill the reactor up to 8000 gal
(30.3 m3) and increase the volumetric flow rate to keep the residence time and
therefore the conversion constant. A third option is to again fill the reactor up to

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