Page 76 - Elements of Chemical Reaction Engineering 3rd Edition

48 Conversion and Reactor Sizing Chap. 2

2.4 Reactors in Series
Many times reactors are connected in series so that the exit stream of one reac-
tor is the feed stream for another reactor. When this arrangement is used it is
often possible to speed calculations by defining conversion in terms of location
at a point downstream rather than with respect to any single reactor. That is,
the conversion X is the total number of moles of A that have reacted up to that
point per mole of A fed to the first reactor. However, this definition can only
be used provided that there are no side streams withdrawn and the feed stream
enters only the first reactor in the series.
As an example, the relationships between conversion and molar floy
rates for the reactor sequence shown in Figure 2-2 are given by the following
equations:

where

total moles of A reacted up to point 2
x2 =
mole of A fed to first reactor
Similar definitions exist for XI and X,.
The volume Vl is given by Equation (2-16):
dX
Reactor 1 '1 = FAO lox' 3
A mole balance on species A for the CSTR in the middle gives

in - out + generation = 0
FAI-FA~ + r~2v2 =o

Rearranging gives us
-rAZ is evaluated
at X, for the CSTR v, = FAI -
in this series
arrangement -%2

Figure 2-2 PFR-CSTR-PFR in series.