Page 118 - The engineering of chemical reactions

102 Single Reactions in Continuous Isothermal Reactors

continuous reactor, we make three moles of product for each mole of reactant fed into the
reactor so that the volumetric flow rate out of the reactor u would be three times the flow
rate into the reactor uO,
v = 3v,
In a tubular reactor of constant diameter the velocity u when the reaction has gone to
completion is three times tbe inlet velocity uO,
u = 34
We call this situation variable density, *and the previous equations clearly do not describe
this situation because v, t, and u in these equations depend on the conversion.
For ideal gases the mole densities do not change if the reaction produces more or less
moles of product than the reactants. However, the mass density of the gas mixture changes,
and this causes the volumetric ilow rate and velocity of gases through the reactor to change
as the conversion increases.
For the batch reactor we saw in the previous chapter that by switching from CA as
the composition variable to fractional conversion X, we could easily write the differential
equation to be solved for compositions versus time. We prefer to use concentration units
whenever possible, but, if the density is a function of composition, concentrations become
cumbersome variables, and we must switch to another designation of density such as the
fractional conversion X.

CSTR

For the CSTR we begin with the mass-balance equation we derived before we substitute
for concentration
dN,
J = Fjo - Fj + Vvjr
dt
which for reactant A in steady state becomes
FAN - FA - Vr = 0
Now since the molar flow rate of A varies with conversion as
FA = FA,(~ - X)
we can write this mass-balance equation as

FAN - FA = F,J~X = Vr(X)
In steady state this equation can be rearranged to become

While this equation is correct for the steady-state CSTR with variable density, it does not
give a correct description of the transient CSTR for variable density because NA (meaning
the number of moles of species A in the reactor) is not given by the preceding expression
unless the density is constant.