Page 104 - The engineering of chemical reactions

88 Single Reactions in Continuous Isothermal Reactors

of this equation for different conditions, specifically depending on (1) steady-state versus
transient conditions and (2) constant density versus variable density.
It is evident that this equation looks identical to the batch-reactor equation in the
previous chapter except for the flow terms Fjo and Fj, which are of course zero in the batch
reactor. In fact, the batch reactor and the CSTR share the characteristic that properties are
identical everywhere in the reactor. However, the solutions in batch and CSTR are quite
different except for transients, and, as we will see, the performance of the batch reactor is
in fact much closer to the plug-flow tubular reactor than to the mixed reactor.
We can relate Nj and Cj by the relation

NJ = VCj
We can also relate the molar flow rates Fjo and Fj of species j to the concentration by the
relationships

Fj = VCj
respectively, where v, and v are the volumetric flow rates into and out of the reactor.
For reactions among liquids and among gases where the total number of moles does
not change, the density of the system does not change with composition, and therefore
v, = v. If we assume that V is constant and the density does not change with composition,
differentiation of Nj yields
dN.
A=“!?&
dt
If the density of the fluid is constant, then the volumetric flow rates in and out of the
reactor are equal, u = v,. The mass-balance equation then simplifies to become

V $$ = V(Cjo - C j ) + VVjr

Next we assume that compositions are independent of time (steady state) and set the time
derivative equal to zero to obtain

V(Cj, - C j ) + VVjr = 0
We call the volume divided by the volumetric flow rate the reactor residence time
rl
V
r=--
V

[We caution that we have not yet proven that this is the true average residence time, and
we will not do this until Chapter 8. Also, whenever v or V is a functions of conversion, we
cannot treat t as a constant that is independent of conversion.]
With these approximations we write the steady-state mass balance on species j in the
CSTR as