Page 103 - The engineering of chemical reactions

The Continuous Stirred Tank Reactor 87

reactor,” which we will call the continuous stirred-tank reactor or CSTR (Figure 3-l).
Our picture is that of a tank with a stirring propeller that is fed and drained by pipes
containing reactants and products, respectively. In this situation the crucial feature is that
the composition is identical everywhere in the reactor and in the exit pipe. Nothing is a
function of position except between the inlet pipe and the reactor entrance, where mixing
is assumed to occur instantly!
The idea that the composition is identical everywhere in the reactor and in the exit
pipe requires some thought. It might seem that, since the concentration changes instantly
at the entrance where mixing occurs, reaction occurs there and nothing else happens in the
reactor because nothing is changing. However, reaction occurs throughout the reactor, but
mixing is so rapid that nothing appears to change with time or position.
The “completely mixed” limit is in fact rather easy to achieve with ordinary mixing
techniques. The approximation can be thought of in terms of “mixing time” rmix versus
residence time t of the fluid in the reactor. If

then the reactor is totally mixed to a good approximation. Temperature variations within
some large reactors also produce enough natural convection to help stir the contents.
The approximation of a well-mixed reactor requires merely that the region of variable
composition (and variable rate) near the entrance be small compared to the volume of the
reactor.
Since the reactor is assumed to be uniform in composition everywhere, we can make
an integral mass balance on the number of moles Nj of species j in a reactor of volume V.
This gives
[accumulation] = [flow in] - [flow out] + [generation]
or

where Fjo and Fj are molarflow rates of species j (in moles/time) in the inlet and outlet,
respectively. Each term in this equation has dimensions of moles/time. This equation as
written is exact as long as the reactor is completely mixed. We will develop several versions

Figure 3-l The continuous stirred
tank reactor (CSTR) of volume V with
inlet molar flow rate Fj, and outlet mo-
lar flOW rate Fj

Fjo = VoCjo Fj = VCj