Page 117 - The engineering of chemical reactions

Variable-Density Reactors 101

we required that the system be closed, meaning that we neither add nor remove fluids after
t = 0, where we assumed we started the process. It is of course possible to add feed or
withdraw product continuously in a “batch” process, and we call this a semibatch reactor.
If the reactor is spatially uniform, the mass balance on species j can be written as
dN,
J = Fj, - Fj + Vvjr
dt
and for reactant A this becomes

- z.z FA,, - FA -
dNA Vr
d t
For a constant-density, constant volume reactor we can write
dCA
V - = t&CA,, - VCA - vr
dt
Note that this is exactly the transient CSTR equation we derived previously, and elimination
of the flow terms yields the batch reactor. Keeping all these terms and allowing v,, u, V,
and CA0 to vary with time yields the semibatch reactor.
In this reactor species A may be added continuously but nothing removed to give
dC.4
V - = vocAo - Vr
dt
but now the volume V of the reactor contents increases linearly with time
v = v, + v,t
We therefore obtain

(v, + v,t) $+ = VocA,., - (v, + v,t)r(cA)
This is a simple first-order differential equation in CA and t, but the equation is not separable
and must be solved numerically.
Semibatch reactors are especially important for bioreactions, where one wants to add
an enzyme continuously, and for multiple-reaction systems, where one wants to maximize
the selectivity to a specific product. For these processes we may want to place one reactant
(say, A) in the reactor initially and add another reactant (say, B) continuously. This makes
CA large at all times but keeps Cg small. We will see the value of these concentrations on
selectivity and yield in multiple-reaction systems in the next chapter.
Semibatch processes are also important in solids processing such as in foods and
microelectronics, where it is more practical to load the reactor with a batch of solids (bread
dough or silicon wafers) and subject the solids to heat and gas or liquid reactants. The
processed solids are then withdrawn after a suitable time, and the reactor is reloaded.

VARIABLE-DENSITY REACTORS

Consider the reaction
A -+ 3B, r=kC;
in a constant-pressure reactor with A and B ideal gases and no diluents present. The density
of the fluid in the reactor clearly changes as the reaction proceeds. At completion in a