Page 47 - Introduction to chemical reaction engineering and kinetics

2.3 Continuous Stirred-Tank Reactor (CSTR) 29

For a reaction represented by A + products, in which the rate, ( -rA), is proportional to CA,
with a prOpOrtiOnality Constant kA, show that the time (t) required to achieve a specified
fractional conversion of A (fA) is independent of the initial concentration of reactant cAO.
Assume reaction occurs in a constant-volume batch reactor.
SOLUTION

The rate law is of the form

(-rA) = kACA

If we combine this with the material-balance equation 2.2-10 for a constant-density reac-
tion,

-dc,ldt = kACA

From this, on integration between CA0 at t = 0 and CA at t,

t = (IlkA) ln(CAo/CA) = (l/k,) h[l/(l - fA)]

from equation 2.2-3. Thus, the time t required to achieve any specified value of fA under
these circumstances is independent of cAO. This is a characteristic of a reaction with this
form of rate law, but is not a general result for other forms.

2.3 CONTINUOUS STIRRED-TANK REACTOR (CSTR)

2.3.1 General Features
A continuous stirred-tank reactor (CSTR) is normally used for liquid-phase reactions,
both in a laboratory and on a large scale. It may also be used, however, for the labora-
tory investigation of gas-phase reactions, particularly when solid catalysts are involved,
in which case the operation is batchwise for the catalyst (see Figure 1.2). Stirred tanks
may also be used in a series arrangement (e.g., for the continuous copolymerization of
styrene and butadiene to make synthetic rubber).
A CSTR, shown schematically in Figure 2.3(a) as a single vessel and (b) as two vessels
in series, has the following characteristics:
(1) The flow through the vessel(s), both input and output streams, is continuous but
not necessarily at a constant rate.
(2) The system mass inside each vessel is not necessarily fixed.
(3) The fluid inside each vessel is perfectly mixed (backmix flow, BMF), and hence
its properties are uniform at any time, because of efficient stirring.
(4) The density of the flowing system is not necessarily constant; that is, the density
of the output stream may differ from that of the input stream.
(5) The system may operate at steady-state or at unsteady-state.
(6) A heat exchanger may be provided in each vessel to control temperature (not
shown in Figure 2.3, but comparable to the situation shown in Figure 2.1).

There are several important consequences of the model described in the six points
above, as shown partly in the property profiles in Figure 2.3: