Page 43 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 1.4 Continuous-Flow Reactors 15

which are, as expected, the same dimension of the molar flow rate FA. After
dividing by AW and taking the limit as AW -+ 0, we arrive at the differential
form of the mole balance for a packed-be4 reactor:
Use differential form
of design equation
for catalyst dzcay (1-13)
and pressure drop
VVhen pressure drop through the reactor (see Section 4.4) and catalyst
decay (see Section 10.7) are neglected, the integral form of the packed-cata-
lyst-bed design equation can be used to calculate the catalyst weight.

(1-14)

To obtain some insight into things to come, consider the following exam-
ple of how one can use the tubular reactor design equation (1-10).

Example 1-3 How Large Is It?

The first-order reaction

A-B
is carried out in a tubular reactor in which the volumetric flow rate, u, is constant.
Derive an equation relating the reactor volume to the entering and exiting concen-
trations of A, the rate constant k, and the volumetric flow rate u. Determine the reac-
tor volume necessary to reduce the exiting concentration to 10% of the entering
concentration when the volumetric flow rate is 10 dm3/min (Le., liters/min) and the
specific reaction rate, k, is 0.23 min-' .

For a tubular reactor, the mole balance on species A (i = A) was shown to be

(1-10)

For a first-order reaction, the rate law (discussed in Chapter 3) is
-rA = kCA (El -3.1)

Since the volumetric flow rate, uo, is constant,
Reactor sizing
(El-3.2)

Substituting for r, in Equation (El-3.1) yields

(El-3.3)