Page 429 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TRANSFER WITH CONVECTION 409

is carried out in a constant pressure batch reactor at 400°C and 5atm pressure.
The reaction is first-order and the time required to achieve 60% conversion was
found to be 50min.
Suppose that this reaction is to be carried out in a plug flow reactor which
operates isothermally at 400 "C and at a pressure of 10 atm. The volumetric flow
rate of the feed entering the reactor is 0.05 m3/ h and at consists of pure A. Calculate
the volume of the reactor required to achieve 80% conversion.

Solution

First, it is necessary to determine the rate constant by using the data given for the
batch reactor. The conservation statement for the number of moles of species A,

(1)
or,
dnA
- k CAV = - (2)
dt
Substitution of the identity nA = CAV into Eq. (2) and rearrangement gives

Integration gives the rate wnstant, k, as

k=-;-ln($)
1
(4)
The fractional conversion, X, is

Therefore, Eq. (4) can be eqressed in tern of the fractional conversion as
In( 1 - X)
k=-
t
Substitution of the numerical values into Eq. (6) gives

For a plug flow reactor, Eq. (9.5148) takes the form