Page 243 - Elements of Chemical Reaction Engineering 3rd Edition

Chap. ,4 Questions and Problems 21 5

(a) Neglecting pressure drop, plot the rate of reaction of 0-cresol and the
concentrations of each species as a function of catalyst weight. What is
the ratio of catalyst weight needed to achieve the last 5% conversion to
the weight necessary to achieve the first 5% conversion (0 to 5%) in the
plug-flow reactor?
(b) Accounting for the pressure drop in the packed bed using a value of
(Y I= 0.034 kg-I, redo part (a) along with a plot of pressure versus cata-
-- lyst weight.
(c) Another engineer suggests that instead of changing catalyst size it would
be better to pack the catalyst in a shorter reactor with twice the pipe dim-
eter. If all other conditions remain the same, is this suggestion better?
P4-23(; The elementary gas-phase reaction
A+B + C+D
is carried out in a packed-bed reactor. Currently, catalyst particles 1 mm in
diameter are packed into 4-in. schedule 40 pipe (4 = 0.82126 dmz). The
value of Bo in the pressure drop equation is 0.001 atmldm. A stoichiometric
mixture of A and B enters the reactor at a total molar flowrate of 10
gmolfmin, a temperature of 590 K, and a pressure of 20 am. Flow is turbulent
throughout the bed. Currently, only 12% conversion is achieved with 1010 kg
of catalyst.
It is suggested that conversion could be increased by changing the. cat-
alyst particle diameter. Use the data below to correlate the specific reaction
rate as a function of particle diameter. Then use this correlation to detenmine
the catalyst size that gives the highest conversion. As you will see in Chapter
12, k’ for first-order reaction is expected to vary according to the follo~wing
relationship
3
k’ = qk = -(@cothQ, - 1) k (P4-:!3.1)
$*
where Q, varies directly with particle diameter, Q,= cd, . Although the raac-
tion is not first-order, one notes from Figure 12-5 the functionality for a sec-
ond-order reaction is similar to Equation (P4-23.1). (Ans.: c = 75)
(a) Make a plot of conversion as a function of catalyst size.
(b) Discuss how your answer would change if you had used the effectiveness
factor for a second-order reaction rather than a first-order reaction.
(c) Discuss what you learned from this problem and what you believe to be
the point of the problem.
Additional information:
Void fraFtion = 0.35 Bulk catalyst density = 2.35 kg/dm3

Catalyst Diameter, d,, (mm) 2 1 0.4 0.1 0.02 0.002
k’ (:dm6/mol. min kg cat) 0.06 0.12 0.30 1.2 2.64 3.00
[Hint: You could use Equation (P4.23-l), which would include dp and. an
unknown proportionality constant which you could evaluate from the data.
For very small values of the Thiele modulus we know q = 1 and for very
large values of the Thiele modulus we know that q = 3/Q, = 3/cd,.]
P4-& (Spherical reuctor) Because it is readily available from coal, methanol has
been investigated as an alternative raw material for producing valuable olefins