Batch Reactor - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 175

The amount of C required is 95 mol/h. In extracting C from the reacted mixture, A and
B are destroyed; hence, recycling of unused reactants is not possible. Calculate the
optimum reactor size as well as feed composition for this process if the total prepara-
tion time for each batch operation is 10 h.
Data: B costs $1.25/mol in crystalline form. It is highly soluble in the aqueous solu-
tion and even when present in large amounts does not change the concentration of A in
solution. Capital and operating costs are $0.015 h 1 $ L 1 .

4.13. One hundred fifty moles of B are to be produced hourly from a feed consisting of
a saturated solution of A (C A0 ¼ 0.1 mol/L) in a batch reactor. The reaction is

A ! B; r ¼ 0:2= h C A

The cost of reactant at C A0 ¼ $0.50/mol A. The cost of reactor including

installation, auxiliary equipment, instrumentation, overhead, labor, depreciation, etc.,
is $ m

0.1mol/l is $A ¼

$ L 1 . The total preparation time for each batch of operation is 9 h.
What reactor size, reactant rate, and conversion should be used for optimum opera-
tions? What is the unit cost of B for these conditions if unreacted A is discarded?
4.14. You wish to design a plant to produce 100 tons/day of ethylene glycol from ethane, air,
and water. The plant has three reactor stages, ethane dehydrogenation, ethylene
oxidation, and ethylene oxide hydration.
(a) What are the reactions?
(b) Both dehydrogenation and hydration have nearly 100% selectivity (with recycle of
unreacted reactants), but ethylene to ethylene oxide has only 70% selectivity with
an old catalyst and 90% selectivity with a new and expensive catalyst. How many
tons/day of ethane do we need to supply to this plant with each of these
catalysts?
4.15. We want to hydrolyze 500 lb/day of an ester at an initial concentration of 5 molar (the
ester has a molecular weight of 120) in aqueous basic solution in a batch process, and
we need product that is 99% hydrolyzed. In bench top experiments in a flask, we find
that 50% of the ester hydrolyzes in 15 min for initial ester concentrations of either 1 or
5 molar. We also find that, when we react for 8 h, all the ester has hydrolyzed. It takes
1 h to empty the reactor and refill and heat it to start another batch.
(a) What size reactor will we need?
(b) What size reactor will we need if we can tolerate 90% conversion?
(c) This process was found to have an activation energy of 12 kcal/mol, and we had
been operating at 40 C. What reactor volumes would we need if we can operate at
80 C?
(d) This hydrolysis reaction is exothermic with

$0.01 h 1

¼

8 kcal/mol. What must be the
average rate of cooling (in watts) during the reaction to maintain the reaction
isothermal?
(e) If we started the batch reactor at 40 C but forgot to turn on the cooling, what would
be the final temperature if the reactor were adiabatic (and the vessel would
withstand the pressure)? Assume the heat capacity of the solution to be that of
water, 1 cal/(cm 3 K).
(f) What cautions do you recommend regarding operation at 80 C?

D H R ¼