Batch Reactor - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 156

t f

V

Q

Q

V

t P

t U

FIGURE 4.2 An illustration of material flow in a bioprocess plant.

conversion f A f ; and the unloading time, t U , for unloading the reaction mixture and returning
the reactor to working conditions.
The reactor volume can be obtained from Eqn (4.21) as

t P þ t f þ t U

V ¼ t B Q ¼ Q (4.22)

Example 4-4. Our winery takes grain in and put the wine on the market. The bottleneck of the
operation is the fermenter operation. The fermenter is loaded with 10% sugar (assuming
a density of 1000 kg/m 3 ) and yeast before fermentation. This leads to a 5-h delay before
fermentation starts. The fermentation takes 5 days to complete to obtain a 4% alcohol
mixture. Finally, to unload the fermenter contents and clean the fermenter requires another
3 h. Assume that the final product wine (4% alcohol) also has a density of 1000 kg/m 3 . Deter-
mine the fermenter size needed if a daily production of 240 L of wine is needed.
Solution. t P ¼

5h; t f ¼ 5days ¼ 120 h; t U ¼ 3 h. Thus, the total time for each batch of fermen-

tation will take t B ¼ 128 h.

The fermenter size can be determined as V

5 þ 120 þ 3h ¼

¼ (240/24) 128 L ¼ 1280 L.

Example 4-5. Consider the reaction:

; k ¼ 0:15 min 1
in a batch reactor. The loading, preparation, unloading, and cleaning of the reactor requires
10 h for each batch of production. A costs $2/mole, and B sells for $5/mole. The cost of oper-
ating the reactor (including the preparation time) is $0.03 per liter per hour. We need to
produce 100 moles of B per hour using C A0 ¼

A ! B

2 mol/L. Assume no value or cost of disposal
of unreacted A (i.e. separation or recovery cost to A is identical to the fresh A cost).

a. Perform a mole balance on the reactor to relate the conversion with reactor size.
b. What is the optimum conversion and reactor size?
c. What is the cash flow (or profit per mole of A feed to the reactor) from the process?
d. At what operating cost do we break even? What is the corresponding conversion?