Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 852

(c) Calculate the steady temperature and concentration in effluent when the feed
temperature is T 0 ¼ 298 K.
(d) Plot T e (effluent temperature) and f A (total conversion in the effluent stream) as
a function of time for the conditions set in part c). Determine the realized steady
state.
16.5. A liquid-phase, exothermic first-order reaction (A

products) is to take place
in a 4000 L CSTR. The Arrhenius parameters for the reacting systems are
k 0 ¼ 2 10 13 s 1 and E a ¼ 100 kJ $ mol 1 ; the thermal parameters are D H RA ¼
50 kJ $ mol 1 and C P ¼ 4J $ g 1

/

) is 1000 g $ L 1 .
(a) For a feed concentration (C A0 ) of 4 mol $ L 1 , a feed rate (Q 0 )of5L $ s 1 , and
adiabatic operation, determine f A and Tat steady state, if the feed temperature (T 0 )
is (i) 290 K, (ii) 297 K, and (iii) 305 K;
(b) What is the minimum value of T 0 for autothermal behavior, and what are the
corresponding values of f A and T at steady state?
(c) For T 0 ¼ 305 K as in a) (iii), explain, without doing any calculations, what would
happen eventually if the feed rate (Q 0 ) were increased.
(d) If the result in c) is adverse, what change could be made to offset it at the higher
throughput?
(e) Suppose the feed temperature (T 0 ) is 297 K, and it is desired to achieve a steady-
state conversion ( f A ) of 0.932 without any alternative possibility of steady-state
operation in the “quench region.” If a fluid stream is available at 360 K (T c , assume
constant) for use in a heat exchanger within the tank, what value of UA H
(J $ K 1

$ K 1 ; the density ( r

$ s 1 ) would be required for the heat exchanger? Show that the “quench”
region is avoided.
16.6. The exothermic gas-phase reaction

A % BþC r ¼ k f p A k b p B p C

is to be carried out in a CSTR operating at a pressure of 50 bar. The required conversion
is 22% with a pure A fed at 5 mol/s.
(a) Calculate the minimum reactor volume.
(b) Heat is removed from the reactor via cooling coils. What heat transfer area
is required for steady operation if the overall heat transfer coefficient is
10 W/(m 2 $ K)?

(c) Comment on the stability of the operating point.
The additional data are:

RT Þ mol $ s 1 $ m 3 $ bar 1 k f ¼ 0:435 exp ð20; 000=

RT Þ mol $ s 1 $ m 3 $ bar 2

k b ¼ 147 exp ð60; 000=

where RT is in J/mol. Feed temperature is 350 K; Coolant temperature is 400 K and
mean heat capacities of A, B, and C are 30, 20, and 10 J/(mol K), respectively.
16.7. The gas-phase decomposing reaction

A / BþC r ¼ kC A