Page 575 - Elements of Chemical Reaction Engineering Ebook

Sec. 92 Unsteady Operation of CSTRs and Semibatch Reactors 545

Substituting the parameter values

5.1 19 m3 3.64 - 2;Y
45 min =
0.0001 167 m3/kmol.min(9.044 kmol:, 3.64( 1 - X)
Solving for X, we find that at z = 45 min, then X = 0.033.
We will calculate the rate of generation Qg at this temperature and conversion and
compare it with the maximum rate of heat removal QR. The rate of generation Qg is

At this time (i.e., t = 45 min, X = 0.033, T = 175°C) we calculate k, then Q, and
Q,. At 175"C, k = 0.0001167 m3/min.kmol.

= 3830 kcal/min
The: corresponding maximum cooling rate is
Q,= UA(T-298)
= 35.85(448 - 298)
= 5378 kcal/min
Thwefore
I Qr>Q, 1
Everything is OK (E9-2.13)

The reaction can be controlled. There would have been no explosion had the cooling
not been turned off.

B. Adiabatic Operation for 10 Minutes

The cooling was turned off for 45 to 55 min. We will now use the conditions at the
end of the period of isothermal operation as our initial conditions for adiabatic oper-
ation period between 45 and 55 min:
t = 45 min X = 0.033 T = 448
Between t = 45 and t = 55 min UA = 0. The POLYMATH program adiabatic oper-
ation is the same as that in Table E9.2-I except that Q, = UA(T - 298)*(0), which
is the same as setting UA = 0.
For the 45- to 55-min period without cooling, the temperature rose from
448 K to 468 K and the conversion from 0.033 to 0.0424. Using this temperature
and conversion in Equation (E9-2.11), we calculate the rate of generation Q, at
55 rnin as
Q, = 6591 kcal/min
The maximum rate of cooling at this reactor temperature is found from Ijxlua-
tion (E9-2.12) to be
Q, = 6093 kcal/min