Page 576 - Elements of Chemical Reaction Engineering Ebook

546 Unsteady-State Nonisothermal Reactor Design Chap. 9

Here we see that
The point of no
return (E9-2.14)
and the temperature will continue to increase. Therefore, the point of no return has
been passed and the temperature will continue to increase, as will the rate of reac-
tion until the explosion occurs.

C. Batch Operation with Heat Exchange
Return of the cooling occurs at 55 min. The values at the end of the period of adia-
batic operation (T = 468 K, X = 0.04.23) become the initial conditions for the
period of operation with heat exchange. The cooling is turned on at its maximum
capacity, Q = UA(298 - T), at 55 min. Table E9-2.1 gives the POLYMATH pro-
gram to determine the temperature-time trajectory.

TABLE E9-2.1. POLYMATH PROGRAM
Equations: Inrtiul Vulues:
d(T)/d(t)=IQg-Qr>/NCp 467.992
d<X)>d( t )=€-ra)WU/Naa 0.0423866
NCp=2504
U=3.26S+1.854
Nao=9.0448
UA=35.83
dH=-590000
Nba=33
k=.b0017#exp~11273/<1.987~X<1/461-1/T>)
Qr=URW<T-298>
Theata=Nbe/Nao
ra=-kXNaoXW2X<1-X)X<Theata-2XX)!U#W2
rate=-ra
Qg=raWUX<dH)
to = 55, tf = 121

Interruptions in the Note that one can change NAo and N,, to 3.17 and 43 kmol in the program and show
cooling system have that if the cooling is shut off for 10 min, at the end of that IO min Q, will still be
happened before greater than Q, and no explosion will occur.
with no ill effects
The complete temperature-time trajectory is shown in Figure E9-2.2. One
notes the long plateau after the cooling is turned back on. Using the values of Q,
and Q, at 55 min and substituting into Equation (E9-2.8), we find that

dT -_ - (6591 kcal/min) - (6093 kcal/min) - 0,2"C,min
-
dt 2504 kcal/"C
Consequently, even though dTldr is positive, the temperatuE increases very slowly
at first, 0.2"C/min. By 11:45, the temperature has reached 240°C and is beginning
to increase more rapidly. One observes that 119 min after the batch was started the