Page 536 - Elements of Chemical Reaction Engineering Ebook

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506 Steady-State Nonisothermal Reactor Design Chap. 8

Rate laws:
-rlA = k,CA = - (E8-12.5)
kl cAO
1 + zk,

k2Tk1 'A0
-r2B = k C - (E8-12.6)
' - (1 +zk,)(l +zk2)
Applyirig Equation (8-92) to this system gives
UA(T,-T)-FAoEpA(T-To)+ V[r,A AHRxiA+rpg AHR,,,] = 0 (E8-12.7)
Substituting for rIA and r2B and rearranging, we have

UA
K= -= 40,000 J/min * K = 0.667
FAoCpA (0.3 mol/dm3)( 1000 dm3/min)200 J/mol.K
T,=-- To+ KT, - 283 + (0.666)(330) = 301.8 (E8- 12.9)
1+K 1 + 0.667

R(T)=Cp(l+~)[T-T,] (E8-12.11)
The POLYMATH program to plot R(T) and G(T) vs. Tis shown in Table E8-12.1,
and the resulting graph is shown in Figure E8-12.1.
TABLE E&-12.1 POLYMATH
-
Equations: Inrrral Values:
d(T) /d(t)=2 273
cp=200
Cao=O. 3
To=283
tau=. 01
DH1=-55000
DH2r-71500
vo= 10 0 0
E2=27 0 0 0
E1=9900
UA=4 0 0 0 0
Ta=330
k2=4.58*exp((E2/1.987)*(1/5~0-1/T))
kl=3.3*exp((E1/1.987) *(1/300-I/T))
Ca=Cao/(l+tau*kl)
kappa=UA/ (vo'cao) /CP
G=-tauokl/(l+kl*tau)*DH~-kl*tau'K2*tau*DH~/((l+tau*kl)*(l+ta
I
u*k2)
Tci(T~+kappa*Ta)/(l+kappa)
cb=tdu*kl*Ca/ (l+k2*cau)
~=~p*(l+kappa)*(~-~c)
Cc=Cao-Ca-Cb
F=G-R
= O, tf = 225