Page 565 - Elements of Chemical Reaction Engineering Ebook

Sec. 9.2 Unsteady Operation of CSTRs and Semibatch Reactors 535

I= 1 [,Il
n n
Esys = 1 N,E, = 1 N,U, = 1 N,(H,-Pv,) lsys (9-2)
r=l
Differentiating Equation (9-2) with respect to time and substituting into E,qua-
tion (8-9) gives

n n
Transient energy
balance Q-k,+C F1H,lln-C F1Hijout
I= 1 ,=I

(9-3)

For brevity we shall write these sums as

n

i= 1
unless otherwise stated.

9.2 Unsteady Operation of CSTRs
and Semibatch Reactors

When no spatial variations are present in the system volume, and variations in
the total pressure and volume are neglected, the energy balance, Equation ('9-3),
reduces to

Q - Ws+c F,~Hr0-~ FIN, = C N, 5+C HI dN, -
dt dt (9-4)
Recalling Equation (8-19),

T
HI = H0(T,d + 1, CpI dT (8-19)

and differentiating with respect to time, we obtain

(9-5)
Then substituting Equation (9-5) into (9-4) gives
. .
Q - MrY + 1 F,oH,o - x F, HI = C N, C dT + E H, dt
Nf
pf dt (9-6)
The mole balance on species i is