Page 488 - Elements of Chemical Reaction Engineering Ebook

Sec. 8.:3 Nonisothermal Continuous-Flow Reactors 459

Recalling Equation (8-47) and ignoring any work done on the reacting
fluid, 'we obtain

T
IO-FAOI COjC,jdT- FAoX=O (13-54)
TO
Differientiating with respect to the volume V and collecting terms gives us

Recalling that -'A = FAo (dXldV), and substituting Equation (8-44) for
(dQldV), we can rearrange Equation (8-55) to obtain

Energy balance on
PER with heat (8-56)
transfer

Energy balance The differential equation describing the change of temperature with volume
(i.e., distance) down the reactor,

Numerical
integration of two
coupled differential must he coupled with the mole balance,
equations is
required
Mole balance
I 1
and solved simultaneously. A variety of numerical integration schemes can be
used to solve these two equations simultaneously.

Energy Balance in Measures Other Than Conversion. If we work in tm-ms
other than conversion, we derive an equation similar to Equation (8-56) by first
differentiating Equation @-lo),

n n
Q-Wx+ F,,Hi0- 2 FiH, = 0 (8-10)
i=l i=l
with respect to the volume, V:

(8-57)