Page 269 - Introduction to chemical reaction engineering and kinetics

250 Chapter 9: Multiphase Reacting Systems

dhldz is determined by differentiating equation 9.2-42, and evaluating the derivative at
z = 0. Thus,

CAb 1 (9.2-44)
cAi cosh(Ha) kAt cAi

on replacement of h, by cAb/cAi, where cAb is the bulk liquid concentration (in Fig-
ure 9.7). Equation 9.2-44 was first obtained by Hatta (1932). It is based on liquid-film
resistance only. To take the gas-film resistance into account and eliminate CAi, we use
equation 9.2-44 together with equations 9.2-3 and -8

NA E NA(Z = 0) = kAg(PA - PAi) (9.2-3)
cAi = PAilHA (9.2-8)
to obtain

HACAb
pA - cosh(Ha)
Np,(z = 0) = (9.2-45)
H,tanh(Ha)
k,eHa

Special cases of equation 9.2-45 result from the two extremes of Ha -+ large and Ha +
0 (see problem 9-13).
Similarly, to obtain NA(z = l), the flux or rate of transfer of A from the liquidfilm to
the bulk liquid, we evaluate the rate of diffusion at z = 1 from equation 9.2-42:
1
N I - Fcosh(Ha) kA$Ai
A
AZ
(9.2~44a)

To eliminate c& and take gas-film resistance into account, we again use 9.2-3 and 9.2-8.
Thus, eliminating CAM, pAi, and NA(z = 0) from 9.2-3, -8, -44a, and -45, we obtain the
following rather cumbersome expression:

kAg tanh(Ha) CAb
PA + cosh(Ha)
NA(z = 1) = kAeHa beHa (9.2-45a)
tanh(Ha) kAgHA tanh(Ha) - CAb
cosh(Ha)[l + 1
kA&a I
Equations 9.2-45 and -45a are used in the continuity equations for reactor models in
Chapter 24.

9.2.3.4.2. Fast jirst-order or pseudo-jr&order reaction in liquid Jilm only. If the
chemical reaction itself is sufficiently fast, without being instantaneous, cA drops to
zero in the liquid film, and reaction takes place only in the liquid film, since A does
not reach the bulk liquid. The difference between this case and that in Section 9.2.4.3.1
above is in the boundary condition at z = 1; equation 9.2-33a is replaced by

at z = 1, CAb = 0; h, = 0 (9.2-3313)