Page 715 - Bird R.B. Transport phenomena

§22.5 Mass Transfer and Chemical Reactions 695
The carbonic acid then reacts with NaOH at a rate proportional to carbon dioxide concentra-
tion. The kinetics of this reaction are well characterized. 1
The solution of this diffusion problem has been given in Problem 20C.3. From Eq. 20.3-3,
2 3
we find that for long times '
W An = Ac A (22.5-3)
which can be solved for the total surface area. It follows that the total surface area A under
consideration is given by

A = 1 dM A (22.5-4)
dt
here M A tot is the number of moles of carbon dioxide absorbed by time t.
This development is readily extended to a falling film of length L and surface velocity v ,
s
provided that k^L/v » 1. First-order reaction in mass transfer boundary layers is discussed
s
in Example 18.4-1 for a simple film model and in Example 20.1-3. The development can be
further extended to estimate the interfacial area in packed columns, in which the liquid phase
is supported as a falling film on solid surfaces, a common design.

EXAMPLE 22.5-2 We next consider gas absorption with first-order reaction in an agitated tank and take as a
starting point the reaction
Estimation of
Volumetric Mass O 2 + 2Na SO -> 2Na SO 4 (22.5-5)
2
3
2
Transfer Coefficients
already discussed in Example 18.4-1, using a thin stagnant film of liquid as a mass transfer
model.
SOLUTION This is not a realistic model, but the development in Example 18.4-1 can be rephrased in a
model-insensitive form by writing

(22.5-6)

so that
УК
and -Jl" A3) АН (22.5-7)
A8
The subscript AB should be changed to O S, where S represents the sulfite solution.
2
One can now test the model sensitivity of the system by comparing the film model with
the penetration model. This is done in Fig. 22.5-1, where it can be seen that there is no signifi-
cant difference between the two. 4 Moreover, there is a substantial region of parameter space
where the predicted rate of oxygen absorption is identical to that for physical absorption in
an oxygen-free tank. This chemical system has therefore proven a popular means for estimat-
ing volumetric mass transfer coefficients. It has long been used to characterize the oxygena-
tion effectiveness of aerobic bioreactors. 5

2
P. V. Danckwerts, Trans. Faraday Soc, 46, 300-304 (1950).
R. A. T. O. Nijsing, Absorptie van gassen in vloeistoffen, zonder en met chemische reactie, Academisch
3
Proefschrift, Delft (1957).
4
E. N. Lightfoot, AIChE Journal 8, 710-712 (1962).
5
A. M. Friedman and E. N. Lightfoot, Ind. Eng. Chem., 49,1227-1230 (1957); J. E. Bailey and
D. F. Ollis, Biochemical Engineering Fundamentals, McGraw-Hill, New York (1986); V. Linek, P. Benes,
and J. Sinkule, Biotechnol.-Bioeng., 35, 766-770 (1990).