Page 695 - Bird R.B. Transport phenomena

§22.1 Definition of Transfer Coefficients in One Phase 675

In much of the chemical engineering literature, the mass transfer coefficients are de-
fined by

N = k° AY (11 l-ол
ЛО 'УхЛос^'М KAZ..L У)
The relation of this "apparent" mass transfer coefficient to that defined by Eq. 22.1-7 is

k° xloc = yJc * (22.1-10)
*' loc [1 - x (l + r)]
A0
in which r = N /N . Other widely used mass transfer coefficients are defined by
A0
B0
N 0 Q
\ n = A", \r and n = k ^ An C22 1-ll^
ДО с loc A CHILI '^A0 oloc г A v^^* i l l /
for liquids and
N = k°, An (11 1-1?}
for gases. In the limit of low solute concentrations and low net mass transfer rates, for
which most correlations have been obtained,
lim = k xloc (22.1-13)

p,loc
k
The superscript 0 indicates that these quantities are applicable only for small mass-trans-
fer rates and small mole fractions of species A.
In many industrial contactors, the true interfacial area is not known. An example of
such a system would be a column containing a random packing of irregular solid parti-
cles. In such a situation, one can define a volumetric mass transfer coefficient, k^, incor-
porating the interfacial area for a differential region of the column. The rate at which
moles of species A are transferred to the interstitial fluid in a volume Sdz of the column is
then given by
dW A0 = (k a)(x A0 - x )Sdz + x (dW AQ + dW )
Ab
x
B0
A0
« <fia)(x AQ ~ x )Sdz (22.1-14)
Ab
Here the interfacial area, a, per unit volume is combined with the mass transfer coeffi-
cient, S is the total column cross section, and z is measured in the primary flow direction.
Correlations for predicting values of these coefficients are available, but they should be
used with caution. Rarely do they include all the important parameters, and as a result
they cannot be safely extrapolated to new systems. Furthermore, although they are usu-
ally described as "local," they actually represent a poorly defined average over a wide
1 5
range of interfacial conditions. "
We conclude this section by defining a dimensionless group widely used in the
mass-transfer literature and in the remainder of this book:

Sh = - ^ (22.1-15)

/
which is called the Sherwood number based on the characteristic length . This quantity
0
can be "decorated" with subscripts \,a,m, In, and loc in the same manner as h.
J. Stichlmair and J. F. Fair, Distillation Principles and Practice, Wiley, New York (1998).
1
H. Z. Kister, Distillation Design, McGraw-Hill, New York (1992).
2
3
J. C. Godfrey and M. M. Slater, Liquid-Liquid Extraction Equipment, Wiley, New York (1994).
4
R. H. Perry and D. W. Green, Chemical Engineers' Handbook, 8th edition, McGraw-Hill, New York
(1997).
J. E. Vivian and C. J. King, in Modern Chemical Engineering (A. Acrivos, ed.), Reinhold, New York (1963).
5