Page 705 - Bird R.B. Transport phenomena

§22.3 Correlation of Binary Transfer Coefficients in One Phase 685

independent of the Reynolds number under the assumption introduced in Eqs. 22.3-36 and
37. This result would also have been obtained by using the Chilton-Colburn relations, which
would give n = \ directly.
The interfacial gas composition x A0 can be accurately predicted, at low mass-transfer
rates, by neglecting the heat and mass transfer resistance of the interface itself (see §22.4
for further discussion of this point). One can then represent x A0 by the vapor-liquid
equilibrium relationship:
= x (T 0/ p) (22.3-39)
A0
A relation of this kind will hold for given species A and В if the liquid is pure A as assumed
above A commonly used approximation of this relationship is
PA,,,
X (22.3-40)
A0 - '
in which p A>vap is the vapor pressure of pure A at temperature T . This relation assumes tacitly
Q
that the presence of В does not alter the partial pressure of A at the interface, and that A and В
form an ideal gas mixture.
If an air-water mixture at 1 atm pressure gives a wet bulb temperature of 70°F and a dry
bulb temperature of 140°F, then

p Ayap = 0.0247 atm
x A0 = 0.0247, from Eq. 22.3-40
C = 6.98 Btu/lb-mole • F at 105°F, the film temperature
p
AH = 18,900 Btu/lb-mole at 70°F
vap
Sc = 0.58 (see Example 22.2-1)
Pr = 0.74, from Eq. 9.3-16
Substitution into Eq. 22.3-37, with n = \, then gives

(0.0247 - x J /058Y /3 6.98
A = (22.3-41)
(140 - 70)(l - 0.0247) \0.74/ 18,900
From this the mole fraction of water in the approaching air is

x = 0.0033 (22.3-42)
Ax
Since we assumed that the film concentration was x A = 0 as a first approximation, we
could go back and make a second approximation by using an average film concentration
of ^(0.0247 4- 0.0033) = 0.0140 in the physical property calculations. The physical proper-
ties are not known accurately enough here to justify recalculation.
The calculated result in Eq. 22.3-43 is in only fair agreement with published humidity
charts, because these are typically based on the adiabatic saturation temperature rather than
the wet bulb temperature. 3

EXAMPLE 22.3-3 Many important adsorptive operations, from purification of proteins in modern biotechnol-
ogy to the recovery of solvent vapor by dry-cleaning establishments, occur in dense particu-
Mass Transfer in late beds and are typically carried out in steady creeping flow—that is, at Re = D v p/ix < 20.
Creeping Flow Through Here D is the effective particle diameter and v is the superficial velocity, defined p o volumet-
as
Packed Beds ric flow p rate divided by the total cross section 0 of the bed (see §6.4). It follows that the dimen-
sionless velocity v/v 0 will have a spatial distribution independent of the Reynolds number.
Detailed information is available only for spherical packing particles.

3
O. A. Hougen, K. M. Watson, and R. A. Ragatz, Chemical Process Principles, Part I, 2nd edition,
Wiley, New York, (1954), p. 120.