Page 146 - Separation process principles 2

Summary 111

The average slope in this range is From (3-229),
, 9.9 kmol 8.1 kmol
k, = - and kk = -
= 9.9----
-
- 8.85-
0.9986 h-m2 0.915 h-m2
From an examination of (3-242) and (3-243), the liquid-phase
is controlling because the term in kx is much larger than From (3-243),
the term in k,. Therefore, from (3-243), using m = m,,
1 kmol
K- = 9.71-
" - (119.9) + [1/56.3(8.85)1 h-m2
From (3-223),
kmol
or Kx = 9.66-
h-m2 kmol
NA = 9.71(0.001975 - 0.001) = 0.00947-
h-m2
From (3-223),
which is only a very slight change from parts (a) and (b), where the
kmol
NA = 9.66(0.001975 - 0.001) = 0.00942- bulk-flow effect was ignored. The effect is very small because here
h-m2 it is important only in the gas phase; but the liquid-phase resistance
is controlling.
(b) From part (a), the gas-phase resistance is almost negligible.
Therefore, y~, x y~, and XA, x xi. (d) The relative magnitude of the mass-transfer resistances can be
From (3-241), the slope my must, therefore, be taken at the written as
point y~~ = 0.085 and xy\ = 0.001975 on the equilibrium line.
From (2), my = 29.74 + 13,466(0.001975) = 56.3. From
(3-243),

1 kmol Thus, the gas-phase resistance is only 2% of the liquid-phase resis-
K- = 9.69-
" - (119.9) + [1/(56.3)(8.1)] h-m2 ' tance. The interface vapor mole fraction can be obtained from
(3-223), after accounting for the bulk-flow effect:
giving NA = 0.00945 kmo~h-m2. This is only a slight change from
part (a).
(c) We now correct for bulk flow. From the results of parts (a)
and (b), we have
Similarly,
YA~ = 0.085, YA, = 0.085, XA, = 0.1975, XA~ = 0.001
(YB)LM = 1.0 - 0.085 = 0.915 and (x~)~~
0.9986
%

SUMMARY

1. Mass transfer is the net movement of a component in a mixture 5. Diffusivity values vary by orders of magnitude. Typical values
from one region to another region of different concentration, often are 0.10, 1 x lop5, and 1 x lop9 cm2/s for ordinary molecular
between two phases across an interface. Mass transfer occurs by diffusion of a solute in a gas, liquid, and solid, respectively.
molecular diffusion, eddy diffusion, and bulk flow. Molecular dif- 6. Fick's second law for unsteady-state diffusion is readily ap-
fusion occurs by a number of different driving forces, including plied to semi-infinite and finite stagnant media, including certain
concentration (the most important), pressure, temperature, and ex- anisotropic materials.
ternal force fields.
7. Molecular diffusion under laminar-flow conditions can be deter-
2. Fick's first law for steady-state conditions states that the mass- mined from Fick's first and second laws, provided that velocity pro-
transfer flux by ordinary molecular diffusion is equal to the product files are available. Common cases include falling liquid-film flow,
of the diffusion coefficient (diffusivity) and the negative of the con- boundary-layer flow on a flat plate, and fully developed flow in a
centration gradient. straight, circular tube. Results are often expressed in terms of a rnass-
3. Two limiting cases of mass transfer are equimolar counterdif- transfer coefficient embedded in a dimensionless group called the
fusion (EMD) and unimolecular diffusion (UMD). The former is Sherwood number. The mass-transfer flux is given by the product of
also a good approximation for dilute conditions. The latter must in- the mass-transfer coefficient and a concentration driving force.
clude the bulk-flow effect. 8. Mass transfer in turbulent flow is often predicted by analogy
4. When experimental data are not available, diffusivities in gas to heat transfer. Of particular importance is the Chilton-Colbum
and liquid mixtures can be estimated. Diffusivities in solids, in- analogy, which utilizes empirical j-factor correlations and the
cluding porous solids, crystalline solids, metals, glass, ceramics, dimensionless Stanton number for mass transfer. A more accurate
polymers, and cellular solids, are best measured. For some solids- equation by Churchill and Zajic should be used for flow in tubes,
for example, wooddiffusivity is an anisotropic property. particularly at high Schmidt and Reynolds numbers.