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14-98 EQUIPMENT FOR DISTILLATION, GAS ABSORPTION, PHASE DISPERSION, AND PHASE SEPARATION
TABLE 14-21 Simulation of Three Heat Exchangers
with Varying Foreign Nuclei
1 2 3
Weight fraction, noncondensable
Inlet 0.51 0.42 0.02
Outlet
Molecular weight
0.80 0.80 0.32
Inert 28 29 29
Condensable
Temperature difference between gas and
liquid interface, K
86 99 210
Inlet 14 24 67
Outlet
Percent of liquid that leaves unit as fog
Nuclei concentration in inlet particles/cm
4 10 4
3
100 0.05 1.1 2.2
1,000 0.44 5.6 3.9
10,000 3.2 9.8 4.9
100,000 9.6 11.4 5.1
1,000,000 13.3 11.6
10,000,000 14.7
∞ 14.7 11.8 5.1
Fog particle size based on 10,000 nuclei/cm3 at inlet, µm
28 25 4
yields the same relative increase in temperature driving force. However,
the interface vapor pressure can only approach the limit of zero.
Because of this, for equal molecular and thermal diffusivities a saturated
mixture will supersaturate when cooled. The tendency to supersaturate
generally increases with increased molecular weight of the
condensable, increased temperature differences, and reduced initial
superheating. To evaluate whether a given condensing step yields fog
requires rigorous treatment of the coupled heat-transfer and masstransfer
processes through the entire condensation. Steinmeyer
[Chem. Eng. Prog., 68(7), 64 (1972)] illustrates this, showing the
impact of foreign-nuclei concentration on calculated fog formation.
See Table 14-21. Note the relatively large particles generated for cases
1 and 2 for 10,000 foreign nuclei per cm 3 . These are large enough to
be fairly easily collected. There have been very few documented problems
with industrial condensers despite the fact that most calculate to
generate supersaturation along the condensing path. The explanation
appears to be a limited supply of foreign nuclei.
Ryan et al. [Chem. Eng. Progr., 90(8), 83 (1994)] show that separate
mass and heat transfer-rate modeling of an HCl absorber predicts 2
percent fog in the vapor. The impact is equivalent to lowering the
stage efficiency to 20 percent.
Spontaneous (Homogeneous) Nucleation This process is
quite difficult because of the energy barrier associated with creation
of the interfacial area. It can be treated as a kinetic process with the
rate a very steep function of the supersaturation ratio (S = partial pressure
of condensable per vapor pressure at gas temperature). For
water, an increase in S from 3.4 to 3.9 causes a 10,000-fold increase in
the nucleation rate. As a result, below a critical supersaturation (Scrit),
homogeneous nucleation is slow enough to be ignored. Generally, Scrit
is defined as that which limits nucleation to one particle produced per
cubic centimeter per second. It can be estimated roughly by traditional
theory (Theory of Fog Condensation, Israel Program for Scientific
Translations, Jerusalem, 1967) using the following equation:
Scrit = exp�0.56 �� 3/2
� �
ρl T
where σ=surface tension, mN/m (dyn/cm)
ρ l = liquid density, g/cm 3
T = temperature, K
M = molecular weight of condensable
�
(14-205)
Table 14-22 shows typical experimental values of S crit taken from the
work of Russel [J. Chem. Phys., 50, 1809 (1969)]. Since the critical
supersaturation ratio for homogeneous nucleation is typically greater
M
σ
TABLE 14-22 Experimental Critical Supersaturation Ratios
Temperature, K Scrit H2O 264 4.91
C2H5OH 275 2.13
CH4OH 264 3.55
C6H6 253 5.32
CCl4 247 6.5
CHCl3 258 3.73
C6H5Cl 250 9.5
than 3, it is not often reached in process equipment. However, fog formation
is typically found in steam turbines. Gyarmathy [Proc. Inst.
Mech. E., Part A: J. Power and Energy 219(A6), 511–521 (2005)]
reports fog in the range 3.5 to 5 percent of total steam flow, with average
fog diameter in the range of 0.1 to 0.2 µm.
Growth on Foreign Nuclei As noted above, foreign nuclei are
often present in abundance and permit fog formation at much lower
supersaturation. For example,
1. Solids. Surveys have shown that air contains thousands of particles
per cubic centimeter in the 0.1-µm to 1-µm range suitable for
nuclei. The sources range from ocean-generated salt spray to combustion
processes. The concentration is highest in large cities and industrial
regions. When the foreign nuclei are soluble in the fog,
nucleation occurs at S values very close to 1.0. This is the mechanism
controlling atmospheric water condensation. Even when not soluble,
a foreign particle is an effective nucleus if wet by the liquid. Thus, a
1-µm insoluble particle with zero contact angle requires an S of only
1.001 in order to serve as a condensation site for water.
2. Ions. Amelin [Theory of Fog Condensation, Israel Program for
Scientific Translations, Jerusalem, (1967)] reports that ordinary air
contains even higher concentrations of ions. These ions also reduce
the required critical supersaturation, but by only about 10 to 20 percent,
unless multiple charges are present.
3. Entrained liquids. Production of small droplets is inherent in
the bubbling process, as shown by Fig. 14-90. Values range from near
zero to 10,000/cm 3 of vapor, depending on how the vapor breaks
through the liquid and on the opportunity for evaporation of the small
drops after entrainment.
As a result of these mechanisms, most process streams contain
enough foreign nuclei to cause some fogging. While fogging has been
reported in only a relatively low percent of process partial condensers,
it is rarely looked for and volunteers its presence only when yield
losses or pollution is intolerable.
Dropsize Distribution Monodisperse (nearly uniform droplet
size) fogs can be grown by providing a long retention time for growth.
However, industrial fogs usually show a broad distribution, as in Fig.
14-91. Note also that for this set of data, the sizes are several orders of
magnitude smaller than those shown earlier for entrainment and
atomizers.
The result, as discussed in a later subsection, is a demand for different
removal devices for the small particles.
While generally fog formation is a nuisance, it can occasionally be
useful because of the high surface area generated by the fine drops.
An example is insecticide application.
GAS-IN-LIQUID DISPERSIONS
GENERAL REFERENCES: Design methods for agitated vessels are presented by
Penney in Couper et al., Chemical Process Equipment, Selection and Design,
Chap. 10, Gulf Professional Publishing, Burlington, Mass., 2005. A comprehensive
review of all industrial mixing technology is given by Paul, Atemo-Obeng,
and Kresta, Handbook of Industrial Mixing, Wiley, Hoboken, N.J., 2004. Comprehensive
treatments of bubbles or foams are given by Akers, Foams: Symposium
1975, Academic Press, New York, 1973; Bendure, Tappi, 58, 83 (1975);
Benfratello, Energ Elettr., 30, 80, 486 (1953); Berkman and Egloff, Emulsions
and Foams, Reinhold, New York, 1941, pp. 112–152; Bikerman, Foams,
Springer-Verlag, New York, 1975; Kirk-Othmer Encyclopedia of Chemical Technology,
4th ed., Wiley, New York, 1993, pp. 82–145; Haberman and Morton,
Report 802, David W. Taylor Model Basin, Washington, 1953; Levich, Physicochemical
Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ, 1962; and Soo,
Fluid Dynamics of Multiphase Systems, Blaisdell, Waltham, Massachusetts,