Page 264 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

236 Applied Process Design for Chemical and Petrochemical Plants

Table 4-8 Solve for settling velocity, V,:
Values of K,,, for Air at Atmospheric Pressure*2

Particle Diameter, 4(32.2) (0.01)(' + o.6) (500 - 0.08) 1 I/( 2-0.6)
Microns 70" F. 212" F. 500" F. vt= [ 3(18.5) (0.02)0.6 (0.08)(' 0.06)
0.1 2.8 3.61 5.14
0.25 1.682 1.952 2.528 V, = 9.77 ft/sec
0.5 1.325 1.446 1.711
1.0 1.160 1.217 1.338
2.5 1.064 1.087 1.133 Reynolds number, N Re = D pV,p, /k
5.0 1.032 1.043 1.067
10.0 1.016 1.022 1.033 (9.77) (0.08)
(0.02) (6.72 x 10-4)

k = (cp) (6.72 X lb/ft sec
m = exponent given by equations in Reynolds num- NRe = 48.46
ber table below
V, = settling velocity for single spherical particle, ft/s Then, m = 4.375(NRe)-0.0875 = 4.375(48.46)-0.0s65 = 3.1179
and m/s (terminal)
V, = settling velocity for hindered uniform spherical For 0.1 volume fraction solids for hindered settling
particle, ft/s or m/s (terminal) velocity:
c = volume fraction solids
K = constant given by equation above
NRe = Reynolds number, D, Vtpf/p v, = v, (1 - c)"
= 9.77(1 - 0.1)3.1'79
= 7.03 ft/sec

Values of m NRe (e) Particles under 0.1 micron:
4.65 < 0.5
4.375(N~~) 0.5 S NRe S 1,300
-0.08"
2.33 NRe > 1,300 Brownian movement becomes appreciable for particles
under 3 microns and predominates when the particle size
reaches 0.1 micron [ 131. This motion usually has little effect
in the average industrial process settling system except for
NRe = D,V,pJp, dimensionless (413) the very fine fogs and dusts. However, this does not mean
that problems are not present in special applications.
Example 4-2: Hindered Settling Velocities Figure 41 gives the limiting or critical diameter above
which the particular settling law is not applicable. Figure
Using the example of Carpenter [ 461 : 47 gives terminal velocities for solid particles falling in
standard air (70°F and 14.7 psia), and Figure 48 gives par-
pf = fluid density = 0.08 lb/cu ft ticles falling through water. If a particle (liquid or solid) is
p = viscosity = 0.02 cp falling under the influence of gravity through a vapor
pp = 500 lb/cu ft stream, the particle will continue to fall until, or unless
D', = particle diameter, in. = 0.01 the vapor flow rate is increased up to or beyond the ter-
c = volume fraction solids, 0.1. minal velocity value of the particle. If the vapor velocity
exceeds this, then the particle will be carried along with
Solving equation for K, for unhindered particle: the vapor (entrained).

0.08 (500 - 0.08) Pressure Drop
K = 34.81 (0.01)
Pressure drop through gravity settlers is usually
K = 16.28 extremely low due to the very nature of the method of
handling the problem.
Then, for K = 16.28 (intermediate range), b = 18.5; n Figure 49 is convenient for quick checks of terminal
= 0.6. settling velocities of solid particles in air and in water [23].