Page 266 - 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 1:
Values of K 111 for Air at Atmospheric Pressure 12
2 0 6
0 6
Particle Diameter, v = [ 4(32.2) (0.01) (] + - ) (500 - 0.08)] l/( - ' )
Microns 70° F. 212° F. 500° F. l 3(18.5) (0.02) 0·6 (0.08) (l - 0 - 06 )
0.1 2.8 3.61 5.14
0.25 1.682 1.952 2.528 vi = 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= DP V p, /µ
1
5.0 1.032 1.043 1.067 -([0.01] )
10.0 1.016 1.022 1.033 (9.77) (0.08)
(12) (0.02) (6.72 X ]0-4)

µ = (cp) (6.72 X 10- 1), lb/ft sec
m = exponent given by equations in Reynolds num-
ber table below NRc = 48.46
V, = settling velocity for single spherical particle, ft/s Then, m = 4.375(NR.,)- 0· 0875 = 4.375(48.46)- 0· 0865 = 3.1179
and m/s (terminal)
V,s = 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
NRc = Reynolds number, DP V,pr/µ Vr.s = V, (1 - c)?"
= 9.77(1 - 0.1)3.1179
= 7.03 ft/sec
Values ofm
(e) Particles under 0.1 micron:
4.65 < 0.5
4.375 (NRc)-0.0875 0.5 � NRe � 1,300
2.33 NRe > 1,300 Brownian movement becomes appreciable for particles
================================� under 3 microns and predominates when the particle size
reaches 0.1 micron [13]. This motion usually has little effect
in the average industrial process settling system except for
NRc = DpVJ)r/µ, dimensionless (4-13)
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 4-1 gives the limiting or critical diameter above
which the particular settling law is not applicable. Figure
Using the example of Carpenter [ 46): 4- 7 gives terminal velocities for solid particles falling in
standard air (70°F and 14. 7 psia), and Figure 4-8 gives par-
Pr= fluid density = 0.08 lb/cu ft ticles falling through water. Ifa particle (liquid or solid) is
µ = viscosity = 0.02 cp falling under the influence of gra\<ity through a vapor
Pp = 500 lb/ cu fl stream, the particle will continue to fall until, or unless
D'P = 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)] 113 Pressure Drop
O 01)
K - 34.81 ( .
(0.02) 2
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 4-9 is convenient for quick checks of terminal
= 0.6. settling velocities of solid particles in air and in water [23].