Page 148 - Chemical Process Equipment - Selection and Design

120 FLOW OF FLUIDS

EXAMPLE 6.15 Eq. (6.128),
Pressure Drop in Flow of Nitrogen and Powdered Coal
Powdered coal of 100 pm dia and 1.28 specific gravity is transported AP/L = 9.806[1282(1- 0.9959) + 1.14(0.9959)]
vertically through a 1-in. smooth line at the rate of 15g/sec. The + (2/0.0254) [0 .0076(1.14) (6.1)'
carrying gas is nitrogen at 1 atm and 25°C at a linear velocity of
6.1 m/sec. The density of the gas is 1.14 kg/m3 and its viscosity is + 0.0031( 1282)(0.0041) (5.608)']
1.7(10-') N sec/m'. The equations of Table 6.10 will be used for the = 51.54 + 11.13 + 25.38 + 40.35 = 128.4 Pa/m.
various parameters and ultimately the pressure gradient AP/L will
be found: With Eqs. (5) and (13), no trial calculations are needed.
9.806(1.14)(1282 - 1.14) Eq. (13), Up = 6.1[1- 0.68(0.0001)0~92(1282)0~5
=
Eq' (8)9 [1,7(10-5)]2 x (1. 14)-0.2(0.0254)-0.54]
0. 153(9.806)0~71(0.0001)"4( 1282 - 1. 14)0.71 = 5.88 m/sec,
Eq. (lo), Ut=
1.14°~29[1.7(10-5)]0~43 Eq. (15), E = 1 -0.0231/5.78=0.9960,
= 0.37 m/sec (0.41 m/sec by Stokes' law), Eq. (5), f, = 0.0285v9.806(0.0254)/5.88 = 0.00242.
0.015 0.0231
Eq. (15), E = 1 - =I-- Therefore, the solid frictional gradient is obtained from the
(~~/4)(0.0254)'(1282 - 1.14)Up UP ' calculated value 40.35 in the ratio of the friction factors.
(1)
Eq. (14), Up = 6.1 - 0.45Vl +f,U;/2(9.806)(0.0254) (AP/L)solidfriction 40.35(0.00242/0.0031) = 31.5 Pa/m.
=
= 6.1 - 0.45Vl+ 2.007fU; (11)
Eq. (71, f,= &3 6.1 - Up (111) 10 ! Example 6.15. Fressi~re rft-o
P in flou of nitrosen and PO
Equations (I), (11), and (111) are solved simultaneously with the wdercd coal
results: 28 IFIPUT U
38 E=1-.8231NU ! (Eq 1)
E = 0.9959 and Up = 5.608, 48 F=.OB3151*(l-E:~,E'3~(.4~~(1-
E)f<6.l-U:>)*-.979 ! (E4 111)
For the calculation of the pressure drop, 58 G=-U+6.1-.45Y~1+2.887~F~~i*~~
*.5 ! <5h#Uld = 8)
f, = 0.0031 (Yang equation), 68 PRI t4T "U=" j U
78 PRINT "G="jG
DU+p,- 0.0254(6.1)( 1.14) - 88 GOTO 28 ! (if G is nor: suffi
Ref = - 10,390.
Pf 1 .7(10r5) cientlr close to zero1
98 END
Therefore, Round's Eq. (6.21) applies:
u= 5.688
f -1 G=-.88#859348861
f - $ ~ = 0.0076 ~ d
~
~

varying complexity have been proposed, of which some important called minimum fluidization. Beyond this point the solid-fluid mass
ones are listed in Table 6.10. exhibits flow characteristics of ordinary fluids such as definite
These equations involve the free settling velocity U,, for which viscosity and flow through lines under the influence of hydrostatic
separate equations also are shown in the table. At lower velocities head difference. The rapid movement of particles at immersed
Stokes' law applies, but corrections must be made at higher ones. surfaces results in improved rates of heat transfer. Moreover,
The particle velocity Up is related to other quantities by Eqs. although heat transfer rate between particles and fluid is only
(12)-(14) of the table, and the voidage in turn is represented by Eq. moderate, 1-4 Btu/(hr)(sqft)("F), the amount of surface is so great,
(15). In a review of about 20 correlations, Modi et al. (Proceedings, 10,000-150,000 sqft/cuft, that temperature equilibration between
Powder and Bulk Solids Handling and Processing Conference, phases is attained within a distance of a few particle diameters.
Powder Advisory Center, Chicago, 1978, cited by Klinzing, 1981) Uniformity of temperature, rapid mass transfer, and rapid mixing of
concluded that the correlations of Konno and Saito (1969) and of solids account for the great utility of fluidized beds in process
Yang (1976, 1978) gave adequate representation of pneumatic applications.
conveying of coal. They are applied in Example 6.15 and give As the gas flow rate increases beyond that at minimum
similar results there. fluidization, the bed may continue to expand and remain homo-
geneous for a time. At a fairly definite velocity, however, bubbles
6.11. FLUIDIZATION OF BEDS OF PARTICLES WITH GASES begin to form. Further increases in flow rate distribute themselves
between the dense and bubble phases in some ways that are not
As the flow of fluid through a bed of solid particles increases, it well correlated. Extensive bubbling is undesirable when intimate
eventually reaches a condition at which the particles are lifted out of contacting between phases is desired, as in drying processes or solid
permanent contact with each other. The onset of that condition is catalytic reactions. In order to permit bubble formation, the