Page 147 - Chemical Process Equipment - Selection and Design

6.10. GAS-SOLID TRANSFER 119
95% whereas voidages obtained with small spherical or cylindrical TABLE 6.10. Equations for the Calcusation of
~
packings normally used as catalysts are less than 40% or so, which Gas-Solid Transport
makes them impractical for countercurrent operation. However,
catalysts are made in the forms of rings or saddles when very low Solid Friction Factor f According to Various Investigators
pressure drop or countercurrent operation is desirable. Investigator t
Even when they are nominally the same type and size, packings Sternerding (1962) 0.003 (1)
made by diffefferent manufacturers may differ substantially in their Reddy and Pei (1969) 0.046U;’ (2)
pressure drop and mass transfer behavior, so that manufacturers Van Swaaij, Buurman, and
data should be obtained for final design. van Breugel (1970) 0.080 U,’ (3)
Many dala on individual packings are given by Billet Capes and Nakamura (1973) 0.048Ui3 (4)
(Distillation Engineering, Chemical Pub. Co., New York), in Konno and Saito (1969) 0.0285VgD W,’ (5)
Chemical Engineers Handbook (McGraw-Hill, New York, 1984, p. Yang (1978), vertical
18.23) and with Figure 13.37.
-f]
[
The uppermost line of Figure 13.37(a) marks the onset of 1 -E (1 - E)U
flooding which is the point at which sharp increase of pressure drop Yang (1976). horizontal 0.0293 7 (7)
d/sD
E
obtains on a plot against liquid rate. Flooding limits also are
represented OR Figure 13.36; in practice, it is customary to operate Free Setting Velocity
at a gas rate that is 70% of that given by the line, although there are
many data points below this limit in this correlation.
Mesh or other open structures as vessel packing have attractive
pressure drop and other characteristics, but each type has quite I( < 3.3
individual behavior so that it is best to consult their manufacturer’s
data.
S-SOLID TRANSFE 43.6<K<2360 (11)
Equipment fer pneumatic conveying is described in Section 5.2
along with some rules for calculating power requirements. Here the Particle Velocity
latter topic will be supplemented from a more fundamental point of ~
view. Investigator
Hinkle (1953) ug - Uf (12)
- o,68~0.92 0.5 -0.2~-0.54
CHOKING VELOCITY IGT (1978) 9 P PP Pf 1 (13)
Although the phenomena are not clearcut, partial settling out of Yang (1976) (14)
solids from the gas stream and other instabilities may develop below
certain linear velocities of the gas called choking velocities. Normal Voidage
pneumatic transport of solids accordingly is conducted above such a
calculated rate by a factor of 2 or more because the best
correlations are not more accurate. Above choking velocities the
process is called dilute phase transport and, below, dense phase Notation: U, is a fluid velocity, Up is particle velocity, Ut is particle
transport. free settling velocity, m, is mass rate of flow of solid, 0 = pipe diameter,
Dp is particle diameter, g = 9.806 m/sec’ at sea level.
What appears to be the best correlation of choking velocities is (Klinzing, Gas-Solid Transport, McGraw-Hill, New York, 1981).
due to Yang [AZChE J. 21, 1013-1015 (1975)], supplemented by
Punwani et al. and Qang (cited by Teo and Leung, 1984, pp.
520-521). The choking velocity lJgc and voidage E, are found by
simultaneous !solution of the equations
PRESSURE DROP
(6.125) The relatively sparse data on dense phase transport is described by
Klinzing (1981) and Teo and Leung (1984). Here only the more
important category of dilute phase transport will be treated.
The pressure drop in simultaneous flow of gas and solid
particles is made up of contributions from each of the phases. When
the particles do not interact significantly, as in dilute transport, the
overall pressure drop is represented by
and
2f U.’L 2;sp (I -E)UiL
(6.127) AP=p,(l-E)Lg+p,sLg+~+ ~ D
D
(6.128)
where G, is the mass rate of flow of solid per unit cross section and
the other terms are defined in Table 6.10. When from Eq. (6.126) for vertical transport; in horizontal transport only the two frictional
is substituted into Eq. (6.127), the single unknown in that equation terms will be present. The friction factor & for gas flow is the
is readily found with a root solving routine. For the case of Example normal one for pipe flow; except for a factor of 4, it is given by Eq.
6.15, G, = 29.6 kg/m2 sec, Ut = 0.45 m/sec, p, = 1282 kg/m3, and (6.19) for laminar flow and by the Round equation (6.21) for
pg = 1.14 kgJm3. Accordingly, Ugc = 1.215 m/sec and E, = 0.9698. turbulent flow. For the solid friction factor J, many equations of