Page 154 - Chemical Process Equipment - Selection and Design

126 FLOW OF FLUIDS
Minimum Fluidization. The fundamental nature of this maximum in level which then collapses and attains a minimum.
phenomenon has led to many correlations for its prediction. That of With increasing gas rate, the bed again continues to expand until
Leva (1959) applies to Reynolds numbers Remf = dPGmf /p < 5, and entrainment develops and no distinct bed level exists. Beyond the
is minimum bubbling point, some fraction of the excess gas continues
through the dense phase but that behavior cannot be predicted with
any accuracy.
(6.132) Some smoothed data of expansion ratio appear in Figure
6.10(c) as a function of particle size and ratio of flow rates at
in the common units Gmf in lb/(hr)(sqft), D, in inches, densities in minimum bubbling and fluidization. The rather arbitrarily drawn
Ib/cuft, and viscosity in cP. In SI units it is dashed line appears to be a conservative estimate for particles in the
range of 100 pm.
Ordinarily under practical conditions the flow rate is at most a
(6.133) few multiples of the minimum fluidizing velocity so the local
maximum bed level at the minimum bubbling velocity is the one
that determines the required vessel size. The simplest adequate
The degree of confidence that can be placed in the correlation is
indicated by the plot of data on which it is based in Figure 6.10(f). equation that has been proposed for the ratio of voidages at
An equation more recently recommended by Grace (1982) covers minimum bubbling and fluidization is
Reynolds numbers up to 1000:
Re, = dpumF/p = v(27.2)* + 0.0408(Ar) = 27.2, (6.134)

where The last equation results from substitution of Eq. (6.138) into
(6.140). Then the relative bed level is found from
(6.135)
Lmb/Lmf = - &mf - %b). (6.142)
Here also the data show much scatter, so that pilot plant
determinations of minimum fluidization rates usually are advisable. Either E,,& or E,,,~ must be known independently before Eq. (6.141)
can be applied, either by application of Eq. (6.139) for or by
reading off a value of E,~ from Figure 6.8(c) or Figure 6.10(e).
Minimum Bubbling Conditions. Minimum bubbling velocities These values are not necessarily consistent.
for Group B substances are about the same as the minimum At high gas velocities the bed level fluctuates. The ratio of
fluidization velocities, but those of Group A substances are maximum disturbed level to the average level is correlated in terms
substantially greater. For Group A materials the correlation of of Gf /Gmf and the particle diameter by the equation
Geldart and Abrahamsen [Powder Technol 19, 133 (1978)l for
minimum bubbling velocity is r = exptm'(Gf - Gmf)/Gmfl, (6.143)

umb = 33dp(p/P)-'.l. (6.136) where the coefficient m' is given in Figure 6.10(d) as a function of
particle diameter.
For air at STP this reduces to
Freeboard. Under normal operating conditions gas rates
umb = lOOd,. (6.137)
somewhat in excess of those for minimum fluidization are
For cracking catalysts represented on Figure 6.10(g), Harriott and employed. As a result particles are thrown into the space above the
Simone (1983) present an equation for the ratio of the two kinds of bed. Many of them fall back, but beyond a certain height called the
velocities as transport disengaging height (TDH), the entrainment remains
essentially constant. Recovery of that entrainment must be
accomplished in auxiliary equipment. The TDH is shown as a
(6.138) function of excess velocity and the diameter of the vessel in Figure
6.10(i). This correlation was developed for cracking catalyst
particles up to 400 pm dia but tends to be somewhat conservative at
The units of this equation are SI; the coefficient given by the larger sizes and for other materials.
Cheremisinoff and Cheremisinoff (1984, p. 161) is incorrect. Figures
6.10(g) and (h) compare the two kinds of velocities over a range of
particle diameters. Voidage at minimum bubbling is correlated by Viscosity. Dense phase solid-gas mixtures may be required to
an equation of Cheremisinoff and Cheremisinoff (1984, p. 163): flow in transfer line catalytic crackers, between reactors and
regenerators and to circulate in dryers such as Figures 9.13(e), (f).
(6.139) In dilute phase pneumatic transport the effective viscosity is nearly
that of the fluid, but that of dense phase mixtures is very much
greater. Some data are given by Schugerl (in Davidson and
Bed Expansion and Fluctuation. The change of bed level with Harrison, 1971, p. 261) and by Yates (1983). Apparent viscosities
increasing gas rate is represented schematically in Figure 6.10(a). with particles of 50-550 pm range from 700 to 1300 cP, compared
The height remains constant until the condition of minimum with air viscosity of 0.017 CP at room temperature. Such high values
fluidization is reached, and the pressure drop tends to level off. of the viscosity place the flow definitely in the laminar flow range.
Then the bed continues to expand smoothly until some of the gas However, information about friction in flow of fluidized mixtures
begins to disengage from the homogeneous dense phase and forms through pipelines is not easy to find in the open literature. Someone
bubbles. The point of onset of bubbling corresponds to a local must know since many successful transfer lines are in operation.