Generalities and Basics of Fluidization
D. Varieties of Fluidization
Depending on the mode of operation and the flow regime, fluidization can be classified in several ways. For example, in normal fluidization, the gas flows upward and the particle density is greater than the fluid density. If a fluidized bed is
Table 1.3 Criteria for Powder Classification Based on Hydrodynamics and Thermal Properties
Group Criteria or Relation
I 3.35 ð Ar ð 21,700 or 1.5 Ψ ð dp ð 27.9 Ψ IIA 21,700 ð Ar ð 13,000 or 27.9 Ψ ð dp ð 50.7 Ψ IIB 13,000 ð Ar ð 1.6 × 106 or 50.7 Ψ ð d p ð 117 Ψ III Ar Š 1.6 × 106 or d p Š 117 Ψ Ar = dp3 ρf (ρs – ρf)g/dp3. Ψ = [µf2/ρf (ρs – ρf)g]1/3.
From Saxena, S.C. and Ganzha, V.L., Powder Technol., 39, 199, 1984. With permission.
homogeneous, it is often referred to as particulate. Heterogeneous fluidization is often bubbling or slugging in nature. Particulate fluidization is akin to liquid fluid- ization. Slugging occurs at high velocities in a gas fluidized bed with a narrow- diameter column and a deep bed.
If the density of the particulate solids is less than that of the fluid, normal fluidization is not possible, and in such a case the fluid flow direction has to be reversed (i.e., the fluid has to flow downward). Such a situation prevails for fluidizing certain polymers. This type of fluidization is termed inverse fluidization.
Fine powders are normally difficult to fluidize due to interparticle forces. In such a case, it is necessary to overcome the cohesive forces by some external forces in addition to the drag force exerted by the fluid flow. Agitation or vibration helps to overcome the interparticle forces. The fluidized bed in such a case is called a vibro fluidized bed.
In all the above types of fluidization, gravitational force plays a key role. There is a minimum fluid flow required to overcome the gravitational force, and the flow rate required just for fluidization may be much more than that demanded by stoichiometry. This would finally result in wasting the unreacted fluid, which in turn increases the cost of recycling. Furthermore, it is not advisable to use such normal fluidization for a costly gas. One alternative is to use centrifugal fluidization.
A new class of fluidized beds comes into play at very high velocities (much higher than or equal to the particle terminal velocity), where carryover or elutriation of the bed inventory occurs. Here the solids are to be recycled into the bed; such a system is called a circulating fluidized bed.
Particulate solids fluidized by either gas or liquid consist of two phases and belong to the category of two-phase fluidization. A bed of solids fluidized by both gas and liquid is known as three-phase fluidization. Three-phase fluidization is more complex than two-phase fluidization and has additional classifications depending on the flow direction of the gas and the liquid. In general, they can flow either cocur- rently or countercurrently. Figure 1.9 shows in a nutshell some common varieties of fluidization.
IV. HYDRODYNAMICS OF TWO-PHASE FLUIDIZATION A. Minimum Fluidization Velocity
1. Experimental Determination a. Pressure Drop Method
This method of determining the minimum fluidization velocity (Umf) involves
the use of data on the variation in bed pressure drop across a bed of particulate solids with fluid velocity. The trend in variation of the bed pressure drop with the superficial gas velocity was shown in Figure 1.3 and discussed in detail. Figure 1.10
depicts the various methods by which the minimum fluidization velocity can be determined. The plot in Figure 1.10A depicts bed pressure drop versus gas velocity. The transition point from the fixed bed to the fluidized bed is marked by the onset of constant pressure. This is also the point at which the increasing trend in the bed pressure drop (∆Pb) of a packed bed terminates. For an ideal case, gas flow reversal
in the fluidized bed condition does not change the magnitude of ∆Pb. However, the
value of ∆Pb is smaller when the bed starts settling during flow reversal compared to
previous values obtained at the same velocity in the increasing flow direction. The pressure drop method is the most popular means of determining Umf experimentally.
Figure 1.10 Various experimental methods to determine minimum fluidization velocity: (A)
b. Voidage Method
Bed expansion in a fixed bed is negligible. Hence, the bed voidage () remains constant. When a fixed bed is brought to the fluidized state, the bed voidage increases due to bed expansion. The onset of fluidization corresponds to the point where the voidage just starts increasing with the gas velocity (U). This is shown in Figure 1.10B. The bed voidage becomes constant and is equal to unity when the gas velocity corresponds to the particle terminal velocity. This method of determining Umf is not
simpler than the bed pressure drop method, because the bed expansion cannot be accurately determined by any simple (i.e., visual) means.
c. Heat Transfer Method
The variation in the wall heat transfer coefficient (h) with gas velocity (U) forms the basis of one of the interesting methods of determining Umf. The wall heat transfer
coefficient increases gradually in a fixed bed as the gas velocity is increased, and it suddenly shoots up at a particular velocity, indicating the onset of fluidization. The velocity that corresponds to the sudden increase in the wall heat transfer coefficient is the minimum fluidization velocity. The trend in the variation of h with U is shown in Figure 1.10C. In this method, another important gas velocity, the optimum gas velocity (Uopt), which corresponds to the maximum wall heat transfer coefficient
(Umax), is also obtained. This method of determining Umf is more expensive than the
two aforementioned methods, and it requires good experimental setup to measure the heat transfer data under steady-state conditions. For these reasons, this method is seldom used to determine Umf in fluidization engineering.
2. Theoretical Predictions
The various methods, based on first principles, available in the literature for the theoretical prediction of the minimum fluidization velocity can be broadly classified into four groups. These methods are derived from (1) dimensional analysis, (2) the drag force acting on single/multiparticles, (3) the pressure drop in a fixed bed extendable up to incipient fluidization, and (4) a relative measure with respect to the terminal particle velocity. Although a significant body of literature pertaining to the above methods exists and numerous correlations are listed by various researchers, there has been no classification of these correlations. The aforementioned methods are briefly described and the correlations based on them are listed in the following sections.
a. Dimensional Analysis (Direct Correlation)
This conventional method of developing a correlation takes into consideration the physical properties of the fluid and the solid. In its most general form, the correlation is given as:
(1.42)
Correlations of the above type are presented in Table 1.4. It can be seen that the factor ( ) is variable because of the dependence of mf on φs. However, many
correlations have been proposed by assuming that the quantity K (1 – mf)p is
a constant. This assumption is valid only within a certain range of experimental parameters. This type of direct correlation has the inherent disadvantage of involving a dimensional constant (K) that changes depending on the system of units used for the variables in Equation 1.42.
b. Drag Force Method
In this method, a force balance is assumed at incipient fluidization. The force balance equation is
Fg = αFD + FB (1.43)
where Fg, FD, and FB are, respectively, the force due to gravity, drag, and buoyancy,
and α is a correction or multiplication factor for a multiparticle system. Because the drag force varies depending on the flow range, there can be several correlations for the prediction of Umf by this method. Taking
(1.44)
and using appropriate expressions for Fg and FB for a particle of diameter dp fluidized
by a fluid of density ρg, a general equation can be written as:
(1.45)
The above equation can be solved if an appropriate value of drag coefficient (CD)
is chosen, depending on the flow regime. For Stokes flow (Remf ð 0.1), CD = 24/Remf.
Hence Equation 1.45 becomes
(1.46)
For Newton’s flow regime (i.e., for turbulent flow condition), Remf > 500 and
CD = 0.44. Hence, (1.47) Umf K dp g a s f b f c f d c s m mf n mf p =
(
ρ –ρ)
ρ µ( )(
φ 1–)
φs m mf n φs m mf n FD=α( )
1 2CDρgUmf( )
π 4dp 2 2 3 4 2 α ⋅CDRemf =Ar Remf = Ar 18α Re . mf 2 0 33 = Ar αIn the intermediate flow regime, there can be as many as six empirical correla- tions for CD, as proposed by Morse.31 The drag force on a single sphere situated in
an infinite expanse of fluid, according to Schiller and Naumann,32 is
(1.48) Table 1.4 Correlation for Minimum Fluidization Velocity Based on Dimensional Analysis
Method