Yang Fluidization, Solids Handling, and Processing
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496 Fluidization, Solids Handling, and Processing
have their copper values recovered selectively by leaching with a very dilute acid; calcined bauxite has been leached in fluidized columns with strong alkali solutions; pyrite cinders containing nonferrous elements have been leached in the fluidized state after chloridizing roasting; in proposed processes for the hydrometallurgical winning of iron from its ores, hydrochloric acid leaching could also be carried out in fluidized columns. Certain brown coals rich in wax content could be leached in the fluidized state with a proper hydrocarbon solvent; in the production of active carbon, crude char could be treated in the fluidized state with acid and then washed with water; oil-bearing seeds as well as medicinal herbs, after proper size preparation, could be leached in fluidized apparatus for the recovery of their valuable ingredients.
2.1Uniform Particles
Fluidized leaching and washing is a countercurrent operation with downflow of solids, called counter-down. The following equation for generalized fluidization
Eq. (1) |
ε n = u´o - u´d ε /(1 - ε) |
can be rewritten in terms more adapted to the practitioner, that is, solids and fluid at their respective weight rates, S and L, added to a fluidized leacher/ washer having a cross-sectional area of A
Eq. (2) |
L |
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Sε |
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= ε n ut |
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ρ f A |
ρ s A(1 |
− ε ) |
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Denote the superficial liquid-solids velocity ratio (L/ρf A)/(S/ρs A) by N, and let (S/ρsut) = At, which is the minimal cross-sectional area if the solids were to flow at their terminal velocity, ut, in the absence of fluid flow, and can, therefore, be called terminal cross-sectional area. Then Eq. (2) can be reduced to a dimensionless form in terms of a reduced area, A´, defined as follows
Eq. (3) |
A′ = |
A |
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A |
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= |
N (1−ε )+ε |
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1 |
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S / ρ |
u |
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n |
(1−ε ) |
u′ |
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A |
t |
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ε |
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t |
s |
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d |
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Bubbleless Fluidization |
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Equation (3) is plotted in the upper diagram of Fig. 2 as A´ versus ε with N as a parameter. It shows that corresponding to any value of N, there exists a minimum value of A´ at which the fluidized leacher/washer possesses the least cross-sectional area or the maximum throughput. This minimum A´ corresponds to the flooding point characteristic of all counter-down systems and can be calculated by setting the derivative dA´/dε = 0, thus yielding
Eq. (4a) |
ε min |
from N (1− ε )+ ε = ε/n(1 − ε ) |
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Eq. (4b) |
N min |
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ε [1 − n(1− ε )] |
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n(1− ε )2 |
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Eq. (4c) |
A′ min |
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1 |
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n(1 − ε )2 ε n −1 |
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These three parameters at maximum throughput are shown in Fig. 3 as functions of the liquid/solids ratio N.
If the leaching or washing of the solids needs an average residence time θ, the required height Z of the fluidized solids bed can be calculated:
Eq. (5) |
θ = |
ZA (1 − ε )ρ s |
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S |
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Substitution of Eq. (2) for A and defining terminal height Zt = θut give the reduced fluidized bed height
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Z′ = |
Z |
Z |
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ε n |
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u′ |
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Eq. (6) |
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= |
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d |
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Zt |
θ ut |
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N(1 − ε )+ ε 1 − ε |
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This equation is plotted in the middle set of curves in Fig. 2 as Z´ versus ε with N as a parameter. It should be noted from these curves that Z´ is always less than unity, signifying the fact that the congregation of particles in fluidization reduces the rate of fall of the particles, thus prolonging their residence time. This same set of curves could, therefore, be interpreted to
Bubbleless Fluidization |
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Figure 3. Fluidized leaching or washing of uniform particles—parameters of maximum throughput: εmin, Zmin, A´min.
Comparison of Eqs. (6) and (3) shows clearly that Z´ and A´ are not independent. Therefore, at the point for minimum cross-sectional area A´min, the corresponding bed height is
Eq. (7) |
Z´ = n(1 - ε )ε n-1 |
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min |
Also, combination of Eqs. (6) and (3) defines a reduced volume for the fluidized solids
Eq. (8) |
V´ = A´Z´ = 1/(1 - ε ) |
502 Fluidization, Solids Handling, and Processing
2.3Staged Fluidized Leaching (SFL)
If the particle size distribution is sufficiently wide, as it often occurs for crushed ores or other disintegrated material products, it should be realized that the volumetric utilization of the leaching/washing apparatus would be rather poor, especially when the value of Me n is down to below 0.2. For this reason, leaching or washing could be carried out in parallel columns operating at successively reduced fluid velocities. This principle of the so-called “staged fluidized leaching” (SFL) is illustrated in Fig. 5. Each leaching or washing column, or stage, together with its entrance region at the top, serves also as a hydraulic classifier. With this provision, the largest particles are treated in the first column, or stage, having the highest fluid velocity so that they may descend slowly in a rather concentrated state, and the required high residence time for these large particles may thus be guaranteed without the need of inappropriate height. The smallest particles are leached or washed in the last column, or stage, of the series operating with the lowest fluid velocity so that they may descend through the fluid at their characteristically low velocity without being carried over. Since this fraction of the smallest particles usually constitutes only a small portion of the solid feed material, the cross-sectional area devoted to their use would be far less than when all the fractions were treated en masse in a single vessel. Computations have indicated that division of the leaching or washing duty into several stages often resulted in a saving of apparatus volume by a factor amounting to as much as two orders of magnitude.
A method for designing SFL has been developed (Kwauk, 1979a), but it will not be discussed in this short presentation.
3.0BUBBLELESS GAS/SOLID CONTACTING
3.1Bubbling Fluidization and G/S Contacting Efficiency
Figure 6 shows that the gas entering a bubbling fluid bed splits into two paths, one through the dense-phase solids with good gas/solid (G/S) contacting and the other in the form of bubbles which essentially bypass the majority of the solid particles with limited G/S contacting. As the total flow through the fluid bed increases, the relative amount of bubble flow increases, and the overall G/S contacting efficiency suffers even greater impair-
504 Fluidization, Solids Handling, and Processing
Figure 6. Split gas flow for a bubbling fluid bubbling bed.
The phenomenon of bubbling has attracted much attention from fluidization technologists to theorize on the origin and mechanics of bubbles and to elaborate on their mathematical modeling, but it has not been sufficiently recognized as indicative of the need for devising better modes of G/S contacting in which bubbles are suppressed or even totally eliminated.
Figure 7 plots the transfer coefficient NuPr-1/3 or ShSc-1/3 to Re for single particles, fixed bed and fluidized solids (Kwauk and Tai, 1964). The sudden drop of the transfer coefficient as soon as fluidization sets in, that is, when bubbling starts, is obvious.
In the case of heat transfer, cooling or heating of a solid particle takes place through convection across the gas film surrounding the particle and conduction inside the particles. Whether or not the overall cooling or heating process could be materially augmented by better G/S contacting depends on the relative resistance to heat transfer through these two mechanisms. Figure 8 presents the solution of the differential equations describing these two processes in series, as the relative resistance to heat flow inside/ outside the particle, as a function of the Biot number defined as Bi = hDp/k s. This plot shows that when Bi is small, say 1, small particles and/or high values for ks, the fractional resistance to heat flow by conduction inside the particle drops to < 0.1, signifying that the overall heat transfer process can be accelerated by improved G/S contacting.