Minimum Fluidization Velocity umf

Rewriting the definition of the friction factor f from equation 21.3-5, and the Ergun correlation for/given by equation 21.3-7, both at mf, we obtain 

If the fluid is a gas, values of range between about 0.005 and 0.5 m s-1. Note that umj is independent of bed depth. 

Two special or limiting cases of equation 23.2-5 arise, depending on the relative magnitudes of the two terms for / in equation 23.2-3. This is shown in the following example. 

Obtain the special forms of equation 23.2-5 for (a) relatively small particles, and (b) relatively large particles. 

This is equivalent to ignoring the first term (n y) in equation 23.2-5, which then may be 

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Minimum Fluidization Velocity (Umf). The lowest velocity at which the full weight of catalyst is supported by the fluidization gas. It is the minimum gas velocity at which a packed bed of solid particles will begin to expand and behave as a fluid. For an FCC catalyst, the minimum fluidization velocity is about 0.02 ft/sec. 

One feature of the process, as in other crystal-growth operations, is that the fluidization velocity must be adjusted as the particles grow. Using the following data, develop a profile of minimum fluidization velocity (umf) versus particle size (dp), if, as the reaction proceeds,... 

Combining equations 9.33 and 9.34, the minimum fluidization velocity umf is given by... 

The best method of determining the minimum fluidization velocity umf is experimentally, by measuring the pressure drop across the bed over a range of fluid velocities. The pressure drop increases linearly until fluidization occurs and then increases very slowly indeed up to about twice the minimum fluidization velocity the pressure drop may appear to be constant within experimental error. When a bed is initially fluidized, there is a tendency for the pressure drop across the bed to be rather high and to go through a peak as incipient fluidization occurs. It is possible that this is caused by a need to unstick the particles. If the fluid velocity of an already fluidized bed is reduced, the peak in the pressure drop is not observed and a much clearer transition to the linear pressure drop—flow... 

At low gas velocities, the bed of particles is practically a packed bed, and the pressure drop is proportional to the superficial velocity. As the gas velocity is increased, a point is reached at which the bed behavior changes from fixed particles to suspended particles. The superficial velocity required to first suspend the bed particles is known as minimum fluidization velocity (umf). The minimum fluidization velocity sets the lower limit of possible operating velocities and the approximate pressure drop can be used to approximate pumping energy requirements. For agglomeration process in the fluid-bed processor, air velocity required is normally five to six times the minimum fluidization velocity. 

The minimum Reynolds number for fluidization Remf as well as the minimum fluidization velocity Umf may be calculated according to the correlation of Riba et al. [20], Mv defining the ratio of particle to liquid density... 

For a gas-solid system, pg is negligibly small compared to (—dp/dH). Consequently, dpd/dH can be approximated by dp/dH. The relationship of pressure drop through the bed, Apb, and superficial gas velocity U for fluidization with uniform particles is illustrated in Fig. 9.5. In the figure, as U increases in the packed bed, Apb increases, reaches a peak, and then drops to a constant. As U decreases from the constant Apb, Apb follows a different path without passing through the peak. The peak under which the bed is operated is denoted the minimum fluidization condition, and its corresponding superficial gas velocity is defined as the minimum fluidization velocity, Umf. 

Figure 5. The dependence of the transition from the slow to fast bubble regime on bubble diameter dg and minimum fluidization velocity umf.

First, the minimum fluidization velocity Umf was deduced from the variation of the pressure drop through the powder bed versus the gas fluidization velocity by applying the the Harrison and Richardson method [4] The experimental Umf at 10 Torrwas 3.8 cm/s. 

A fluid passing through a bed of particles at a relatively low velocity merely percolates through the interparticle voids. The particles in this case retain their spatial entity and the bed is in the fixed bed state. As the flow velocity increases further, the drag exerted on the particles just counterbalances the weight of the bed. At this point the bed is in incipient fluidization and the corresponding velocity is called the minimum, fluidization velocity Umf. As the fluid velocity increases beyond Um, the bed is in a completely fluidized state. 

A simple two-phase model of fluidized bed drying treats the fluidized bed to be composed of a bubble phase (dilute phase) and an emulsion phase (dense phase). The bubble phase contains no particles or the particles are widely dispersed. This model assumes that all gas in excess of minimum fluidization velocity, umf, flows through the bed as bubbles, whereas the emulsion phase stays stagnant at the minimum fluidization conditions [47]. Figure 8.5 shows a schematic diagram of the simple two-phase model. 

Ratio of Minimum Bubbling Velocity to Minimum Fluidization Velocity (Umb/Umf). This ratio can be calculated as follows ... 

As the fluid velocity is increased the drag on the particles increases and a point is reached where the pressure drop balances the effective weight of bed per unit cross-sectional area. At this point the fluid drag just supports the solid particles. A small increase in the flow rate causes a slight expansion of the bed from its static, packed state. Further increase in the flow rate allows the bed to expand more and the particles become free to move around and the bed is said to be fluidized. The state when the bed just becomes fluidized is known as incipient, or minimum, fluidization. The fluid velocity required to cause incipient fluidization is called the minimum fluidization velocity and is denoted by umf. 

Particulate Fluidization Fluid beds of Geldart group A powders that are operated at gas velocities above the minimum fluidizing velocity (U ) but below the minimum bubbling velocity (U ) are said to be particulately fluidized. As the gas velocity is increased above Umf, the bed further expands. Decreasing (ps - py), dp and/or increasing if increases the spread between Umf and U. Richardson and Zaki [Trans. Inst. Chem. Eng., 32, 35 (1954)] showed that U/Ut = n, where n is a function of system properties, 8 = void fraction, U = superficial fluid velocity, and Ut = theoretical superficial velocity from the Richardson and Zaki plot when 8 = 1. 

For small particles, bubbling starts at a gas velocity much higher than minimum fluidization velocity (3-8 times Umf) and continues way beyond the terminal velocity f/f For large particles, bubbling occurs at a gas velocity close to Umf. 

Ug = superficial velocity in the emulsion phase Umf - minimum fluidization velocity (cmis)... 

To establish the appropriate fluidization regime for any given application, one needs to calculate the minimum fluidization velocity and the terminal velocity of the bed particles. The superficial velocity of the gas for minimum fluidization (Umf) can be calculated by solving the following equation for Re if ... 

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