Fluid minimum fluidization velocity

Fig. 1. Fluidized-bed behavior where U is the superficial gas velocity and is the minimum fluidization velocity (a) packed bed, no flow (b) fluid bed,...

Minimum Fluidizing Velocity U,nj, the minimum fluidizing velocity, is frequently used in fluid-bed calculations and in quantifying one of the particle properties. This parameter is best measured in small-scale equipment at ambient conditions. The correlation by Wen audYu [A.l.Ch.E.j., 610-612 (1966)] given below can then be used to back calculate d. This gives a particle size that takes into account effects of size distribution and sphericity. The correlation can then be used to estimate U, at process conditions, if U,nj cannot be determined experimentally, use the expression below directly. 

Particulate Fluidization Fluid beds of Geldart class A powders that are operated at gas velocities above the minimum fluidizing velocity (L/, y) but belowthe minimum bubbhngvelocity (L/, i) are said to be particulately fluidized. As the gas velocity is increased above L/, y, the bed further expands. Decreasing (p, — Py), d and/or increasing increases the spread between L/, yand U, b until at some point, usually at high pressure, the bed is fully particulately fluidized. Richardson and Zald [Trans. Inst. Chem. Eng., 32, 35 (1954)] showed that U/U = E , where /i is a function of system properties, = void fraction, U = superficial fluid velocity, and Uj = theoretical superficial velocity from the Richardson and Zald plot when = 1. 

This reaction is carried out in tall fluidized beds of high L/dt ratio. Pressures up to 200 kPa are used at temperatures around 300°C. The copper catalyst is deposited onto the surface of the silicon metal particles. The product is a vapor-phase material and the particulate silicon is gradually consumed. As the particle diameter decreases the minimum fluidization velocity decreases also. While the linear velocity decreases, the mass velocity of the fluid increases with conversion. Therefore, the leftover small particles with the copper catalyst and some debris leave the reactor at the top exit. 

At any instant, pressure is uniform throughout a bubble, while in the surrounding emulsion pressure increases with depth below the surfaee. Thus, there is a pressure gradient external to the bubble which causes gas to flow from the emulsion into the bottom of the bubble, and from the top of the bubble back into the emulsion. This flow is about three times the minimum fluidization velocity across the maximum horizontal cross section of the bubble. It provides a major mass transport mechanism between bubble and emulsion and henee contributes greatly to any reactions which take place in a fluid bed. The flow out through the top of the bubble is also sufficient to maintain a stable arch and prevent solids from dumping into the bubble from above. It is thus responsible for the fact that bubbles can exist in fluid beds, even though there is no surface tension as there is in gas-liquid systems. 

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. 

The velocity at which gas flows through the dense phase corresponds approximately to the velocity that produces incipient fluidization. The bubbles rise, however, at a rate that is nearly an order of magnitude greater than the minimum fluidization velocity. In effect, then, as a consequence of the movement of solids within the bed and the interchange of fluid between the bubbles and the dense regions of the bed, there are wide disparities in the residence times of various fluid elements within the reactor and in... 

To obtain proper fluidization, the actual fluid velocity, up, must be considerably greater than the minimum fluidization velocity, ump However, to avoid excessive entrainment, Up should be less than the terminal velocity, ut. Thus, the ratio utlumj is a guide to selection of the value of Up. 

First, the minimum fluidization velocity ( umj) is calculated from 23.2-5. After substitution of the particle and fluid properties provided, the resulting quadratic equation is ... 

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. 

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... 

Minimum Fluidizing Velocity LO, the minimum fluidizing velocity, is frequently used in fluid-bed calculations and in quantifying one ol the particle properties. This parameter is best measured in small-scale equipment at ambient conditions. The correlation by Wen... 

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. 

Figure 3.53 corresponds to an upflow operation, where the fluidized-bed pressure drop remains constant after the minimum fluidization velocity. On the contrary, if a fixed bed is operated in downflow mode, the pressure drop continues to increase by increasing the fluid velocity (dense line). This is the reason that fluidized beds may exhibit a lower pressure drop and thus the power cost is lower, for high fluid velocities. 

A trial-and-error procedure is needed. Note that when using correlations for the determination of minimum fluidization velocity (or other relevant parameters) as in eqs. (3.459) and (3.460), it is reasonable to assume that the fluid-phase density involved is measured at inlet or ambient conditions, and thus no collection is needed. This is why, in analogy to the case of the hydraulic density of solids (Section 3.9.6), the minimum fluidization velocity is directly correlated to the inlet fluid density. 

A suspension of partides in turbulent gas or liquid, or a mixture of both, behaves much like a fluid, hence the terms fluidization and fluidized beds. In the fluidized state, much larger particles can be maintained in suspension than would be possible under static or laminar flow conditions. This provides a means, for example, to make large particles flow like a fluid. The minimum fluidization velocity is the ve-lodty of gas or liquid that is just needed to support the weight of the particles. At... 

The gas flow velocity through the emulsion phase is close to the minimum fluidization velocity When the particles are spherical and have diameters of several tens of microns, this flow condition gives a quite small particle Peclet number, dpUmf/Dc. For example, the Peclet number is estimated as 0.1-0.01 when 122-/Lim-diam. cracking catalyst is fluidized by gas, with Umt = 0.73 cm/sec and Dq = 0.09 cmVsec and it is estimated as 0.001-0.01 for 58-/u.m-diam. particles, with Umt = 0.16 cm/sec. The mechanism of mass transfer between fluid and particles in packed beds is controlled by molecular diffusion under such low Peclet numbers, and the particle Sherwood number kfdp/Dc, is well over 10 (M24). Consequently with intraparticle diffusion shown to be negligible (M21), instantaneous equilibrium is established to be a good approximation [see Eq. (6-24)]. 

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