Fluidization minimum

The state of fluidization begins at the point of minimum fluidization. This section provides a detailed account of the characteristics of minimum fluidization and particulate fluidization. 

Incipient or minimum fluidization can be characterized by the relationship of the dynamic pressure drop, Apd, to the gas velocity. The dynamic pressure gradient, dpd/dH, can be related to the total pressure gradient, dp/dH, by 

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. 

For particles with nonuniform properties, the hysteresis effect noted previously may also occur however, the transition of Apb from the fixed bed to the fluidized bed is smoother and t/mf can be obtained from the interception of the Apb line for the fixed bed with that for the fluidized bed. Thus, the expression for t/mf can be analytically obtained on the basis of 

The pressure drop in the fixed bed can be described by the Ergun equation, as given by Eq. (5.377). Under the minimum fluidization condition, we have 

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The basic concepts of a gas-fluidized bed are illustrated in Figure 1. Gas velocity in fluidized beds is normally expressed as a superficial velocity, U, the gas velocity through the vessel assuming that the vessel is empty. At a low gas velocity, the soHds do not move. This constitutes a packed bed. As the gas velocity is increased, the pressure drop increases until the drag plus the buoyancy forces on the particle overcome its weight and any interparticle forces. At this point, the bed is said to be minimally fluidized, and this gas velocity is termed the minimum fluidization velocity, The bed expands slightly at this condition, and the particles are free to move about (Fig. lb). As the velocity is increased further, bubbles can form. The soHds movement is more turbulent, and the bed expands to accommodate the volume of the bubbles. 

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,...

Group B soHds have higher minimum fluidization velocities than Group A soHds. For best results for Group B soHds flowing ia standpipes, standpipe aeration should be added at the bottom of the standpipe, not uniformly along the standpipe. 

Analysis of a method of maximizing the usefiilness of smaH pilot units in achieving similitude is described in Reference 67. The pilot unit should be designed to produce fully developed large bubbles or slugs as rapidly as possible above the inlet. UsuaHy, the basic reaction conditions of feed composition, temperature, pressure, and catalyst activity are kept constant. Constant catalyst activity usuaHy requires use of the same particle size distribution and therefore constant minimum fluidization velocity which is usuaHy much less than the superficial gas velocity. Mass transport from the bubble by diffusion may be less than by convective exchange between the bubble and the surrounding emulsion phase. 

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. 

At high ratios of fluidiziug velocity to minimum fluidizing velocity, tremendous solids circulation from top to bottom of the bed assures rapid mixing of the solids. For aU practical purposes, beds with L/D ratios of from 4 to 0.1 can be considered to be completely mixed continuous-reaction vessels insofar as the sohds are concerned. 

For group B and D particles, nearly all the excess gas velocity (U — U,nj) flows as bubbles tnrough the bed. The flow of bubbles controls particle mixing, attrition, and elutriation. Therefore, ehitriation and attrition rates are proportional to excess gas velocity. Readers should refer to Sec. 17 for important information and correlations on Gel-dart s powder classification, minimum fluidization velocity, bubble growth and bed expansion, and elutriation. 

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. 

Figure 30. Particle size effects on minimum fluidization and bubbling velocities.

Cocurrent three-phase fluidization is commonly referred to as gas-liquid fluidization. Bubble flow, whether coeurrent or countereurrent, is eonveniently subdivided into two modes mainly liquid-supported solids, in which the liquid exeeeds the minimum liquid-fluidization veloeity, and bubble-supported solids, in whieh the liquid is below its minimum fluidization velocity or even stationary and serves mainly to transmit to the solids the momentum and potential energy of the gas bubbles, thus suspending the solids. 

This equation has been experimentally verified in liquids, and Figure 2 shows that it applies equally well for fluidized solids, provided that G is taken as the flow rate in excess of minimum fluidization requirements. In most practical fluidized beds, bubbles coalesce or break up after formation, but this equation nevertheless gives a useful starting point estimate of bubble size. 

For fluidized beds, part of the gas flows through the emulsion at minimum fluidization velocity Uo, leaving U - Ug to influence bubble behavior. Then equation (4) is modified to read ... 

The fraction q can be expressed in terms of the expanded bed height H and minimum fluidization height H , and terms may be substituted for U -... 

This may be solved to give the expansion compared to minimum fluidization conditions. 

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. 

The flow pattern of gas within the emulsion phase surrounding a bubble depends on whether the bubble velocity Ug is less than or greater than minimum fluidization velocity U . For Ubflow lines. For Ub> U , the much different case of Figure 4(B) results. Here a gas element which leaves the bubble eap rises much more slowly than the bubble, and as the bubble passes, it remms to the base of the bubble. Thus, a cloud of captive gas surrounds a bubble as it rises. The ratio of eloud diameter to bubble diameter may be written... 

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