Fluidization velocity, minimum

The minimum fluidization velocity Mnif can be usually obtained from resolving the following equations 

While 1/ and ds denote the kinematic viscosity and the particle diameter according to Equation (3.70), the Archimedes nimiber Ar additionally requires the gas density Pg, the apparent density of the coal p, and the gravitational acceleration gQ. The constants, which are frequently applied in gasification systems, are given in Table 3.19, where the minimum fluidization velocities increase with increase in constant Ci for the same conditions. Recent investigations in bed material from an industrial fluid-bed gasifier revealed that all sets of constants given in Table 3.19 predict the minimum fluidization velocity fairly well at pressures up to 25 bar. The minimal error was found for the Chitester et al. approach [17]. 

One of the basic parameters to be determined when designing bubbling fluidized-bed systems is the minimum fluidization velocity, Ump The effect of temperature and pressure on IJhas been investigated by many researchers (Botterill and Desai, 1972 Botterill and Teoman, 1980  

Generally, correlations predict the effects of temperature and pressure on t/ well. One of the more widely-used correlations to predict Umjris the Wen and Yu Correlation (Wen and Yu, 1966). The simplified form of the Wen and Yu correlation is  

The first term in this equation is important if laminar, or viscous, flow predominates in a system, while the second term is important if turbulent, or inertial, flow predominates. Equation (1) can be rearranged to the form shown in Eq. (2). This form expresses Umfm terms of known system parameters. 

The effect of temperature and pressure on Umy is strongly influenced by particle size. For small particles (Rep mf 20), the simplified Wen and Yu Equation reduces to  

Because gas viscosity does not vary significantly with pressure, the only parameter in Eq. (3) which changes with pressure is the gas density. However, because pp for most materials is so much larger than pg even at elevated pressures, the term (pp - pg) essentially does not change with pressure. Therefore, for small particles, Eq. (3) predicts that t/m will not change with pressure, and agrees with experimental findings. 

When gas is passed upward through a bed of solid particles, a minimum flow of air is needed to fluidize the particles. The corresponding minimum fluidization superficial velocity (volumetric gas flow divided by total column cross-sectional area) is commonly predicted, with approximately 20% accuracy, by an equation of the form 

7 and C2 = 0.0408, fitted by Wen and Yu [20], are the most common values of these constants among many pairs proposed in the literature. Ar is the Archimedes number given by 

Cross-sectional shape Circular Rectangular or circular Circular Rectangular 

Solid feeding Minor makeup Major factor Minor makeup Major factor 

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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. 

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. 

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 ... 

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... 

Apparent Bulk Density—ABD. The density of the catalyst at which it is shipped either in bulk volume or bags. It is density of the catalyst at minimum fluidization velocity. 

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. 

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

Fluidized bed dryers work best on particles of a few tenths of a mm dia, but up to 4 mm dia have been processed. Gas velocities of twice the minimum fluidization velocity are a safe prescription. In continuous operation, drying times of 1-2 min are enough, but batch drying of some pharmaceutical products employs drying times of 2-3 hr. 

Cracking catalysts are members of a broad class characterized by diameters of 30-150 im, density of 1.5 g/mL or so, appreciable expansion of the bed before fluidization sets In, minimum bubbling velocity greater than minimum fluidizing velocity, and rapid disengagement of bubbles. 

Rough correlations have been made of minimum fluidization velocity, minimum bubbling velocity, bed expansion, bed level fluctuation, and disengaging height. Experts recommend, however, that any real design be based on pilot plant work. 

Practical operations are conducted at two or more multiples of the minimum fluidizing velocity. In reactors, the entrained material is recovered with cyclones and returned to process. In dryers, the fine particles dry most quickly so the entrained material need not be recycled. 

FIGURE 11.9 Fluidization regimes in a batch fluidized bed at low multiples of the minimum fluidization velocity. 

The catalyst was prepared by impregnating porous alumina particles with a solution of nickel and lanthanum nitrates. The metal loading was 20 w1% for nickel and 10 wt% for lanthanum oxide. The catalyst particles were A group particles [8], whereas they were not classified as the AA oup [9]. The average particle diameter was 120 pm, and the bed density was 1.09 kg m . The minimum fluidization velocity was 9.6 mm s. The settled bed height was around 400 mm. The superficial gas velocity was 40-60 mm s. The reaction rate was controlled by changing the reaction temperature. 

Fig. 5. Estimated minimum fluidization velocity vs. centrifugal acceleration...

Fig. 1 shows that minimum fluidization velocities of activated carbon, activated alumina, molecular sieve 5A and molecular sieve 13X are 8.0 cm/s, 8.5 cm/s, 6.2 cm/s and 6.5 cm/s, respectively. Also, theoretical calculation values of minimum fluidization velocity and terminal velocity of each dry sorbent were summarized in Table 1. 

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