Minimum fluidization superficial velocity

Using the Ergun (1952) equation for the interfacial friction factor, Wen and Yu (1966) derived the following general equation to estimate the minimum fluidization superficial velocity Umf for spherical particles ... 

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... 

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,...

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. 

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. 

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. 

The first term in the list multiplied by the third term has been shown by Glicksman (1988) to be equivalent to the ratio of superficial and minimum fluidization velocities in the viscous limit. The controlling parameters can therefore be written as... 

A model was developed to describe this phenomenon by assuming that the gas leaks out through the bubble boundary at a superficial velocity equivalent to the superficial minimum fluidization velocity. For a hemispherical bubble in a semicircular bed, the rate of change of bubble volume can be expressed as ... 

The superficial velocity of gas in a fluidized bed, relative to the minimum fluidizing velocity, is the quantity which has the greatest influence on the behaviour of a given particle bed. Consequently, a knowledge of minimum fluidizing velocity is vital to the operation of fluidized beds and much research effort has been expended in attempting to predict it. 

In equation 2.28 Up is the lower of the two minimum fluidizing velocities of the two types of particle in the mixture and Ufo is the velocity at which mixing takes over or begins to dominate segregation. Thus, as the superficial gas velocity in the bed is increased, the mixing index increases from M = 0 at the lower minimum fluidizing velocity (m = Mp), where the bed is quiescent with no particle movement because of the absence of bubbles, to M = 0.5 when, by definition, the velocity is equal to Uto- The mixing index approaches a value of unity as the velocity increases still further (Nienow and Chiba, 1985). 

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. 

Gfm = the superficial mass velocity based on the minimum fluidization velocity... 

In this equation, Re is tlie particle Reynolds number based on the minimum superficial velocity for fluidization. Moreover, for fixed-beds, we can set = 1 and sf = s. The correlation is applicable for void fractions between 0.4 and 0.8 with particle density up to 480 lb/ft3. Note that by changing the Rep number, the fluidized bed voidage ef is changed. 

Fluidized bed For the specified system and particle size, the minimum fluidization velocity is 4.24 cm/s (eq. 3.451). Flere, we note that the operating superficial velocity in the fixed bed is higher than the minimum fluidization velocity. This means that to retain a fixed-bed operation, we should operate in a downflow mode. 

If we use smaller particle size, the fluidised bed performance is different. For example, for dp = 0.15 mm, the minimum fluidization velocity is 1.34 cm/s. If we operate the fluidized bed with this particle size, to have a contact time of 5 min, we need a superficial velocity of 5.85 cm/s, where the fluidized bed height is 17.51 m, and the resulting conversion is somewhat lower, equal to 25.8 %. 

The next step is to use the Ergun equation for the determination of the minimum fluidization velocity (eq. 3.451). For this step, we need a goal-seek procedure and the minimum fluidization velocity is found to be equal to 0.0057 cm/s, which is almost 10 times lower than the operation superficial velocity ... 

---