Minimum fluidization flow rate

The cross sectional average global pressure drop over a fluidized bed op>-erated at minimum fluidization conditions is normally calculated by an extrapolation of the Ergun [42] equation (6.13) for fixed packed beds, the flow regime that is prevailing until the minimum fluidization flow rate has been reached, as described in chap 6 ... 

If turndown is desired, the grid pressure drop criteria (Eqs. 3 and 4) should apply at the minimum gas flow rate. This can be a problem for circulating fluidized bed combustors, since this means that under full load the grid pressure drop will be unacceptably high. Also, if the grid is curved, i.e., concave, convex, or conical, the criterion must apply with respect to the lowest hole on the grid. Take an example of a fluid bed with curved grid, as shown in Fig. 3. 

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 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. 

The process essentially involves passing air through a bottom furnace distributor plate and a fixed bed of sand. As air flow rates increase, the fixed bed becomes more unstable and bubbles of air appear (minimum fluidized condition). Above this minimum level, higher air flow rates produce—depending on design—either bubbling fluidized beds or circulating fluidized beds, and the fuel is introduced onto these beds. 

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... 

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. 

Vibro-fluidization is used for cohesive, sticky solids or friable foods (Bahu, 1997) and for materials which would defluidize in a conventional plug flow drier (Reay and Baker, 1985). Vibration of the bed increases the drying rate due to an increase in the surface-to-bed heat transfer coefficient (Reay and Baker, 1985), particularly below minimum fluidizing velocity. A detailed treatment of the mechanisms of vibration fluidization is given by Reay and Baker (1985). 

Equation (293) cannot be applied to gas fluidized beds because in the latter case, the fluidized bed contains a large number of bubbles. The rate of heat transfer between the bed and wall is determined in the latter case by the heat transfer in the packets (clusters) of solid particles (through which the gas flows at the minimum fluidization velocity) which are exchanged, because of bubbling, between the wall and the bulk of the fluidized bed [74], The heat transfer coefficient is given in the latter case by an expression similar to Eq. (282) ... 

Relative flow rate limits According to Ruthven (1984), a maximum linear velocity should not be exceeded in order to avoid extended friction between the packing material in both down- and upflow operations. This velocity is 0.8 times the minimum fluidization velocity for upflow operation and 1.8 times the same velocity for downflow operation (for further analysis see Chapter 6). Using eq. (3.451), the minimum fluidization velocity for the specific system is 2.36 cin/s. Thus, the maximum allowable velocities for down- and upflow operations are 4.24 and 1.89 cm/s, respectively. In terms of the relative flow rate, the corresponding values are 65.35 and 29.13 BV/h. These values are fairly high for ion-exchange systems and are rarely used in practical applications. 

As the gas flow rate increases beyond that at minimum fluidization, the bed may continue to expand and remain homogeneous for a time. At a fairly definite velocity, however, bubbles begin to form. Further increases in flow rate distribute themselves between the dense and bubble phases in some ways that are not well correlated. Extensive bubbling is undesirable when intimate contading between phases is desired, as in drying processes or solid catalytic reactions. In order to permit bubble formation, the... 

Some smoothed data of expansion ratio appear in Figure 6.10(c) as a function of particle size and ratio of flow rates at minimum bubbling and fluidization. The rather arbitrarily drawn dashed line appears to be a conservative estimate for particles in the range of 100 pm. 

Ordinarily under practical conditions the flow rate is at most a few multiples of the minimum fluidizing velocity so the local maximum bed level at the minimum bubbling velocity is the one that determines the required vessel size. The simplest adequate equation that has been proposed for the ratio of voidages at minimum bubbling and fluidization is... 

A freely bubbling fluidized bed has a higher flow rate of the gas than the minimum fluidization limit. It will reach the case of three phases solid, gas in contact with solid, and gas in bubbles inside the tube. 

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