Minimum fluidizing condition

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

Equation 6-108 is also a good approximation for a fluidized bed reactor up to the minimum fluidizing condition. However, beyond this range, fluid dynamic factors are more complex than for the packed bed reactor. Among the parameters that influence the AP in a fluidized bed reactor are the different types of two-phase flow, smooth fluidization, slugging or channeling, the particle size distribution, and the... 

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 results of an example calculation for a recirculating fluidized bed coal devolatilizer of 0.51 m in diameter handling coal of average size 1200 pm at 870°C and 1550 kPa are presented in Fig. 11. The calculation is based on operating the fluidized bed above the draft tube at 4 times the minimum fluidization velocity. It is also based on the selection of a distributor plate to maintain the downcomer at the minimum fluidization condition. If the two-phase theory applies, this means that the slip velocity between the gas and the particles in the downcomer must equal to the interstitial minimum fluidizing velocity as shown below. 

It was also shown both theoretically and experimentally (Tardos et al., 1985a,b) that there is a strong correlation between the excess temperature above the minimum sintering point, T-Ts, and the excess gas velocity above minimum fluidization conditions (measured below the sintering point) U-lJm required to maintain fluidization. A general correlation was developed between the excess temperature and the excess gas velocity, which takes the form... 

Wilhelm and Kwauk (1948), in one of the earliest papers on fluidization, suggested that the Froude number, written for the minimum fluidizing condition, could be used to indicate the prevalent fluidization behaviour. Thus... 

Writing Ergun s equation for minimum fluidizing conditions, and assuming the particles to be spherical ( =1), gives... 

The emulsion stays at minimum fluidization conditions, thus the relative G/S velocity stays constant in the emulsion. 

The emulsion phase stays at minimum fluidizing conditions. Thus, the relative velocity of the gas and solid remains unchanged. 

The concentration of solids in the wake is the same as the concentration of solids in the emulsion phase, and therefore, the gaseous void fraction in the wake is also the same as in the emulsion phase. Because the emulsion phase is at the minimum fluidizing condition, the void fraction in the wake is equal to film. The wake, however, is quite turbulent, and the average velocities of both the solid and gas in the wake are assumed to be the same and equal to the upward velocity of the bubbles. 

The minimum fluidization condition refers to the situation in which AP, the pressure drop across the bed, is equal to the bed weight. 

All the advantages of minimum fluidization conditions. Disadvantages of fluidized beds... 

The superficial velocity at minimum fluidizing conditions is given by the correlation... 

The physical understanding of gas flows through a packed bed is important for the study of the gas-solid transport system as it represents the limiting case of the gas-solid transport. A typical example is the minimum fluidization condition of gas-solid fluidization. In a gas-solid flow system, the presence of unsuspended particles is also common, and, thus, understanding the gas flow in a packed bed is essential. 

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. 

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... 

In the experimental study of single-bubble behavior, the gas-solid fluidized bed to which a single bubble is introduced is usually maintained at the minimum fluidization condition. Characteristics of a single gas bubble in a gas-solid fluidized bed are similar to those in a liquid medium [Clift and Grace, 1985 Fan and Tsuchiya, 1990 Krishna, 1993]. 

Maintaining the downcomer or a standpipe under a moving bed condition allows a large pressure buildup along the downcomer. For a given quantity of particles in the downcomer, the pressure at the bottom of the downcomer is closely associated with the relative velocity between the gas and particles. The pressure drop rises with the relative velocity as the particles are in a moving packed state. The maximum pressure drop in the downcomer is established when particles are fluidized, a state which can be expressed in terms of the pressure drop under the minimum fluidization condition as... 

Solution The maximum solids circulation rate through an L-valve is limited by the pressure drop across the downcomer under minimum fluidizing conditions. Thus, the pressure balance can be written in terms of voidage and solids inventory in the downcomer as (see Fig. 10.6)... 

As a first approximation a convective term in the film region has been negleted, u is the superficial gas velocity and u f denotes the gas velocity at minimum fluidization conditions. Tne specific mass transfer area a(h) is based on unit volume of the expanded fluidized bed and e OO is the bubble gas hold-up at a height h above the bottom plate. Mathematical expressions for these two latter quantities may be found in detail in (20). The concentrations of the reactants in the bubble phase and in film and bulk of the suspension phase are denoted by c, c and c, respectively. The rate constant for the first order heterogeneous catalytic reaction of the component i to component j is denoted... 

The ultimate cause of bubble formation is the universal tendency of gas-solid flows to segregate. Many studies on the theory of stability [3, 4] have shown that disturbances induced in an initially homogeneous gas-solid suspension do not decay but always lead to the formation of voids. The bubbles formed in this way exhibit a characteristic flow pattern whose basic properties can be calculated with the model of Davidson and Harrison [30], Figure 5 shows the streamlines of the gas flow relative to a bubble rising in a fluidized bed at minimum fluidization conditions (e = rmf). The characteristic parameter is the ratio a of the bubble s upward velocity u, to the interstitial velocity of the gas in the suspension surrounding the bubble ... 

The state of fluidization begins at the point of minimum or incipient fluidization. At the minimum fluidization point, the pressure drop for a fixed bed and that for a fluidized bed are equivalent. This relationship is used as the basis for the formation of the predictive equation for the minimum fluidization velocity. The pressure drop in the fixed bed can be described by the Ergun equation. Under the minimum fluidization condition, the Ergun equation can be expressed as... 

Increasing the gas flow just passing the point of minimum fluidization conditions the onset of particle fluidization will occur when the drag forces acting on the particles due to the upward moving gas are balanced by the weight of the solid particles [30]. 

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