Fluidized beds minimum porosity

Before the bed can become fluidized, however, the particles must dislodge from their packed state, which expands the bed. Thus, the porosity (s) in Eqs (14-5) and (14-9) is not the initial packed bed porosity but the expanded bed porosity at the point of minimum fluidization ( ml ), i.e., the minimum bed voidage in the bed just prior to fluidization. Actually, the values of C and C2 in Eq. (14-8) that give the best results for fluidized beds of uniform spherical particles have been found from empirical observations to be ... 

Due to their complexity, the model equations will not be derived or presented here. Details can be found elsewhere [Adris, 1994 Abdalla and Elnashaie, 1995]. Basically mass and heat balances arc performed for the dense and bubble phases. It is noted that associated reaction terms need to be included in those equations for the dense phase but not for the bubble phase. Hydrogen permeation, the rate of which follows Equation (10-51b) with n=0.5, is accounted for in the mass balance for the dense phase. Hydrodynamic parameters important to the fluidized bed reactor operation include minimum fluidization velocity, bed porosity at minimum fluidization, average bubble diameter, bubble rising velocity and volume fraction of bubbles in the fluidized bed. The equations used for estimating these and other hydrodynamic parameters are taken from various established sources in the fluidized bed literature and have been given by Abdalla and Elnashaie [1995]. 

At incipient fluidization, e is the minimum porosity (If the particles themselves are porous, s is the external void fraction of the bed.) Thus... 

A packed bed of coal has a porosity in the range of 0.4-0.5. The porosity of a fluidized bed can vary over a wide range, depending on the gas flow velocity (y/ = 0.4-1). The minimum velocity of fluidization for the coal and other friable materials for which the porosity y/Q = 0.4 can be calculated from the formula... 

J. Minimum velocity and porosity for fluidization. When a fluid flows upward through a packed bed of particles at low velocities, the particles remain stationary. As the fluid velocity is increased, the pressure drop increases according to the Ergun equation (3.1-20). Upon further increases in velocity, conditions finally occur where the force of the pressure drop times the cross-sectional area just equals the gravitational force on the mass of particles. Then the particles just begin to move, and this is the onset of fluidization or minimum fluidization. The fluid velocity at which fluidization begins is the minimum fluidization velocity v f in m/s based on the empty cross section of the tower (superficial velocity). 

As stated earlier, the pressure drop increases as the gas velocity is increased until the onset of minimum fluidization. Then as the velocity is further Increased, the pressure drop decreases very slightly and then remains practically unchanged as the bed continues to expand or increase in porosity with increases in velocity. The bed resembles a boiling liquid. As the bed expands with increase in velocity, the bed continues to retain its top horizontal surface. Eventually, as the velocity is increased much further, entrainment of particles from the actual fluidized bed becomes appreciable. 

The minimum bed porosity at incipient fluidization for nonspherical particles can be estimated from... 

Accordingly, to calculate un,r, the characteristics of the gas (pf, q), the density ps of the particles, the porosity 6mf of the bed at minimum fluidization, and the volume-specific surface area Sv of the solids must be known. The specific surface area defined by... 

Adris et al. [1991] also determined that the reactor performance is weakly sensitive to the bubble size, bed porosity at minimum fluidization and flow distribution between bubble and dense phases. Furthermore, the bubbles which remove the products from the reaction mixture in the dense phase enhance the forward reaction and consequently breaks the barrier of the reaction equilibrium. 

Tardos, 1997) using glass particles of a mean size of 300 micrometers so that 80% of the particles lay within the range of 350 to 250 jtrm. The density of particles was within the range of 2.42 to 2.5 g/cc under Geldart s classification scheme (Kunii and Levenspiel, 1991), these particles classify as class B. The minimum fluidization velocity of the particles was found experimentally to be about 8 cm/s. The volume fraction or the porosity s of the bed at minimum fluidization conditions was taken as 0.4 (Kunii and Levenspiel, 1991). 

The minimum fluidization velocity needed for bed expansion depends on the size, shape, density of the particles, porosity of the fixed bed, and on the density and viscosity of the fluid. Fluidizing the bed requires a large power input but, once fluidized, practically no further input is needed to increase the flow rate, and the pressure drop is almost constant (Figure 3.4.4). The minimum fluidization velocity Ws.min IS Calculated based on a balance of forces, as the weight of the bed, Wb, (less the lifbng force) equals the hydrodynamic resisting force by the flow ... 

Using the correlation equations presented above, all the required quantities PBb> Pbo and PBe (bulk densities in the bubble, cloud, and emulsion phases, respectively), as well as the volume fractions for the respective phases (8b, 8c, and 8e) in the balance equations, can be predicted from the basic quantities, bed porosity at minimum fluidization (Snif),... 

JVcstokes is the expression of the Stokes fall velocity for small particles, and JVcNewton that of thc Newton fall velocity for large particles (see Table 15.1). Relation [15.39] shows that the porosity of the bed (and therefore its thickness) increases with velocity. The porosity and thickness of the bed also increase when the diameter of the particles diminishes. Relation [15.39] can be used to evaluate the minimum fluidization velocity U f theoretically. This only requires solving the second-degree equation constituted by [15.39], by taking the porosity equal to the porosity eq of the settled bed (derived from the mass balance [15.37] if the mass Mp of the bed and the thickness Hfo of the settled bed are known). 

Ruiz et al. (2005) studied the hydrodynamic characteristics of ebullated-bed systems operated at high pressure and temperature. The purpose of the work was to examine the effect of both variables on the hydrodynamic properties of ebullated-bed systems. The bed porosity and liquid minimum fluidization were measured and... 

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