Hydrodynamics minimum fluidization velocity

This set of equations is sufficient to characterize a particulate matrix which should be used in fluidized bed adsorption regarding its fluidization behavior. It has to be noted, however, that the correlations have been developed for the fluidization of spherical particles of uniform diameter. In reality, most adsorbents are provided with a certain distribution of particle diameter. In this case, classified fluidization occurs and a modified equation should be used to describe the hydrodynamics of bed expansion [21]. For an estimation of the suitability of a certain matrix for fluidized bed adsorption the correlations shown above are convenient to use and provide sufficient information. The minimum fluidization velocity may be calculated using an average particle diameter as recommended by Couderc [22], In the next section, conventional as well as new matrices shall be described under this respect. 

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]. 

A pseudo-2D setup was used to investigate the effect of gas penneation on the fluidized bed hydrodynamics using a small-scale fluidized bed. The bed width, depth, and height were 4, 1, and 50 cm, respectively. These dimensions have been chosen to have the setup as large as possible, yet being able to perform DPM simulations with the resulting number of particles in this domain. Apart from the dimensions, the experimental setup and measurement procedures have been kept identical to that described in Section 2.3.1, i.e., glass beads with diameter 400—600 pm have been used, which results in a measured minimum fluidization velocity of 0.25 m/s. 

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 ... 

As examined in Section 3.4.1.2, the minimum fluidization velocity is calculated based on a balance of forces, as the weight of the bed (less the lifting force) equals the hydrodynamic resisting force by the flow [Eq. (3.4.26)] ... 

Various aspects of three-phase fluidization have been the subject of numerous investigations due to its high potential for industrial applications in areas such as catalytic processes, hydrocracking and desulphurization of petroleum products, coal liquefaction, hydrogenation of unsaturated fats, and production of calcium bisulfite liquor. Extensive studies have been published concerning the hydrodynamics of three-phase fluidized beds, such as expansion [l-S], pressure drop [ 9 J, gas and liquid hold up [10-14], minimum fluidization velocity [izj and axial mixing [8, 10, 14-17]. 

Hydrodynamics of slurry reactors includes the study of minimum gas velocity or power input to just suspend the particles (or to fully homogeneously suspend the particles), bubble dynamics and the holdup fractions of gas, solids and liquid phases. A complicating problem is the large number of slurry reactor types in use (see fig. 1) and the fact that most correlations available are at least partially of an empirical nature. We will therefore restrict ourselves to sparged slurry columns and slurries in stirred vessels. A second problem is the difference with three phase fluidization. To avoid too much overlap we will only consider those cases where superficial liquid velocities are so low that its contribution to suspension of the particles is relatively unimportant. 

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