Fluidization bubble rise velocity

The bubble size at formation varied with particle characteristics. It was further observed that the bubble size decreased with increasing fluidization intensity (i.e., with increasing liquid velocity). The rate of coalescence likewise decreased with increasing fluidization intensity the net rate of coalescence had a positive value at distances from 1 to 2 ft above the orifice, whereas at larger distances from the orifice the rate approached zero. The bubble rise-velocity increased steadily with bubble size in a manner similar to that observed for viscous fluids, but different to that observed for water. An attempt was made to explain the dependence of the rate of coalescence on fluidization intensity in terms of a relatively high viscosity of the liquid fluidized bed. 

Glicksman and McAndrews (1985) determined the effect of bed width on the hydrodynamics of large particle bubbling beds. Sand particles with a mean diameter of 1 mm were fluidized by air at ambient conditions. The bed width ranged from 7.6 cm to 122 cm while the other cross sectional dimension remained constant at 122 cm. Most experiments were carried out with an open bed. The bubble rise velocity increased with the bed width, in the representation of bubble velocity as... 

For the discrete bubble model described in Section V.C, future work will be focused on implementation of closure equations in the force balance, like empirical relations for bubble-rise velocities and the interaction between bubbles. Clearly, a more refined model for the bubble-bubble interaction, including coalescence and breakup, is required along with a more realistic description of the rheology of fluidized suspensions. Finally, the adapted model should be augmented with a thermal energy balance, and associated closures for the thermophysical properties, to study heat transport in large-scale fluidized beds, such as FCC-regenerators and PE and PP gas-phase polymerization reactors. 

At bubble rise velocities greater than minimum fluidizing velocity, the approximately spherical shell of gas which surrounds a bubble and circulates through it as it rises through the bed. 

K. Tsuchiya, A. Furumoto, L.S. Fan, J. Zhang, Suspension viscosity and bubble rise velocity in liquid-solid fluidized beds, Chem. Eng. Sci. 52 (1997) 3053-3066. 

The performance of a fluidized bed combustor is strongly influenced by the fluid mechanics and heat transfer in the bed, consideration of which must be part of any attempt to realistically model bed performance. The fluid mechanics and heat transfer in an AFBC must, however, be distinguished from those in fluidized catalytic reactors such as fluidized catalytic crackers (FCCs) because the particle size in an AFBC, typically about 1 mm in diameter, is more than an order of magnitude larger than that utilized in FCC s, typically about 50 ym. The consequences of this difference in particle size is illustrated in Table 1. Particle Reynolds number in an FCC is much smaller than unity so that viscous forces dominate whereas for an AFBC the particle Reynolds number is of order unity and the effect of inertial forces become noticeable. Minimum velocity of fluidization (u ) in an FCC is so low that the bubble-rise velocity exceeds the gas velocity in the dense phase (umf/cmf) over a bed s depth the FCC s operate in the so-called fast bubble regime to be elaborated on later. By contrast- the bubble-rise velocity in an AFBC may be slower or faster than the gas-phase velocity in the emulsion... 

In bubble columns, the estimation of parameters is more difficult than in the case of either gas-solid or solid-liquid fluidized beds. Major uncertainties in the case of bubble columns are due to the essential differences between solid particles and gas bubbles. The solid particles are rigid, and hence the solid-hquid (or gas-solid) interface is nondeformable, whereas the bubbles cannot be considered as rigid and the gas-liquid interface is deformable. Further, the effect of surface active agents is much more pronounced in the case of gas-liquid interfaces. This leads to uncertainties in the prediction of all the major parameters such as terminal bubble rise velocity, the relation between bubble diameter and terminal bubble rise velocity, and the relation between hindered rise velocity and terminal rise velocity. The estimation procedure for these parameters is reviewed next. 

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]. 

Uh Bubble rise velocity in the fluidized bed, 1/t Uo Superficial gas velocity in the fixed-bed and moving-bed reactors, 1/t... 

There is another factor that needs to be taken into consideration the need to reduce oil vapor degradation (Wish 1), requiring us to reduce the oil vapor residence time in the reactor. In bubbling fluidized beds (R-2) and turbulent fluid beds (R-3), the bubble rise velocities are of the order of 1.5 m/s, and in a shallow bed of, say, 2 m the oil vapor residence time may be restricted to below 2 s. 

The bubble rise velocity, important in determining gas-phase residence time, is estimated by a correlation reminiscent of fluidized beds. 

The critical velocity for the transition to turbulent fluidization, u, depends on the gas and solid properties, and for porous catalysts it is generally between 0.2 and 0.5 m/sec. Complex empirical correlations for have been published, but the transition can be understood by considering the major factor, which is the average bubble rise velocity, compared to the superficial velocity, <,. In a bubbling bed, a is the fraction of bed volume occupied by bubbles, and (1 — a) is the fraction of dense bed, where the velocity is close to u (. The bed expansion and a are related as follows ... 

A greater understanding of bubbles in fluidized beds has come from theoretical studies and pictures of bubbles in two-dimensional and three-dimensional beds [3,9]. If the bubble rise velocity is greater than the superficial velocity, gas leaving the top of the bubble is carried back to the bottom... 

It is proposed that turbulent fluidization is achieved when the bubble diameter reaches its maximum value and the corresponding bubble rise velocity is the terminal velocity of individual bed particles, U,. A slight increase in the gas velocity breaks these bubbles and allows the gas to flow in a continuous phase forming clusters of particles. These clusters may be assumed to move at a velocity equal to the maximum stable bubble rise velocity (U, = U,). 

While it is often helpful to consider the analogy between bubbles in liquids and in gas-fluidized beds, for example, affecting bubble rise velocities, shapes, and coalescence dynamics, one needs to recognize some very significant differences between gas-solid and gas-liquid systems, with profound impact ... 

A powder of mean sieve size 60 gm and particle density 1800 kg/m is fluidized by air of density 1.2kg/m and viscosity 1.84 x 10 Pas in a circular vessel of diameter 0.5 m. The mass of powder charged to the bed is 240 kg and the volume flow rate of air to the bed is 140 m /h. It is known that the average bed voidage at incipient fluidization is 0.45 and correlation reveals that the average bubble rise velocity under the conditions in question is 0.8 m/s. Estimate ... 

Four types of bubbling fluidized bed flow in standpipes are possible depending on the direction of motion of the gas in the bubble phase and emulsion phases relative to the standpipe walls. These are depicted in Figure 8.16. In practice, bubbles are undesirable in a standpipe. The presence of rising bubbles hinders the flow of solids and reduces the pressure gradient developed in the standpipe. If the bubble rise velocity is greater than the solids velocity, then the bubbles will... 

Figure 4.41 (Top) Equivalent bubble diameter as a function of axial (left) and lateral positions (right), (center) bubble aspect ratio as a function of axial (left) and lateral positions (right), and (bottom) number of bubbles per frame as a function of the axial position (left) and average bubble rise velocity as a function of the equivalent bubble diameter (right) for different gas permeation ratios of 0%, 10%, 20%, and 40% with respect to the background fluidization velocity. In all cases, the background fluidization velocity was kept constant (100%). Reprinted from De Jong et al. (2013) with permission from Elsevier.

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