Dense-phase fluidized beds minimum fluidization

Group A The bed particles exhibit dense phase expansion after minimum fluidization and before the beginning of bubbling. Gas bubbles appear at the minimum bubbling velocity. 

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... 

Essentially aggregative fluidization is a two-phase system there is a dense phase (sometimes reterred to as the emulsion phase), which is continuous, and a discontinuous phase called the lean or bubble phase. The simplitied assumption that all the gas over and above that required tor minimum fluidization flows up through the bed in the form ot bubbles is known as the two-phase theory. It the total volumetric flow ot gas is Q then... 

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... 

Flow Distribution between Phases. One of the principal assumptions underlying many of the models of fluidized bed reactors is the two-phase theory of fluidization. This theory, really no more than a postulate, holds that the flow beyond that required for minimum fluidization passes through the bed as translating void units. Although not included in what the originators of this postulate (38) appeared to have in mind, the two phase theory is often held to imply, in addition, that the dense phase voidage remains constant and equal to e - for all U > U. ... 

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]. 

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. 

Because it is the bubbles which are largely responsible for mixing in fluidized beds, it is important to know how much of the gas flowing into the bed forms bubbles. A first estimate of the bubble flow rate, (2b> is provided by the two phase theory. This pictures the bed as consisting of a dense phase in which the gas velocity is equal to that at minimum fluidization, U f, and a bubble phase which carries all the additional gas. Thus, at a superficial velocity U ... 

A simple two-phase model of fluidized bed drying treats the fluidized bed to be composed of a bubble phase (dilute phase) and an emulsion phase (dense phase). The bubble phase contains no particles or the particles are widely dispersed. This model assumes that all gas in excess of minimum fluidization velocity, umf, flows through the bed as bubbles, whereas the emulsion phase stays stagnant at the minimum fluidization conditions [47]. Figure 8.5 shows a schematic diagram of the simple two-phase model. 

We consider here an application to a fluidized bed catalytic chemical reactor whose performance is affected by coalescence between gas bubbles. The problem has been considered in detail by Sweet et al (1987) (based on the earlier work of Shah et al, 1977, which addressed the bubbling process without chemical reaction) and we shall discuss here the formulation aspects of the model. The process of interest consists in blowing a gas containing a reactant A through a bed of catalyst particles at a velocity in excess of the minimum fluidization velocity. The excess gas forms bubbles at the bottom of the bed, which ascend by virtue of their buoyancy up the bed of a dense phase of catalyst particles, and eventually escape from the top surface. The catalyst particles in the dense phase are in vigorous circulatory motion through the bed. The reactant in the gas bubbles has inadequate contact with the catalyst particles so that no reaction takes place. However, the gas in the dense phase does undergo reaction to products. 

In the above equation, the reaction term features the bed height at minimum fluidization, which gives the volume of the dense phase per unit cross-section. The mutually coupled Eqs. (3.3.25) and (3.3.26) represent the mathematical formulation of the population balance model. Since the reaction rate is linear it is possible in this case to solve explicitly for q to obtain... 

In order to describe the behaviour of three-phase fluidized beds it is very important to achieve a good understanding of the characteristics of liquid-solid fluidization. This is because the particles in three-phase beds are essentially fluidized by the liquid. An important question then is to define the conditions of minimum fluidization in liquid-solid systems. At minimum fluidization the pressure drop in the dense bed, frequently represented by the Ergun equation for fixed beds, becomes equal to the buoyant weight of the particles. The following identity then results. 

Almost all of the models proposed to date are based on the two phase theory of fluidization originally proposed by Toomey and Johnstone (97) and later modified by Davidson and Harrison (98). According to the theory, the fliiidized bed is assumed to consist of two phases, viz., l) a continuous, dense particulate phase (emulsion phase) and 2) a discontinuous, lean gas phase (bubble phase) with exchange of gas between the bubble phase and emiilsion phase. The gas flow rate through the emulsion phase is assumed to be at minimum fluidization and that in excess of the minimum fluidization velocity passes throu the bubble phase. This formulation of the two phase theory is based on the ass mq)tion that the voidage of the emulsion phase remains constant. However, as pointed out by Rowe (22) and Horio and Wen (lOO) this assumption may be an over-simplification. In particular, experiments with fine powders (dp < 60 ym) conducted by Rowe show that the dense phase voidage changes with gas velocity, and as much as 30 percent of the gas flow occurs interstitially. This effect can be... 

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