Modeling fast fluidization

A well-defined bed of particles does not exist in the fast-fluidization regime. Instead, the particles are distributed more or less uniformly throughout the reactor. The two-phase model does not apply. Typically, the cracking reactor is described with a pseudohomogeneous, axial dispersion model. The maximum contact time in such a reactor is quite limited because of the low catalyst densities and high gas velocities that prevail in a fast-fluidized or transport-line reactor. Thus, the reaction must be fast, or low conversions must be acceptable. Also, the catalyst must be quite robust to minimize particle attrition. 

Models and Correlations. A multitude of different models and correlations have been proposed for prediction of the heat transfer coefficient at vertical surfaces in fast fluidized beds. To organize the various models in some context, it is helpful to consider the total heat transfer coefficient as comprised of convective contributions from the lean-gas... 

The lean/gas phase convection contribution has received the least attention in the literature. Many models in fact assume it to be negligible in comparison to dense phase convection and set hl to be zero. Compared to experimental data, such an approach appears to be approximately valid for fast fluidized beds where average solid concentration is above 8% by volume. Measurements obtained by Ebert, Glicksman and Lints (1993) indicate that the lean phase convection can contribute up to 20% of total... 

The parameter C in Eq. (25) is a dimensionless parameter inversely proportional to the average residence time of single particles on the heat transfer surface. It is suggested that this parameter be treated as an empirical constant to be determined by comparison with actual data in fast fluidized beds. The lower two dash lines in Fig. 17 represent predictions by Martin s model, with C taken as 2.0 and 2.6. It is seen that an appropriate adjustment of this constant would achieve reasonable agreement between prediction and data. 

The three-dimensional voidage distribution provides the basic correlation for building a reactor model for fast fluidization, given data on particle-fluid transfer coefficients and intrinsic particle reaction kinetics. 

At gas velocities higher than those used for BFBs we successively enter the turbulent (TB), fast fluidized (FF), and the pneumatic conveying (PC) regimes. In these contacting regimes solids are entrained out of the bed and must be replaced. Thus in continuous operations we have the CFB, shown in Fig. 20.1. Flow models are very sketchy for these flow regimes. Let us see what is known. 

On the basis of the observations in the macroscale, the flow of a fast fluidized bed can be represented by the core-annulus flow structure in the radial direction, and coexistence of a bottom dense region and a top dilute region in the axial direction. Particle clusters are an indication of the heterogeneity in the mesoscale. A complete characterization of the hydrodynamics of a CFB requires the determination of the voidage and velocity profiles. There are a number of mathematical models accounting for the macro- or mesoaspects of the flow pattern in a CFB that are available. In the following, basic features of several types of models are discussed. 

Kwauk, M., Fast Fluidization, in three parts on mathematical modeling (in Chinese, unpublished), Inst. Chem. Metall. (1979c). 

Bader et al. (1988) used common salt as a solid tracer, which was injected into a flowing catalyst bed. Solids samples, withdrawn downstream of tracer injection, were leached with water and the salt concentration determined by electrical conductivity of the solution. Their results indicated substantial solids backmixing. Li et al. (1991) observed solids mixing in a fast fluidized bed combustor by using raw coal as a tracer, which was injected into the ash bed. Their results also showed that near-perfect mixing prevailed. Similar experiments was also conducted by Chesonis et al. (1991) in a cold model. 

The simplest case is called the one-fluid model, that is, k — 1, assuming that particles are distributed in the fluid discretely. It was used for modeling voidage distributions in fast fluidized beds (Li and Kwauk, 1980 Bai et al., 1988 Zhang et al., 1990). 

By analyzing the turbulent kinetic energy of the fluid, the two-fluid model was modified to the so-called k-e model (Militzer, 1986 Zhou and Huang, 1990) for dilute two-phase flow, which has been extended to calculating radial distributions in fast fluidized beds (Yang, 1992). 

Then, overall hydrodynamics of fast fluidization—region—will be discussed by extending the EMMS model to both axial and radial directions. Other two aspects of local hydrodynamics—regime and pattern—will not be involved as this book is limited to the fast fluidization regime. 

Arastoopour, H., and Gidaspow, D. Analysis of IGT pneumatic conveying data and fast fluidization using a thermohydrodynamic model, Powder Technology 22, 77 (1979). 

In this chapter, emphasis will be given to heat transfer in fast fluidized beds between suspension and immersed surfaces to demonstrate how heat transfer depends on gas velocity, solids circulation rate, gas/solid properties, and temperature, as well as on the geometry and size of the heat transfer surfaces. Both radial and axial profiles of heat transfer coefficients are presented to reveal the relations between hydrodynamic features and heat transfer behavior. For the design of commercial equipment, the influence of the length of heat transfer surface and the variation of heat transfer coefficient along the surface will be discussed. These will be followed by a description of current mechanistic models and methods for enhancing heat transfer on large heat transfer surfaces in fast fluidized beds. Heat and mass transfer between gas and solids in fast fluidized beds will then be briefly discussed. 

The second and the third components become significant only at high temperatures (> 700°C) and low solids concentrations (< 30 kg/m3). In fast fluidized beds, the motion of the particles plays an overriding role in the heat transfer process, since the solids particles have larger heat capacity and higher thermal conductivity. Most of the heat transfer models reported in the literature give emphasis to particle convective transfer. 

Li, Y., Lin, X., and Wang, F. Modelling for fast fluidized bed combustion of coal, Research report (in Chinese), Institute of Chemical Metallurgy, Academia Sinica (1992). 

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