Fluidized beds dispersion coefficient

Yerushalmi and Avidan (1985) suggest that the axial dispersion coefficient of solids in slugging and turbulent flow varies approximately linearly with the bed diameter, similar to Thiel and Potter (1978). The data are shown in Fig. 17 although May s results are probably in the bubbling fluidization regime rather than turbulent flow. 

Despite this, the expected heat transfer coefficients obtainable in a fluidized bed are greater than those for forced convection in a gas (Ditchev and Richardson, 1999) although not as high as in the dynamic dispersion medium (DDM) method described by these authors. Comparative data are presented in Table 3.3. 

Vazquez and Calvelo (1983b) presented a model for the prediction of the minimum residence time in a fluidized bed freezer which can then be equated to the required freezing time. The model is defined in terms of a longitudinal dispersion coefficient D, which is a measure of the degree of solids mixing within the bed in the direction of flow (and has the dimensions of a diffusivity, and hence units of m s ), a dimensionless time T... 

The modeling of real immobilized-enzyme column reactors, mainly the fluidized-bed type, has been described (Emeiy and Cardoso, 1978 Allen, Charles and Coughlin, 1979 Kobayashi and Moo-Young, 1971) by mathematical models based on the dispersion concept (Levenspiel, 1972), by incorporation of an additional term to account for back-mixing in the ideal plug-flow reactor. This term describes the non-ideal effects in terms of a dispersion coefficient. 

In Fig. 5, the liquid phase axial dispersion coefficient Daxi and the Bodenstein number Bo calculated from this relationship according to Eqs. (9), (10) and (13) are plotted for a range of linear velocities used in fluidized bed adsorption. The physical parameters of the commercial Streamline SP adsorbents (average particle size 247 pm, average particle density 1143 kg/m3, terminal settling velocity 0.0044 m/s, n = 4.7 as described by Chang and Chase [37]) were... 

If the flow and mixing of gas in the bubbling fluidized bed are described by a simple one-phase dispersion model, the coefficients Dgv and Dgh of gas dispersion in the vertical and horizontal directions have similar... 

The dimensionless term (9/u0 L, where 9 is the axial dispersion coefficient, u0 is the superficial fluid velocity, and L is the expanded-bed height) is the column-vessel dispersion number, Tc, and is the inverse of the Peclet number of the system. Two limiting cases can be identified from the axial dispersion model. First, when 9/u0L - 0, no axial dispersion occurs, while when 9/u0 L - 00 an infinite diffusivity is obtained and a stirred tank performance is achieved. The dimensionless term Fc, can thus be utilized as an important indicator of the flow characteristics within a fluidized-bed system.446... 

Computation of axial dispersion coefficients for solids was provided by Patience et al. (1991), in the following simple one-dimensional model using the data obtained from RTD measurements of a radioactive solid tracer in a 82.8 mm i.d. by 5 m high circulating fluidized bed, that is,... 

Recommendations For estimating the liquid- and solid-phase axial dispersion coefficients in a three-phase fluidized-bed column, use of Eqs. (9-37) and (9-39) are recommended. Future work on this subject should include the measurement of axial dispersion coefficients in the gas phase, particularly in large-diameter columns. 

The dispersion coefficient is orders of magnitude larger than the molecular diffusion coefficient. Some rough correlations of the Peclet number are proposed by Wen (in Petho and Noble, eds.. Residence Time Distribution Theory in Chemical Engineering, Verlag Chemie, 1982), including some for fluidized beds. Those for axial dispersion are ... 

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

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