Solid dispersion coefficient

Provided the particle settling velocities vt are known, this equation allows the calculation of )e,s Usually, experiments at non-zero liquid rates are used to evaluate t , and )e,s separately. A similar concentration profile might occur in practice if slurry column reactors are operated close to the conditions given by the minimum suspension criterium. In this case, reactor calculations should take the solids concentration profiles into account. A recommended correlation for the solids dispersion coefficient for small particles is given by Kato et al. [15] ... 

Kato, et al (5 ) measured solid concentration profiles, solid dispersion coefficients and terminal settling velocities for glass spheres in water, using 6.6, 12.2 and 21.k cm bubble columns. They developed a dimensionless, empirical correlation for the solid dispersion coefficients which agreed with their observed values to within 20%. 

The value of the solid dispersion coefficient, Ezs, may be calculated from the experimental data as follows, with the assumption that E g is independent of V-. ... 

Solid Dispersion Coefficients. Solid dispersion coefficients,... 

Figure 6. Solid dispersion coefficient, literature comparison, silicon oxide, isoparaffin system.

The sedimentation diffusion model, when applied to the iron oxide system, gave solid settling velocities in agreement with theory. Solid dispersion coefficients were in the range predicted hy the Kato correlation, hut showed considerable experimental scatter. 

For gas velocities ranging 4.1 to 6.3 m/s, the measured axial solids dispersion coefficients Ds varied from 0.39 to 0.91 m2/s for dilute solid suspension, while for the whole fast bed, in the same gas velocity range, Ds was 0.22 to 1.67 m2/s. Axial solid dispersion coefficient generally increases with both gas velocity and solids circulation rate. Milne and Berruti (1991) have also given their own model for solids mixing. 

Due to density differences the particles have the tendency to settle. Thus, solid concentration profiles result which can be described on the basis of the sedimentation-dispersion model (78,79,80). This model involves two parameters, namely, the solids dispersion coefficient, E3, and the mean settling velocity, U5, of the particles in the swarm. Among others Kato et al. (81) determined 3 and U3 in bubble columns for glass beads 75 and 163 yum in diameter. The authors propose correlations for both parameters, E3 and U3. The equation for E3 almost completely agrees with the correlation of Kato and Nishiwaki (51) for the liquid phase dispersion coefficient. 

The catalyst distribution is governed by the solid dispersion coefficient, E, mean settling velocity of the particles in swarm, u g and in the case of cocurrent flow by the liquid velocity, Uj, which acts against the settling. 

Dp, catalyst density) and the hydrodynamic parameters (gas, liquid and solid dispersion coefficients, catalyst settling velocity, gas holdup, gas-liquid interfacial area, liquid-solid mass transfer coefficient). The influence of these parameters on the catalyst concentration, reaction rate and conversion is indicated by the arrows. As the gas velocity varies with the conversion, the hydrodynamic parameters, while depending on the gas velocity, will be influenced by the conversion as well. This causes also a modification of the catalyst concentration profile in the reactor. 

In general, catalyst sedimentation has to be accounted for in slurry reactors. The distribution of the catalyst along the reactor can be computed using the sedimentation-dispersion model. As to the results of Kato et al. (73), the solid dispersion coefficients do not differ much from those of the liquid phase. From the data provided by Cova (74), Imafuku et al (75), and Kato et al. (73), the solids concentration profiles can be calculated. As in the FT process the catalyst particles are usually small, according to Kolbel and Ralek (35) the diameter should be less than 50 um, the catalyst profiles are not very pronounced, in accordance to the measurements of Cova (74). 

If catalyst particles of larger size and density are used and sedimentation might be important the correlations proposed by Kato et al. (73) are recommended to calculate the solids dispersion coefficient and the settling velocity of the particle. From this data the solids concentration profile can be computed with the sedimentation-dispersion model. 

Analytical solutions of equation (54) for pulse injection of solid tracers can be obtained with proper boundary conditions by assuming that is independent of radial and axial location (van Zoonen, 1962 Wei et al., 1995b Patience and Chaouki, 1995). If velocity and solids concentration profiles are nonuniform, equation (54) must be solved numerically (Koenigsdorff and Werther, 1995), and the axial and radial solids dispersion coefficients are then obtained by fitting. 

Figure 25 Radial solids dispersion coefficient as a function of solids concentration and gas velocity in CFB risers. Data FCC, df = 54 m, = 5.7 m/s (Wei et al., 1995b) O...

The analysis of concentration profiles showed that measured turbulent profiles could be successfully approximated by the Rouse-Schmidt turbulent dif sion model with the implemented settling velocity effect [2]. For both the fine sand (0.10-0.15 mm s uid) and the medium sand (0.2-0. 5 imn sand) (Fig. 1), the solids dispersion coefficient s,meaii (the mean value obtained by integrating local s values over the flow core) seems to be virtually independent of solids concentration in a pipehne. 

Secondly, it is assumed that in each layer the upward and downward solids velocities as well as the axial solids dispersion coefficient are constant and do not change as a function of the bed height. The only change is observed at the boundary between the two layers in the bed. 

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