Solids concentration profile

The first two profiles are hrniting cases of solid concentration profiles, and most situations may be somewhere between those limits, as shown in the third panel. 

Figure 9-9 Solid concentration profiles expected for partially reacted films or pellets that have both ciystal grains and pores.

This correlation has been verified for a wide range of operating conditions and Group A and Group B particles. Measurements of radial solids concentration profiles in a large-scale CFB combustor also confirm the validity of this correlation [Werther, 1993]. 

When the particle holdup is high, the contribution of h plays a dominant role and hgc is less important. The radial distribution of the heat transfer coefficient is nearly parabolic, as shown in Fig. 12.16(a). Such a heat transfer profile is similar to the solids concentration profile described in Chapter 10. 

Data on solids phase dispersion are similar to those of the liquid phase, at least for small particle diameters as generally prevailing in slurries [15, 76]. At zero liquid rates, if the particles are only suspended by the gas flow, a solids concentration profile will be established ... 

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] ... 

In the design of upflow, three phase bubble column reactors, it is important that the catalyst remains well distributed throughout the bed, or reactor space time yields will suffer. The solid concentration profiles of 2.5, 50 and 100 ym silica and iron oxide particles in water and organic solutions were measured in a 12.7 cm ID bubble column to determine what conditions gave satisfactory solids suspension. These results were compared against the theoretical mean solid settling velocity and the sedimentation diffusion models. Discrepancies between the data and models are discussed. The implications for the design of the reactors for the slurry phase Fischer-Tropsch synthesis are reviewed. 

As part of the work undertaken by APCI under contract to the DOE, to develop a slurry phase Fischer-Tropsch process to produce selectively transportation fuels, a study of the hydrodynamics of three phase bubble column reactors was begun using cold flow modelling techniques (l ). Part of this study includes the measurement of solid concentration profiles over a range of independent column operating values. 

Cova (3 ) measured the solid concentration profiles of a Raney nickel catalyst with an average diameter of 15.7 ym in a h.6 cm id reactor, using water and acetone as the liquids. He developed a sedimentation diffusion model, assuming solid and liquid dispersion coefficients were equal, and slurry settling velocities were independent of solid concentration. The model was then applied to data for Raney nickel in 6.35 and kk.J cm id bubble columns, in both cocurrent and countercurrent flow. 

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%. 

Sivasubramanian, et al (6 ) and Moujaes, et al (7 ) measured solid concentration profiles of sand in water and ethanol/water, using 12.7 and 30.5 cm bubble columns. They developed a solids accumulation model, which correlated successfully with an actual 30.5 cm solvent refined coal dissolver. 

The vork described in this paper extends the understanding of solid concentration profiles in three phase huhhle column reactors, with emphasis on the Fischer-Tropsch synthesis, by ... 

Solid concentration profiles are produced from a balance of gravitational with buoyancy and kinetic energy transfer forces. For a single particle in a stagnant liquid, the settling velocity,... 

The three upper slurry samples taken for each solid concentration profile, along with equation 9 provided three independent equations, from which two parameters, V /E g, a least squares technique was used to estimate the two parameters. Since is known, experimental values for Egg and VgT were then independently determined. 

In every case, as expected by theory, larger particle sizes produced greater solid concentration slopes. In the 30.5 cm column, no effect from the heat transfer internals on solid concentration profiles was observed for any of the three size ranges studied. 

Effect of Slurry Velocity on Solid Concentration Profiles. 

Figures 2a and 2b show axial solid concentration profiles for the iron oxide system in hatch and continuous mode, respectively. Figures 3a and 3h show the same information for the silicon oxide system. For "both systems, concentration profiles were much more uniform in continuous mode than in hatch mode. This is to he expected from equation 6, because of the dependence shown on the difference between the solids settling velocity and the upward slurry velocity.

Solid/Liquid Interaction Effects. Figures ka. and kb show the effect of different solid/liquid pairs on solid concentration profiles. In ka. and kb9 the steepest profiles were observed for the silicon oxide/isoparaffin and iron oxide/water systems. The other solid/liquid pairs, silicon oxide/water and iron oxide/ isoparaffin, gave much less pronounced concentration profiles, and in fact, for the continuous runs, were essentially horizontal. 

ZS were calculated from the same Qk experimental runs as the solid settling velocity results. Many of the solid concentration profiles for the 0.5-5 ym size particles were uniform to within 0.2 weight percent. As uniform profiles suggest an infinite dispersion coefficient, scatter for the smallest size particles was too large to be included in the analysis. For the iron oxide... 

Effect of Solid Concentration Profiles on Reactor Performance. 

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. 

Thin L-shaped probes are commonly used to measure solids concentration profile in slurry pipelines (28-33), However, serious sampling errors arise as a result of particle inertia. To illustrate the effect of particle inertia on the performance of L-shaped probes, consider the fiuid streamlines ahead (upstream) of a sampling probe located at the center of a pipe, as shown in Figure 2. The probe has zero thickness, and its axis coincides with that of the pipe. The fluid ahead of the sampler contains particles of different sizes and densities. Figure 2A shows the fluid streamlines for sampling with a velocity equal to the upstream local velocity (isokinetic sampling). Of course, the probe does not disturb the flow field ahead of the sampler, and consequently, sample solids concentration and composition equal those upstream of the probe. 

Figure 18 shows the solids concentration profile 22 pipe diameters downstream of a short-radius elbow. The concentration profile is symmetrical, and a minimum solids concentration appears at the center of the pipe. Also, the solids concentration gradually increases toward the pipe wall. This variation in concentration across the pipe is evidently a consequence of the centrifuging action of the secondary flow that is generated by the bend upstream. Figure 18 also shows that the concentration profiles are concentration dependent, and as the solids concentration is increased, the profiles become flatter. Other results (55) showed that these profiles are also functions of the particle size and the radius of curvature of the elbow. 

Figure 20. Effect of particle size on solids concentration profile downstream of a short-radius elbow. (Reproduced with permission from reference 55. Copyright 1987.)...

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

Magelli, F. Fajner, D. Nonentini, M. Pasquali, G. Solid distribution in vessels stirred with multiple impellers. Chem. Eng. Sci. 1990, 45, 615-625. Fajner, D. Magelli, F. Nocentini, M. Pasquali, G. Solids concentration profiles in a mechanically stirred and staged column slurry reactor. Chem. Eng. Res. Des. 1985, 63, 235-240. 

Low values of the RSD mean better uniformity. Dual impellers help establish better uniformity by effectively distributing flow, hence solids, throughout the vessel. Recent CFD studies have shown reasonably good agreement between measured and calculated solids concentration profiles. 

Velocity and concentration profiles are two important parameters often needed by the operator of slurry handling equipment. Several experimental techniques and mathematical models have been developed to predict these profiles. The aim of this chapter is to give the reader an overall picture of various experimental techniques and models used to measure and predict particle velocity and concentration distributions in slurry pipelines. I begin with a brief discussion of flow behavior in horizontal slurry pipelines, followed by a revision of the important correlations used to predict the critical deposit velocity. In the second part, I discuss various methods for measuring solids concentration in slurry pipelines. In the third part, I summarize methods for measuring bulk and local particle velocity. Finally, I review models for predicting solids concentration profiles in horizontal slurry pipelines. 

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