Radial profile, nonuniform

Radial profile Uniform and nonuniform (radial and corner peaking)... 

Figure 33 Nonuniform radial profiles of concentration determined experimentally in CFB reactors (a) concentration of ozone undergoing decomposition in 0.25mdia x 10.5m tall riser (Ouyang et al., 1995a) (b) concentration of NOj. in 0.15 X 0.15m X 7.3m CFB pilot scale combustor (Brereton et al., 1995).

Preliminary residence time distribution studies should be conducted on the reactor to test this assumption. Although in many cases it may be desirable to increase the radial aspect ratio (possibly by crushing the catalyst), this may be difficult with highly exothermic solid-catalyzed reactions that can lead to excessive temperature excursions near the center of the bed. Carberry (1976) recommends reducing the radial aspect ratio to minimize these temperature gradients. If the velocity profile in the reactor is significantly nonuniform, the mathematical model developed here allows predictive equations such as those by Fahien and Stankovic (1979) to be easily incorporated. 

As opposed to the relatively uniform bed structure in dense-phase fluidization, the radial and axial distributions of voidage, particle velocity, and gas velocity in the circulating fluidized bed are very nonuniform (see Chapter 10) as a result the profile for the heat transfer coefficient in the circulating fluidized bed is nonuniform. 

Fig. 28 shows growth under base conditions, but at a resist wall angle of 70 °. In this case, there is an enduring basis for radially enhanced diffusion near the sides of the feature, since the electrode profile forms an obtuse angle with the resist wall. Nonuniformity increases fairly steadily during growth and reaches 8 percent at... 

The present model could be refined by introducing a velocity profile. This was done by Valstar [128], who used the velocity profiles published by Schwartz and Smith [8S] that exhibit a maximum at 1.5 dp of the wall, and also by Lerou and Froment [144]. The latter authors concluded from a simulation of experimental radial temperature profiles that a radial velocity profile inversely proportional to the radial porosity profile led to the b t fit. Such a radial velocity profile exhibits more than one peak. It follows from these studies that the influence of radial nonuniformities in the velocity profile are worthwhile accounting for in the simulation of severe operating conditions. Progress in this field will require more extensive basic knowledge of the packing pattern and hydrodynamics of fixed beds. 

Vapor nonuniformity may be troublesome with those structured pa ngs that permit substantial radial spread only parallel to their sheets (155). The orientation of structured packing sheets usually alters every 8 to 12 in of bed depth, and the changes of orientation mitigate this nonuniformity. However, the disturbance created to the composition profile may linger for a greater depth. 

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. 

Axial dispersion and wall effects in narrow fixed beds with aspect ratios < 10 were investigated, both by classical methods and by NMR imaging." The residence time distribution (RTD) in the center and at the wall was measured by using water/NaCl-soln. as tracer, and subsequently compared with radial velocity profiles based on NMR imaging. The effects of the aspect ratio and particle Reynolds number on dispersion and on the degree of nonuniformity of the velocity profile were studied. The NMR results are consistent with the RTD and also with literature data of numerical simulations. For low aspect ratios, dispersion/wall effects have a strong effect on the reactor behavior, above all, in cases where a low effluent concentration is essential, as proven by breakthrough experiments with the reaction of H2S with ZnO. 

---