Radial gas velocity profiles

Figure 29. Calculated axial and radial gas velocity profiles for Run GJ18.

Fig. 30. Effect of average voidage on radial gas velocity profile (after Zhang, 1990).

Figure 1. Radial gas velocity profiles Data from Van Breugel"squares, Gs 390 kg/(m. s)", "triangles, Gs kg/(m, s)". Solid lines are computed with the engineering model for two-phase flow (Nieuwland et al. ") ... 

HYDRODYNAMIC MODELING, 278 Radial Gas Velocity Profiles, 278 Gas Mixing, 280 Radial and Axial Dispersion, 281 Core-Annular Flow, 284 Contact Efficiency, 285... 

The behavior of the gas phase is, however, extremely important, not only for design and scale-up, but also for reactor optimization. The radial gas velocity profile affects gas-particle backmixing, influences the radial solids volume fraction distribution, and solids velocity profile, which, in turn, regulates the rates of chemical reaction, and heat and mass transfer. 

Yang el al. developed Pitot-static tube probes to measure radial gas velocity profiles at different heights in their riser [68]. They encased 0.5 mm ID hypodermic needles in a 5 mm OD tube. The static tube was sealed at the tip, and two 0.5 mm holes were drilled perpendicular to the planes of the tube 10 mm from the tip. The tip of the impact tube was flush with the surface. Using a standard equation for Pitot static tubes gives the local velocity. 

In this chapter, we propose a simple expression for the radial gas velocity profile... 

In summary, a single model has not been developed that can fully characterize riser gas phase hydrodynamics. The studies indicate that under dense phase conditions, typical of commercial FCC riser operation, a simple axial dispersion model may be adequate to characterize gas mixing. Under dilute conditions, a two-phase core-annular model is a good first approximation to the flow structure. However, both radial dispersion and radial gas velocity profiles must be accounted for to provide a realistic and reliable interpretation. The model suggested by Martin et al. should be further developed and applied to risers of different geometry operating with different powders [83]. However, contact efficiency may provide the simplest means from which scale-up criteria can be developed. 

Figure 11 Radial gas velocity profiles in a 50.8 mm and 101.6 mm diameter bed. (Adapted from Schwarz and Smith, 1953.)...

The flow configuration is oriented upward so that the buoyancy effect on the stagnation-flow field is diminished. This configuration provides a stagnation-flow field with a radially uniform velocity profile at the inlet. Gas fines are also heated to prevent the condensation of liquids. The gases are exhausted through an annular pipe and burned in a Bunsen burner which is also housed in the reactor. 

Experimental data for gas velocity profiles in high-den-sity risers are very limited. Radial profiles of the gas... 

Gas exchange between the jet and the outside emulsion phase was studied by tracer gas injection and by integration of gas velocity profiles in the jet at various heights above the jet nozzle in a 28.6 cm diameter bed with a 3.5 cm jet using polyethylene beads as bed material (Yang et al., 1984a). The concentration profiles obtained at different elevations were found to be approximately similar if the local tracer concentration is normalized with the maximum tracer concentration at the axis, C/Cm, and plotted against a normalized radial distance, r/(ri/2)c, where (ri/2)( is the radial position where the tracer concentration is just half the maximum tracer concentration at the axis. Thus in a permanent flamelike jet in a fluidized bed, not only the velocity profiles in the jet but also the gas concentration profiles are similar. 

Clearly, there is a need for complete mapping of liquid and gas velocities and turbulence intensities in bubble columns. Until recently only data of Hills (1974) reported liquid time averaged velocities and radial gas holdup profiles taken under identical operating conditions. Yao et al. (1990) present in addition to such data also gas velocity and turbulence intensity profiles. Some data on radial holdup distribution and axial liquid velocity in industrial size columns were presented by Kojima et al. (1980) and Koideetal. (1979). 

Radial density gradients in FCC and other large-diameter pneumatic transfer risers reflect gas—soHd maldistributions and reduce product yields. Cold-flow units are used to measure the transverse catalyst profiles as functions of gas velocity, catalyst flux, and inlet design. Impacts of measured flow distributions have been evaluated using a simple four lump kinetic model and assuming dispersed catalyst clusters where all the reactions are assumed to occur coupled with a continuous gas phase. A 3 wt % conversion advantage is determined for injection feed around the riser circumference as compared with an axial injection design (28). 

The bubble size distribution is closely related to the hydrodynamics and mass transfer behavior. Therefore, the gas distributor should be properly designed to give a good performance of distributing gas bubbles. Lin et al. [21] studied the influence of different gas distributor, i.e., porous sinter-plate (case 1) and perforated plate (case 2) in an external-loop ALR. Figure 3 compares the bubble sizes in the two cases. The bubble sizes are much smaller in case 1 than in case 2, indicating a better distribution performance of the porous sinter-plate. Their results also show the radial profile of the gas holdup in case 1 is much flatter than that in case 2 at the superficial gas velocities in their work. 

Figure 3 shows the radial profile of the gas holdup in the riser with increasing superficial gas velocity under different solid holdups. The gas holdup increases with increasing superficial gas velocity at the different solid holdups. At a low superficial gas velocity, the liquid velocity... 

As noted earlier, air-velocity profiles during inhalation and exhalation are approximately uniform and partially developed or fully developed, depending on the airway generation, tidal volume, and respiration rate. Similarly, the concentration profiles of the pollutant in the airway lumen may be approximated by uniform partially developed or fully developed concentration profiles in rigid cylindrical tubes. In each airway, the simultaneous action of convection, axial diffusion, and radial diffusion determines a differential mass-balance equation. The gas-concentration profiles are obtained from this equation with appropriate boundary conditions. The flux or transfer rate of the gas to the mucus boundary and axially down the airway can be calculated from these concentration gradients. In a simpler approach, fixed velocity and concentration profiles are assumed, and separate mass balances can be written directly for convection, axial diffusion, and radial diffusion. The latter technique was applied by McJilton et al. 

Fig. 8 shows the time and azimuthally averaged radial liquid saturation profiles at varying superficial gas and liquid velocities at the middle axial position (2.5D). The figure shows that liquid saturation is nearly flat, which suggests a fair uniformity of liquid distribution. Moreover, with increasing liquid velocities, liquid saturation increases. Similar trends were obtained at all scan heights. 

Fig. 6 presents the experimental results on the gas holdup profiles with and without the internal at the axial position of 74 cm for different superficial gas velocities. The internal causes extra flow resistance, which in turn decreases the liquid circulation velocity and increases gas holdup [5]. In addition, the experimental results show that the radial profiles of the local gas holdup with an internal are flatter than those without the internal. Therefore, a properly designed internal can have dual function of increasing the gas holdup and improving its radial profile. 

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