Dispersion number, vessel

Swaroop et al. [Powder Technology, 28, 253-260 (Mar.-Apr. 1981)] found that the material holdup is higher and the vessel dispersion number Dl/L (see subsection on Continuous Mill Simulation) is lower in the rod mill than in the ball mill under identical dimensionless conditions. This indicates that the known narrow-product-size distribution from rod mills is partly due to less mixing in the rod mill, in addition to different breakage kinetics. 

On the assumption that the closed vessel of Example 11.1, Chapter 11, is well represented by the dispersion model, calculate the vessel dispersion number D/uL. The C versus t tracer response of this vessel is... 

Find the vessel dispersion number of this system. 

Find the vessel dispersion number in a fixed-bed reactor packed with 0.625-cm catalyst pellets. For this purpose tracer experiments are run in equipment shown in Fig. E13.3. 

RTD studies were carried out by Jagadeesh and Satyanarayana (lEC/PDD 11 520, 1972) in a tubular reactor (L = 1.21 m, 35 mm ID). A squirt of NaCl solution (5 N) was rapidly injected at the reactor entrance, and mixing cup measurements were taken at the exit. From the following results calculate the vessel dispersion number also the fraction of reactor volume taken up by the baffles. 

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... 

The dimensionless group D KuL) is called the vessel dispersion number, and the reciprocal value is called the Bodenstdn number Bo, which can be used in place of Dax as the parameter for axial dispersion and represents the ratio of convective flux to diffusive (dispersed) flux. 

Bodenstein number Bo —u LjD with Dax = axial dispersion coefficient Reciprocal of vessel Dispersion number... 

Figure 6. Plot of pseudo vessel dispersion number (D/UgL) for axial mixing versus total pressure drop in a recirculating bed with two types of exits. (D = axial dispersion coefficient, Ug = gas velocity, L = column length), (Brereton et al, 1988).

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