Aeration number

Read aeration number (Na) from Figure 6.7, Chapter 6. 

This method can be easily used to show the logic behind the scale-up from original R D batches to production-scale batches. Although scale-of agitation analysis has its limitations, especially in mixing of suspension, non-Newtonian fluids, and gas dispersions, similar analysis could be applied to these systems, provided that pertinent system variables were used. These variables may include superficial gas velocity, dimensionless aeration numbers for gas systems, and terminal settling velocity for suspensions. 

L T ), and v is the kinematic viscosity ofthe hquid (L" T ). Ihe dimensionless groups include N/v) = Reynolds number (Re) d N /g) = Froude number (Fr) and (Q/N d = aeration number (Na), which is proportional to the ratio of the superficial gas velocity with respect to the tank cross section to the impeller tip speed. 

For gas-liquid systems, the power dissipated by the stirrer at the same stirrer speed N is lower than the corresponding power input for liquid systems due to reduced drag on the impeller. The power of the gassed system PG is related to that of the ungassed system P0 by using the power number NP correlation with the aeration number Y, ... 

FIG. 19-35 Effect of aeration number and stirrer speed on the power number— N increases in order of Nx < N% < < N4. [Adapted from Baldi, Hydrodynamics... 

Na aeration number in stirred tank (= todJuQ), dimensionless... 

The flow rate required for the transition from regimes a to b or b to c is correlated to the Froude number and other system parameters, as shown in Table VI. The flowrate for the a-b transition depends on the direction in which JV is changed, as well as on the reactor scale (Zlokarnik and Judat, 1967). Van t Riet and Smith (1975) showed that the dispersion does not occur if Fr < 0.1. The aeration number for the b-c transition is mainly a function of the Froude number. 

Aeration Numbers for Regime Transitions (Rushton Turbine)... 

The power number Neg depends on the aeration number NA. The aeration number represents the ratio between the gas feed rate that must be handled by the stirrer and a quantity proportional to the delivery rate of the stirrer. The behavior of Neg as a function of the aeration number (varied by changing the stirrer speed) at different gas feed rates is illustrated in Fig. 12. As N increases, the power number first decreases and then rapidly increases. The maximum at very high speeds corresponds to the development of a secondary recirculation loop (Nienow et al., 1977), and the minimum in P0i is very close to the transition between b and c regimes (Sicardi et al., 1982). 

This relation suggests that PJPt is largely influenced by the aeration number. 

Nagata (1975) showed that in aerated suspensions, a significantly higher stirrer speed and thus power consumption per unit volume is required to establish the state of complete suspension. Furthermore, the propeller normally requires a higher stirrer speed for complete suspension than the turbine. Arbiter et al. (1969) reported that drastic sedimentation of suspended particles occurs when the aeration number JVA = QJN d (here Qg is the volumetric gas flow rate) exceeds a critical value. This critical gas flow coincided with the point where the power drawn by the agitator decreased suddenly with a small increase in the gas sparger rate. Thus, an increase in gas... 

In order to achieve simultaneous suspension of solid particles and dispersion of gas, it is necessary to define the state when the gas phase is well dispersed. Nienow (1975) defined this to be coincident with the minimum in Power number, Ne, against the aeration number, 1VA, relationship (see Fig. 12 [Sicardi et al., 1981]). While Chapman et al. (1981) accept this definition, their study also showed that there is some critical particle density (relative to the liquid density) above which particle suspension governs the power necessary to achieve a well-mixed system and below which gas dispersion governs the power requirements. Thus, aeration at the critical stirrer speed for complete suspension of solid particles in nonaerated systems causes partial sedimentation of relatively heavy particles and aids suspension of relatively light particles. Furthermore, there may be a similar (but weaker) effect with particle size. Wiedmann et al. (1980), on the other hand, define the complete state of suspension to be the one where the maximum in the Ne-Ren diagram occurs for a constant gas Reynolds number. 

FIGURE 12.7 Gassed power factor as a function of aeration number. 

Determine impeller size for required power input. The impeller required for the process must draw 7.91 hp per 1000 gal or 79.1 hp for the 10,000-gal batch. This power level must be achieved at the gas flow rate required by the process, which is, Qa = 1507 ft3/min. The power required to operate an agitator impeller for gas dispersion can be much less than the power required for a liquid without gas. The ratio of power with gas to power without P/Po is shown in Fig. 12.7 and is a function of the dimensionless aeration number NAe =Qa/ND3. 

Since impeller diameter is unknown, aeration number and, therefore, gassed power factor cannot be determined however, an estimate for power factor P/P0of 0.4 is usually a good initial estimate. By rearranging the expression for power number, that is, Np = P/(pN3D5), an expression for impeller diameter can be derived. The factor P/ Pf] must be introduced for the effect of gas and a conversion for units makes... 

For the low range of aeration numbers (Na), this corrrelation predicts ratios of Pg/Pu in the range of 0.3 to 0.68, which is lower than one normally expects. Thus, one is advised to use this correlation with a bit of caution. If the gassed power requirement seems somewhat low, a vendor should be consulted. 

Solution One can calculate the aeration number (Na,fl) at which the 6BD impeller is flooded. For the present example, Na,fl = 0.13. The impeller operates at Na = 0.21, which is significantly greater than the aeration number at which the flat-blade turbine is flooded. This confirms the suspicion of the operator that the impeller is flooded. Poor gas dispersion is most likely the cause of the unsatisfactory performance of the reactor. 

MuR Viscosity ratio bulk viscosity/wall viscosity = (ptb/pw) Na Aeration number, Qg/ND ... 

Na,Flood Aeration number at flooding, Qg,Fiood/ND5 Npr Impeller Frounde number, N D/g... 

FIG. 19-35 Effect of aeration number and stirrer speed on the power number— N increases in order of Ni< Ni< N < N4. [Adapted from Baldi, Hydrodynamics and Mass Transfer in SUrred-Slurry Reactors," in Gianetto and Silveston (eds.). Multiphase Chemical Reactors, Hemisphere Publishing Corp., 1986, Fig. 14.8.]... 

Fig. 8 k- Factor of multiple impeller system (Rushton -I- PBT) as a function of aeration number. (View this art in color at h>h>h>. dekker.com.)... 

In the same water system, gas is completely dispersed at transition aeration numbers (A a co) given by the following correlation ... 

The aeration number (A a) is the ratio of gas flow rate to impeller discharge flow and is written as... 

In water, the maximum aeration number at which flooding occurs (A(i,fl) with one of several different impellers is correlated as ... 

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