Power solid-liquid agitated systems

G. Highly agitated systems solid particles, drops, and bubbles continuous phase coefficient [E] Use arithmetic concentration difference. Use when gravitational forces overcome by agitation. Up to 60% deviation. Correlation prediction is low (Ref. 118). (PA, ar.k) = power dissipated by agitator per unit volume liquid. [79][83]p.231 [91] p. 452... 

Loiseau et al. (1977) found that their data for nonfoaming systems agreed well with Eq. (3.3). Calderbank (1958), Hassan and Robinson (1977), and Luong and Volesky (1979) have also proposed correlations for power consumption in gas-liquid systems. Nagata (1975) suggested that power consumption for agitated slurries can be reasonably predicted from these correlations by the correction factor psi/pL, where psl is the density of the slurry. Power consumption for a gas-liquid-solid system has also been studied by Wiedmann et al. (1980). They examined the influence of gas velocity, solid loading, type of stirrer, and position of the stirrer blades on power consumption plots of power numbers vs. Reynolds numbers for propeller and turbine type impellers proposed by them are shown in Fig. 13. 

These results show that in solid-liquid systems increases only modestly with power dissipation. For example, a 20% increase in N increases P by 73%, but by only 12%. In conclusion, at agitation speeds below Njs, increases significantly with AT (as shown in Fig. 9), primarily because the solids exposed surface area increases with N, as more particles become suspended.f Above Njs, the value of a, = AjVi is constant and increases only modestly with N [Eqs. (15), (16), and (18)]. In many cases, operating slightly above Njs is economically optimal. 

The Kolmogoroff theory can account for the increase in mass transfer rate with increasing system turbulence and power input, but it does not take into consideration the important effects of the system physical properties. The weakness of the slip velocity theory is the fact that the relationship between terminal velocity and the actual slip velocity in a turbulent system is really unknown. Nevertheless, on balance, the slip velocity theory appears to be the more successful for solid-liquid mass transfer in agitated vessels. 

In this chapter, solid/liquid systems are treated, where the particle size and the density difference between both phases are large enough and at the same time the liquid viscosity is low enough. Due to gravitation and presumably also due to inertial forces generated by the flow scheme in those systems, both phases tend to separate. The power needed to lift the particles off the bottom and keep them homogeneously suspended has to be introduced by the agitator. 

Gas holdup is an important hydrodynamic parameter in stirred reactors, because it determines the gas-liquid interfacial area and hence the mass transfer rate. Several studies on gas holdup in agitated gas-liquid systems have been reported, and a number of correlations have been proposed. These are summarized in Table VIII. For a slurry system, only a few studies have been reported (Kurten and Zehner, 1979 Wiedmann et al, 1980). In general, the gas holdup depends on superficial gas velocity, power consumption, surface tension and viscosity of liquids, and the solid concentration. The dependence of gas holdup on gas velocity, power consumption, and surface tension of the liquid can be described as... 

For a conventional mechanically agitated biological reactor, the information provided for aqueous gas-liquid and gas-liquid-solid systems in Sections II, III, and VII is applicable here. For power consumption, the most noteworthy works are those by Hughmark (1980) (see Eqs. (6.15) and (6.16)) and Schiigerl (1981). For gas-liquid mass transfer, the relationship kLaL = (P/V, ug) is applicable for biological systems. The relationships (6.19) and (6.20) are also valuable, and their use is recommended. The most generalized relation for kLaL is provided by Eq. (6.18). The intrinsic gas-liquid mass transfer coefficient is best estimated by Eq. (6.23). For liquid-solid mass transfer, the use of the study by Calderbank and Moo-Young (1961) (Eqs. (6.24)-(6.26)) is recommended. For viscous fluids, Eq. (6.27) should be used. 

Hirsekorn and Miller (H2) made visual qualitative observations of the suspension of solids by paddle agitation in very viscous liquids (to about 50,000 cp.). For low impeller Reynolds numbers (about 10) in geometrically similar systems (6-, 12-, 18-in. vessels) the major factor in effecting particle suspension appeared to be power input per unit volume. In any given case the power required for complete suspension of all the particles was affected by system geometry and the settling velocity of the solids. No detailed correlation of the observations was presented. 

Slow sedimentation of particles will occur, for example, in an activated sludge or in fine particle catalyst suspensions. For those lands of systems, a homt eneous distribution of solids is characteristic. Here, the liftoff from the vessel bottom as well as the state of a homogeneous suspension can be achieved with a comparably low power input or only slight movement of the liquid. On the other hand, at higher solids concentrations a pseudoplastic flow characteristic of the suspension can occur. As an example, concentrations of only 6% of fibrous material - typically known from paper industry - can lead to this non-Newtonian behavior Frequently observed in suspensions with high solids concentrations is a Bingham plastic behavior. In this case, if a certain amount of shear is not introduced by agitation, the system behaves like an elastic solid body or a gel. 

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