Power stirred vessels

Stirred Vessels Gases may be dispersed in hquids by spargers or nozzles and redispersed by packing or trays. More intensive dispersion and redispersion is obtained by mechanical agitation. At the same time, the agitation will improve heat transfer and will keep catalyst particles in suspension if necessaiy. Power inputs of 0.6 to 2.0 kW/m (3.05 to 10.15 np/1,000 gal) are suitable. 

From a practical point of view, power consumption is perhaps the most important parameter in the design of stirred vessels. Because of the very different flow patterns and mixing mechanisms involved, it is convenient to consider power consumption in low and high viscosity systems separately. 

Considering a stirred vessel in which a Newtonian liquid of viscosity p, and density p is agitated by an impeller of diameter D rotating at a speed N the tank diameter is DT, and the other dimensions are as shown in Figure 7.5, then, the functional dependence of the power input to the liquid P on the independent variables (fx, p, N, D, DT, g, other geometric dimensions) may be expressed as ... 

The power input in stirred tanks can be calculated using the equation P = Ne pnM if the Newton number Ne, which at present still has to be determined by empirical means, is known. For stirred vessels with full reinforcement (bafQes, coils, see e.g. [20]), the only bioreactors of interest, this is a constant in the turbulent flow range Re = nd /v> 5000-10000, and in the non-aerated condition depends only on geometry (see e.g. [20]). In the aerated condition the Newton number is also influenced by the Froude number Fr = n d/g and the gas throughput number Q = q/nd (see e.g. [21-23]). 

Fig. 10. Comparison of stirred vessels with and without baffles Reference floe diameter dpv in dependency on specific impeller power P/V H/D = 1 D = 0.4 m...

Fig. 18. Comparison of results from various particle systems for stirred vessel with baffles and bubble columns Activity a/ao of Acylase resin after t = 300 h, equilibrium drop diameter dg of silicon oil-water-surfactant emulsion and reference floe diameter dpv of floe system in dependency on specific power P/V H/D = 1 D = 0.15 m 0.4 m...

Much higher shear forces than in stirred vessels can arise if the particles move into the gas-liquid boundary layer. For the roughly estimation of stress in bubble columns the Eq. (29) with the compression power, Eq. (10), can be used. The constant G is dependent on the particle system. The comparison of results of bubble columns with those from stirred vessel leads to G = > 1.35 for the floccular particle systems (see Sect. 6.3.6, Fig. 17) and for a water/kerosene emulsion (see Yoshida and Yamada [73]) to G =2.3. The value for the floe system was found mainly for hole gas distributors with hole diameters of dL = 0.2-2 mm, opening area AJA = dJ DY = (0.9... 80) 10 and filled heights of H = 0.4-2.1 m (see Fig. 15). 

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

First of all, the increased computer power makes it possible to switch to transient simulations and to increase spatial resolution. One no longer has to be content with steady flow simulations on relatively coarse grids comprising 104-105 nodes. Full-scale Large Eddy Simulations (LES) on fine grids of 106—107 nodes currently belong to the possibilities and deliver realistic reproductions of transient flow and transport phenomena. Comparisons with quantitative experimental data have increased the confidence in LES. The present review stresses that this does not only apply to the hydrodynamics but relates to the physical operations and chemical processes carried out in stirred vessels as well. Examples of LES-based simulations of such operations and processes are due to Flollander et al. (2001a,b, 2003), Venneker et al. (2002), Van Vliet et al. (2005, 2006), and Flartmann et al. (2006). 

An example rather than linking average bubble size to just or essentially the (overall) power input of a particular vessel-impeller combination, dedicated CFD (preferably DNS and LES) allows for studying ( tracking ) the response of bubble size to local and spatial variations in the turbulence levels in a stirred vessel. In this way, the validity of certain modeling assumptions may be affirmed or disproved. Particularly, effects of spatial variations in e which... 

In Figure 11.2 a schematic view of a stirred vessel is given. The vessel is cyhndrical with a height (m) and a diameter T (m). Usually is equal to or greater than 2 T. It is equipped with a stirrer in the lower compartment. TTiis stirrer is mounted near the bottom, usually at a distance equal to the stirrer diameter. At a lower position the stirrer and bottom interact, leading to a decrease in power consumption. At a higher position hquid circulation problems can occur because, at increased gas flow rate in case of aeration, the bubbles will not be recirculated in the lower compartment. Sometimes the upper compartment (s) are also equipped with a stirrer. The vessel is equipped with baffles to prevent rotation of the contents as a whole. For aeration an air sparger is mounted below the stirrer. For mass transfer... 

It is decided to model a full-scale prototype, unbaffled, stirred vessel with a one-tenth scale model. The liquid in the prototype has a kinematic viscosity, v. of 10 7 m2 s As we have seen above, power number is a function of both Reynolds number and Froude number for unbaffled vessels. To ensure power number similarity, we need to ensure both Reynolds number and Froude number are similar from prototype to model. 

Stirring vessels. Upon the examination of different stirring operations it was indeed found that the intensively formulated process parameter P/V represented the pertinent scale-up criterion only if the stirring power has to be dissipated in the volume as evenly as possible (micro-mixing, isotropic turbulence). Examples of this are the dispersion of a gas in a liquid or the dispersion of immiscible liquids s. [22]. 

Hydrodynamics of slurry reactors include the minimum gas velocity or power input to just suspend the particles (or to fully homogeneously suspend the particles), bubble dynamics and the holdup fractions of gas, solids and liquid phases. A complicating problem is the large variety in reactor types (sec Fig. I) and the fact that most correlations are of an empirical nature. We will therefore focus on sparged slurry columns and slurries in stirred vessels. 

In recent years attempts have been made to improve the gas-liquid mass transfer by changing the design of the mechanically agitated vessel. Mann et al. (1989) evaluated the use of horizontal baffles mounted near the gas-liquid surface. Horizontal baffles prevent vortex formation, generate less shear than standard baffles, increase gas holdup, and improve gas-liquid mass transfer. The latter two results are due to the rotational flow below the baffles, which causes gas bubbles to move upward in a spiral trajectory and induces surface aeration. For a 12-inch i.d. and 18-inch-tall stirred vessel, they showed kLat to be improved by a factor of 1.6 to 2.3 with 30 to 50% lower agitation power compared to the standard vessel. 

Nienow, A.W. Wisdom, D.J. Middleton, J.C. The effect of scale and geometry on flooding, recirculation and power in gassed stirred vessels. 

Geisler R.K., Buurman C., Mersmann A.B., Scale-up of the necessary power input in stirred vessels... 

Heuven van J.W., Beek W.J., Power input, drop size and minimum stirrer speed for liquid-liquid dispersions in stirred vessels, Proc. Int. Solvent Extr. Conf. (1977) 1, p. 70-81... 

In practice, the Reynolds number must first be determined to obtain the power number. The impeller Reynolds number is defined for stirred vessels and given by... 

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