Impellers, agitation location

Determine the reactor volume required for one reactor and that for two equal-sized reactors in series for 80 percent conversion of A. And if the capital cost of a continuous-flow stirred-tank reactor unit is given by 200,000(17/100)° 6 (where V is reactor volume in m3), the life is 20 years with no salvage value, and power costs 3 cents per kilowatt-hour, determine which system has the economic advantage. Assume that overhead, personnel, and other operating costs, except agitation, are constant. The operating year is 340 days. Each reactor is baffled (with a baffle width to tank diameter of 1/12) and equipped with an impeller whose diameter is one-third the tank diameter. The impeller is a six-bladed turbine having a width-to-diameter ratio of 1 /5. The impeller is located at one-third the liquid depth from the bottom. The tank liquid-depth-to-diameter ratio is unity. 

To design the agitator, the gas density at the impeller location should be used for computing the superficial gas velocity. Because of liquid head, this necessitates a pressure correction. The total liquid level for 10,000 gal in a 12-ft-diameter tank is roughly 12 ft (see Table 12.2). If the impeller is located one-sixth of the liquid level off bottom, as it should be for gas dispersion, the additional static liquid head is 10 ft of water that must be added to the atmospheric pressure (34 ft of water). The pressure correction makes the actual volumetric flow rate of gas QA equal (1950 ft3/min) (34 ft of water)/ (34 + 10 ft of water) = 1507 ft3/min. Flow rate divided by cross-sectional area of tank, that is, 7t(12 ft)2/4 =113 ft2, gives a superficial gas velocity us of (1507 ft3/min)/l 13 ft2 = 13.3 ft/min or 0.22 ft/s (0.067 m/s). 

Two studies have been concerned with measurement of the interfacial area obtained by agitation of liquid-liquid systems. Each of these investigations relied on the use of a photoelectric probe which measured the light transmission of the two-phase dispersion. Vermeulen and co-workers (V2) made measurements in two geometrically similar, baffled vessels of 10- and 20-in. diameter. They used a very simple four-blade paddle-like stirrer, with a tank-to-impeller diameter ratio of about 1.5, and a 0.25 blade-width/impeller-diameter ratio. The impeller was located midway between the top and bottom of the vessel, which had a cover and was run full. Impeller speeds varied from about 100 to 400 r.p.m. A wide variety of liquids was employed. Volume fractions of dispersed phase varied from 10% to 40%. The mean droplet diameters observed ranged from 0.003 to 0.1 cm. The results were correlated with a mean deviation of about 20% by an empirical equation relating the specific interfacial area near the impeller to several system and operating variables as follows ... 

In this section, the flow produced by a classical two-blade impeller is considered. The ratio between the blade height and the impeller diameter is lower for this impeller than in the case of a paddle agitator (W/T = 0.25). The ratio between the impeller diameter and the tank diameter is D/T = 0.7. The impeller is located near mid-height of the tank (C/T = 0.4). 

SpiralTlevator Materials are moved upward by the centrally located spiral-type conveyor in a cylindrical or cone-shaped Nautamix vessel (Fig. 37c and d). Blending occurs by the downward movement at the outer walls of the vessel. The vessel serves the dual purposes of blending and storage. In these mixers the screw impeller actively agitates only a small portion of the mixture and natural circulation is used to ensure all the mixture passes through the impeller zone. In the case of Nautamix, an Archimedian screw lifts powder from the base of a conical hopper while progressing around the hopper wall. 

The models presented correctly predict blend time and reaction product distribution. The reaction model correctly predicts the effects of scale, impeller speed, and feed location. This shows that such models can provide valuable tools for designing chemical reactors. Process problems may be avoided by using CFM early in the design stage. When designing an industrial chemical reactor it is recommended that the values of the model constants are determined on a laboratory scale. The reaction model constants can then be used to optimize the product conversion on the production scale varying agitator speed and feed position. 

Above the critical agitator speed, the active volume rises linearly to unity with r.p.m. This rate of rise is a function of impeller blade size (hence energy input) but is independent of feed location (or vessel geometry). 

Figure 10.4. Agitator flow patterns, (a) Axial or radial impellers without baffles produce vortexes, (b) Offcenter location reduces the vortex, (c) Axial impeller with baffles, (d) Radial impeller with baffles.

The agitator in each stage is provided with two impellers. The impeller that is located at the liquid surface causes surface aeration. It creates turbulence at the liquid surface and generates liquid flow in the downward direction. Because of this impeller action, the oxygen from the gas space is dispersed... 

One measure of the amount of liquid motion in an agitated tank is velocity. However, by the very nature of mixing requirements, liquid velocities must be somewhat random in both direction and magnitude. Since actual velocity is difficult to measure and depends on location in the tank, an artificial, defined velocity called bulk velocity has been found to be a more practical measure of agitation intensity. Bulk velocity is defined as the impeller pumping capacity (volumetric flow rate) divided by the cross-sectional area of the tank. For consistency, the cross-sectional area is based on an equivalent square batch tank diameter. A square batch is one in which the liquid level is equal to the tank diameter. 

A 137.5-in-diameter tank has a cross-sectional area of (jr/4)(137.5 in)2 = 14,849 in2 or 103 ft2, so the required impeller pumping capacity is bulk velocity times cross-sectional area (0.4 ft/s)(103 ft2) = 41.2 ft3/s or 2472 ft3/min (1.17 m3/s). Geometry of the actual tank will be taken into consideration by location and number of impellers after the horsepower and speed of the agitator are determined. 

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