Agitated vessel:

It will be useful first to establish the characteristics of these vessels when used simply for stirring single-phase liquids, as in blending, for example. Applications to particular mass-transfer operations will be considered separately later. 

Typical agitated vessels are vertical circular cylinders rectangular tanks are unusual, althou not uncommon in certain liquid-extraction applications. The liquids are usually maintained at a depth of one to two tank diameters. 

There are literally scores of designs. The discussion here is limited to the most popular, as shown in Fig. 6.3. These are usually mounted on an axially arranged, motor-driven shaft, as in Fig. 6.4. In the smaller sizes, particularly, the impeller and shaft may enter the vessel at an angle to the vessel axis, with the motor drive clamped to the rim of the vessel. 

Typical flow patterns for single-phase Newtonian liquids of moderate viscosity are shown in Fig. 6.4. For an axially located impeller operating at low speeds in 

Closed tanks, operated full, with no gas-liquid surface [70]. This is especially convenient for cases where the liquid flows continuously through the vessel, as in Fig. 6.4c. A circular flow pattern is superimposed upon the axial flow directed toward the center of the impeller. The arrangement is not practical, of course, for gas-liquid contact, where baffles should be used. 

Sensible heat transfer coefficients for agitated vessels can be predicted using the following correlation  

Because of the higher heat transfer rates, dropwise condensation would be preferred to film condensation, but it is extremely difficult to maintain since most surfaces become wetted after exposure to a condensing vapor over an extended period of time. Various surface coatings and vapor additives have been used in attempts to maintain dropwise condensation, but these methods have not met with general success to date, 

Under normal conditions a continuous fiow of liquid is formed over the surface and the condensate flows downward under the influence of gravity. Unless the velocity is very high or the liquid film relatively thick, the motion of the condensate is laminar and heat is transferred from the vapor-liquid interface to the surface merely by conduction. The rate of heat flow depends on the rate at which vapor is condensed and the rate at which the condensate is removed. On a vertical surface the film thickness increases continuously from top to bottom. As the surface is inclined from the vertical, the drainage rate decreases and the liquid film becomes thicker. This causes a decrease in the rate of heat transfer. 

However, even at relatively low film Reynolds numbers, the assumption that the condensate layer is in laminar flow is open to some question. Experiments have shown that the surface of the film exhibits considerable waviness (turbulence). This waviness causes increased heat transfer rates. Better heat transfer correlations for vertical condensation were presented by Dukler in 1960. He obtained velocity distributions in the liquid film as a function of the interfacial shear (due to the vapor velocity) and film thickness. From the integration of the velocity and temperature profiles, liquid film thickness and point heat-transfer coefficients were computed. According to the Dukler development, there is no 

Vertical Tubes Heat transfer coefficients for condensation on vertical tubes may be calculated from laminar theory as given below  

The values of constant C and the indices a, b and c depend on the type of agitator, the use of baffles, and whether the transfer is to the vessel wall or to coils. Some typical correlations are given below. 

Baffles will normally be used in most applications. 

Flat blade paddle, baffled or unbaffled vessel, transfer to vessel wall, Re 4000  

N = agitator, speed, rps (revolutions per second) p = liquid density, kg/m kf — liquid thermal conductivity, Wm °C  

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The pot extractor is a batch extraction plant in which extraction and solvent recovery from the exhausted soHds can be carried out in a single vessel. These extractors are normally agitated vessels having capacities in the range of 2 to 10 m, beyond which the battery system becomes a preferred technical alternative. 

This correlation is valid when turbulent conditions exist in an agitated vessel, drop diameter is significantly bigger than the Kohnogoroff eddy length, and at low dispersed phase holdup. The most commonly reported correlation is based on the Weber number ... 

Framing. The framed bar process is by far the oldest and the most straightforward process utilized in the production of bar soaps. The wet base soap is pumped into a heated, agitated vessel commonly referred to as a cmtcher. The minor ingredients used in soap bars such as fragrance or preservative are added to the wet soap in the cmtcher or injected in-line after reduction of product stream temperature. The hot mixture is then pumped into molds and allowed to cool. 

The mbber is then separated from its solvent by steam stripping. The viscous cement is pumped into a violently agitated vessel partly full of boiling water. The hexane flashes off and, together with water vapor, passes overhead to a condenser and to a decanter for recovery and reuse after drying. Residual unpolymerized ethylene and propylene appear at the hexane condenser as noncondensibles, and are recovered for reuse after drying. The polymer, freed from its carrier solvent, falls into the water in the form of cmmb. 

A. Solid particles suspended in agitated vessel containing vertical baffles, continuous phase coefficient -2 + 0.6Wi f,.Wi D Replace Osi p with Vj = terminal velocity. Calculate Stokes law terminal velocity [S] Use log mean concentration difference. Modified Frossling equation K, -< T.d,P. [97] [146] p.220... 

Agitated vessel Complete mixing Integral Liquid Absorption... 

Foam Production This is important in froth-flotation separations in the manufac ture of cellular elastomers, plastics, and glass and in certain special apphcations (e.g., food products, fire extinguishers). Unwanted foam can occur in process columns, in agitated vessels, and in reactors in which a gaseous product is formed it must be avoided, destroyed, or controlled. Berkman and Egloff (Emulsions and Foams, Reinhold, New York, 1941, pp. 112-152) have mentioned that foam is produced only in systems possessing the proper combination of interfacial tension, viscosity, volatihty, and concentration of solute or suspended solids. From the standpoint of gas comminution, foam production requires the creation of small biibbles in a hquid capable of sustaining foam. 

The difference between the curves for pure water and seawater again illustrates the significance of small concentrations of solute with respecl to bubble behavior. In commercial bubble columns and agitated vessels coalescence and breakup are so rapid and violent that the rise velocity of a single bubble is meaningless. The average rise velocity can, however, be readily calculated from holdup correlations that will be given later. 

The choice of a bubble column or an agitated vessel depends primarily on the solubihty of the gas in the liquid, the corrosiveness of the liquid (often a gas compressor can be made of inexpensive material, whereas a mechanical agitator may have to be made of exotic, expensive materials), and the rate of chemical reac tion as compared with the mass-transfer rate. Bubble columns and agitated vessels are seldom used for gas absorption except in chemical reac tors. As a general rule. 

Mass Transfer Mass transfer in plate and packed gas-liquid contactors has been covered earHer in this subsection. Attention nere will be limited to deep-bed contactors (bubble columns and agitated vessels). Theory underlying mass transfer between phases is discussed in Sec. 5 of this handbook. 

Gas Holdttp in Agitated Vessels Sensei et al. (op. cit.) have also developed the following correlation for six-bladed disk-type impellers ... 

Interfacial Area This consideration in agitated vessels has been reviewed and summarized by Tatterson (op. cit.). Predictive methods for interfacial area are not presented here because correlations are given for the overall volumetric mass transfer coefficient liquid phase controlhng mass transfer. 

An equihbrium, or theoretical, stage in liquid-liquid extraction as defined earlier is routinely utilized in laboratory procedures. A feed solution is contacted with an immiscible solvent to remove one or more of the solutes from the feed. This can be carried out in a separating funnel, or, preferably, in an agitated vessel that can produce droplets of about 1 mm in diameter. After agitation has stopped and the phases separate, the two clear liquid layers are isolated by decantation. 

Measurements simply of the extent of extrac tion in an agitated vessel lead to the overall Volumetric mass-transfer coefficients, Kca, or... 

Scale-Up of Mixers For the details associated with the design and scale-up of agitated vessels, the reader is referred to Section 18 which covers this topic in great detail. The intention here is to provide only some of the generalprinciples involved which have particular apphcation to liquid-hquid extraction. 

Mixing in Agitated Vessels Agitated vessels may frequently be used for either batch or continuous service and for the latter may be sized to provide any holding time desired. They are useful for liquids of any viscosity up to 750 Pa s (750,000 cP), although in contacting two liquids for reaction or extraction purposes viscosities in excess of 0.1 Pa s (100 cP) are only rarely encountered. 

The following summary of operating characteristics of mechanically agitated vessels is confined to the data available on liquid-liquid contacting. 

A wide variety of configurations exists for coils in agitated vessels. Correlations of data for heat transfer to helical coils have been of two forms, of which the following are representative ... 

The hold-up and bubble diameter in mechanically agitated vessels are given by the following empirical expressions ... 

A common process task involves heating a slurry by pumping it through a well-stirred tank. It is useful to know the temperature profile of the slurry in the agitated vessel. This information can be used to optimize the heat transfer process by performing simple sensitivity studies with the formulas presented below. Defining the inlet temperature of the slurry as T, and the temperature of the outer surface of the steam coil as U then by a macroscopic mass and energy balance for the system, a simplified calculation method is developed. 

This chapter reviews the various types of impellers, die flow patterns generated by diese agitators, correlation of die dimensionless parameters (i.e., Reynolds number, Froude number, and Power number), scale-up of mixers, heat transfer coefficients of jacketed agitated vessels, and die time required for heating or cooling diese vessels. 

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