Mass transfer coefficients in agitated vessels

Mass transfer involving tower packings, which we have considered in the previous section, is our first introduction to systems with complex and highly irregular geometries. The approach we had to take there was to make direct use of experimental data or else convert them by means of some simple empirical rates for use in similarly structured systems. 

Agitated vessels represent yet another example of an unusual and not easily quantifiable geometry. The prominent irregularity here is the shape and size of the impeller and the geometry of its blades. Internal baffles, which are frequently used to enhance transport rates, are an additional unusual feature. 

Agitated vessels find their use in a considerable number of mass transfer operations. At the simplest level, they are employed to dissolve granular or powdered solids into a liquid solvent in preparation for a reaction or other subsequent operations. The reverse process of precipitation or crystallization 

Fundamental work in this area dates to the 1940s and 1950s, and has been refined in subsequent decades. These studies have revealed that mass transfer coefficients in these systems can be correlated by the same combination of Sherwood, Reynolds, and Schmidt mmibers we have encountered in simpler geometries, provided the former two are suitably modified to account for the altered system geometry and operation. These modifications are implemented as follows  

Using these modified dimensionless groups, it has been found possible to correlate a host of experimental data for a wide range of operations. The following correlations, tabulated in Table 5.7, have been found useful in predicting transport coefficients in the continuous phase of the stirred tanks. 

Fxmdamental work in this area dates back to the 1940s and 1950s and has been refined in subsequent decades. These studies revealed that mass transfer 

Illustration 5.7 Dissolution of Granular Solids in an Agitated Vessel 

The assumption made at the outset is that the concentration at the surface of the particles equals the satmation concentration of the solid material, and that the mass transfer is driven by the linear potential (Q - C), where C is the prevailing concentration in the liquid at any particular instant. 

An initial imsteady mass balance over the solid leads to the following expression  

---

Zlokarnik (1978) examined the effect of coalescence on the volumetric mass-transfer coefficient in agitated vessels. 

The double lines in Figure 3.44 represent the Sh number based on the mass transfer coefficient, in the case of a single-particle fall in water, for three different particle densities (Harriot, 1962). This value is considered to be the minimum mass-transfer coefficient in liquid-solid films in agitated vessels. Taking into account the fact that the actual Sh value in an agitated vessel is 1.5 -8 times its minimum value, it is apparent that the mass transfer coefficients are much higher in the case of agitated vessels. 

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. 

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

The mass transfer coefficient is expected to relate gas power per unit volume and gas terminal velocity. Measurement of gas bubble velocity is troublesome in the experimental stage of aeration. Extensive research has been conducted for an explanation of the above correlation. Gas-liquid mass transfer in low viscosity fluids in agitated vessels has been reviewed and summarised as stated in (3.5.1.7)—(3.6.2) 3... 

Acording to Fishwick et al. (2003), the injection of gas in a baffled vessel leads to a decrease in the mass transfer coefficients and this effect becomes more intense at higher gas rates. The significance of gas dispersion is, however, less pronounced at higher agitation speeds. It is also observed that under high agitation speeds in baffled vessels, a considerable amount of ah is dispersed inside the vessel even in the absence of an injected gas. 

This form is particularly appropriate when the gas is of low solubility in the liquid and "liquid film resistance" controls the rate of transfer. More complex forms which use an overall mass transfer coefficient which includes the effects of gas film resistance must be used otherwise. Also, if chemical reactions are involved, they are not rate limiting. The approach given here, however, illustrates the required calculation steps. The nature of the mixing or agitation primarily affects the interfacial area per unit volume, a. The liquid phase mass transfer coefficient, kL, is primarily a function of the physical properties of the fluid. The interfacial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dSM, which is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraction of the total fluid volume (gas plus liquid) which is occupied by gas bubbles. 

For mold pellets and other suspended particles with densities close to that of the continuous phase, the agitation in a stirred mixing vessel creates the dominant force for relative fluid motion between the two phases. The intrinsic gas-liquid mass-transfer coefficient under these conditions is given by Calderbank (1967) as... 

Perez and Sandall (1974) studied the absorption of carbon dioxide in aqueous carbopol solution. The rheological behavior of the solution was described by the power law model with flow behavior indices varying from 0.91 to 0.59. For an agitated vessel with a turbine impeller, the mass-transfer coefficient across the unbroken interface was correlated as... 

The gas-liquid volumetric mass-transfer coefficient for the agitation of power-law fluid in an aerated vessel can be expressed in the form kLaL = f PJV, ug) (Hocker et al, 1981). For the mass transfer in a vessel with an unbroken interface, the relationship Sh = /(Re, Sc) given by Eq. (7.4) is recommended. 

Oyama and Endoh (012) studied the solution of sugar in water in 6.7- and 10.8-in. baffled vessels using paddles and flat-blade turbines. They report a mass-transfer coefficient which was proportional to the cube root of the particle diameter and to the cube root of the impeller power consumption per unit mass of agitated liquid. 

---