Vessels interfacial area

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. 

Coughlin and von Berg [Chem. Eng. Sci., 21, 3 (1966)]. Continuous heat transfer and extraction of ethylbiityric acid between kerosine and water unbaffled vessel, Pump-Mix design (Fig. 15-28). Interfacial area measured. 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

To apply the mass transfer equation for design, the interfacial area, a, and mass transfer coefficient kL must be calculated. The interfacial area is dependent upon the bubble size and gas hold-up in the mixing vessel as given by ... 

Horizontal vessels as cylinders are generally more suitable for diameters up to about 8 feet than other shapes, or vertical, due in part to the increased interfacial area for interface formation. For a horizontal drum (See Figure 4-12) ... 

This dispersion of the gas passes through several stages depending on the gas feed rate to the underside of the impeller and the horsepower to the impeller, varying from inadequate dispersion at low flow to total gas bubble dispersion throughout the vessel. The open, without disk, radial flow type impeller is the preferred dispersing unit because it requires lower horsepower than the axial flow impeller. The impeller determines the bubble size and interfacial area. 

For a horizontal, cylindrical, decanter vessel, the interfacial area will depend on the position of the interface. 

Falling-film column. A falling-film column (Figure 24.1(d)) is also an empty vessel with liquid, introduced at the top, flowing down the wall as a film to con-tad an upward-flowing gas stream. Ideal flow for each phase is PF. Since neither liquid nor gas is dispersed, the interfacial area developed is relatively small, and gas-liquid contact is relatively inefficient This type is used primarily in the exper-imental determination of mass transfer characteristics, since the interfacial area is w ell defined... 

Table 24.1 Typical values of gas4iquid interfacial area (a,- and a ) for various types of vessels...

The liquid-film mass transfer coefficient may be given as a correlation for kA( (k, in general for species i, or often denoted simply by kL), or for kAta, the product of the mass transfer coefficient and the interfacial area based on vessel volume (often denoted simply as kLa). 

Considering a cylindrical vessel (Figure 1.20) in which one substance A is poured into the bottom and the second B on top, then the boundary surface between the two materials is a minimum. The process of mixing consists of making some of A enter the space occupied by B, and some of B enter the lower section originally filled by A. This may be considered as the diffusion of A across the initial boundary into B, and of B into A. This process will continue until there is a maximum degree of dispersion, and a maximum interfacial area between the two materials. This type of process is somewhat akin to that of diffusion, and tentative use may be made of the relationship given by Fick s law discussed in Volume 1, Chapter 10. This law may be applied as follows. 

The interfacial area, a, was the subject of an investigation by Westerterp et al.(60> though the correlations proposed are complex. Maximum values of a are about 1000 m2/m3. Further work on the interfacial area in agitated vessels has been reviewed and summarised by Sridar and potter 61 who found that the correlation of Calderbank(62) was applicable for most situations. Calderbank proposed that, for pure... 

In these equations, a is the specific interfacial area for a significant degree of surface aeration (m2/m3), I is the agitator power per unit volume of vessel (W/m3), pL is the liquid density, o is the surface tension (N/m), us is the superficial gas velocity (m/s), u0 is the terminal bubble-rise velocity (m/s), N is the impeller speed (Hz), d, is the impeller diameter (m), dt is the tank diameter (m), pi is the liquid viscosity (Ns/m2) and d0 is the Sauter mean bubble diameter defined in Chapter 1, Section 1.2.4. 

Agitated vessels (liquid-solid systems) Below the off-bottom particle suspension state, the total solid-liquid interfacial area is not completely or efficiently utilized. Thus, the mass transfer coefficient strongly depends on the rotational speed below the critical rotational speed needed for complete suspension, and weakly depends on rotational speed above the critical value. With respect to solid-liquid reactions, the rate of the reaction increases only slowly for rotational speed above the critical value for two-phase systems where the sohd-liquid mass transfer controls the whole rate. When the reaction is the ratecontrolling step, the overall rate does not increase at all beyond this critical speed, i.e. when all the surface area is available to reaction. The same holds for gas-liquid-solid systems and the corresponding critical rotational speed. 

Earlier studies in mass transfer between the gas-liquid phase reported the volumetric mass-transfer coefficient kLa. Since kLa is the combination of two experimental parameters, mass-transfer coefficient and mterfacial area, it is difficult to identify which parameter is responsible for the change of kLa when we change the operating condition of a fermenter. Calderbank and Moo-Young (1961) separated kta by measuring interfacial area and correlated mass-transfer coefficients in gas-liquid dispersions in mixing vessels, and sieve and sintered plate column, as follows ... 

---