Plate columns, mass-transfer coefficients

Stewart, W. S., Heat and Mass Transfer Coefficients for the System Air-Water in a Perforated Plate Column, thesis presented in partial fulfillment of Master s Degree in chemical engineering, Louisiana State University (1958). 

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 ... 

Mass-Transfer Correlations Because of the tremendous im-ortance of mass transfer in chemical engineering, a veiy large num-er of studies have determined mass-transfer coefficients both empirically and theoretically. Some of these studies are summarized in Tables 5-17 to 5-24. Each table is for a specific geometry or type of contactor, starting with flat plates, which have the simplest geometry (Table 5-17) then wetted wall columns (Table 5-18) flow in pipes and ducts (Table 5-19) submerged objects (Table 5-20) drops and... 

On a perforated plate the liquid-side mass-transfer coefficient k a and gas-side mass-transfer coefficient kca, based on the column volume, vary... 

The mass transfer coefficient depends on the flow condition of gas and liquid phases, the interface area is influenced by the geometry of the column internals and local velocity of the two phases. The largest driving force for the mass transfer is the concentration difference when the two phases are uniformly distributed over the entire flow area. This is achieved when a countercurrent flow pattern of the two phases without remixing is reached in a theoretical plate. 

Mobile phase mass-transfer coefficient, CmU A quantity that affects band broadening and thus plate height nonlinear in solvent velocity u and influenced by the diffusion coefficient of the analyte, the particle size of the stationary phase, and the inside diameter of the column. 

Plate efficiency is a function of the rate of mass transfer between liquid and vapor. The prediction of mass-transfer coefficients in sieve trays and their relationship to plate efficiency are discussed in Chap. 21. Some published values of the plate efficiency of a 1.2-m column are shown in Fig. 18.34. This column had sieve trays with 12.7-mm holes and 8.32 percent open area, a 51-mm weir height, and... 

The mobile-phase mass-transfer coefficient (sec Table 26-3) reveals that Cm in liquation 26-23 is directly related to the square of the diameter dp of the particles making up a packing, Because of this, the efficiency of an LC column should improve dramatically as the particle size decreases, lugure 28-2 is an experimental demonstration of this effect, where it is seen that a reduction of particle size from 45 to 6 pm results in a len-fold or more decrease in plate height. Noie that none of the plots in this figure exhibits ihe minimum that is predicted by Equation 26-23, Such minima ate, in fact, observable in I.C (see Figure 26-8a) but usually at flow rates loo low for most practical applications. 

Finite speed of equilibration, inability of solute molecules to truly equilibrate in one theoretical plate, the C term, present in all chromatographic columns. This term is also called the resistance to mass transfer term and, in more contemporary versions, consists of two mass transfer coefficients Cs, where S refers to the stationary phase, and Cm, where M refers to the mobile phase. Equilibrium is established between M and S so slowly that a chromatographic column always operates under nonequilibrium conditions. Thus, analyte molecules at the front of a band are swept ahead before they have time to equilibrate with S and thus be retained. Similarly, equilibrium is not reached at the trailing edge of a band, and molecules are left behind in S by the fast-moving mobile phase (23). 

Values of the mass transfer coefficients and interfacial areas for the more common contactors (packed columns, plate columns, bubble columns, mechanically agitated contactors, and static mixers) are usually known, or can be estimated from correlations published in the literature, or are supplied by the manufacturers. Typical values are given in Table 16.1. 

Sotelo, J.L., Benitez, RJ., Beltran-Heredia, J., and Rodriguez, C. (1994), Gas holdup and mass transfer coefficients in bubble columns. 1. Porous glass-plate diffusers, International Chemical Engineering, 34(1) 82-90. 

On a perforated plate the liquid side mass transfer coefficient kLa and gas side mass transfer coefficient k( a, based on the column volume, vary linearly with the dispersion height. The true liquid- and gas-side mass transfer coefficients and first increase with the dispersion height and then go through a maximum and decrease slightly (123). Sharma and Gupta (124) attribute this to different behavior of the density of dispersion and the average bubble size with increase in gas flowrate, which leads to a phase inversion point. These authors correlate their experimental data for 10 cm i.d. perforated plates without downcomers by the following expressions... 

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