Mass transfer overall

Overall mass transfer is the transportation of matter through a phase boundary, from one fluid phase into another. 

Resistance to the mass transfer is analogous to resistance to heat transfer in that it may be considered as being divided into individual resistances this will be demonstrated later. The main differences between mass transfer and heat transfer are  

Individual resistances in heat transfer operations may easily be determined by experimentation. In mass transfer operations between two fluid phases, only the total resistance can be found experimentally, and only under complex experimental conditions. During heat transfer the individual resistances are resistance due to convection in fluid 1, heat conduction 

PB Phase boundary (Interfacial area) c Concentration of key component X Space coordinate 

In the case of equilibrium at the phase boundary, which we want to discuss here, with given values for pressure and temperature, the mole fractions yAI and xAl at the phase boundary are linked by the relationship 

The mole fractions yA1 and xAl at the interface are dependent on each other according to the thermodynamic relationship given in (1.212). As gases are only slightly soluble in liquids the mole fraction xAl is normally very small. Then because of Henry s18 law eq. (1.212) can be approximated by the linear relationship 

18Named after William Henry (1775-1836), a factory owner from Manchester, who first put forward this law in 1803. 

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Equation 28 and its liquid-phase equivalent are very general and valid in all situations. Similarly, the overall mass transfer coefficients may be made independent of the effect of bulk fiux through the films and thus nearly concentration independent for straight equilibrium lines ... 

Mass-transfer theory (eq. 17) iadicates that the overall mass-transfer resistance 1 /consists of contributions from each phase, so that the overall HTU is also the sum of two contributions ... 

K a overall mass-transfer coefficient per volume of contacting column ... 

Comparison of Eqs. (5-255) and (5-257) shows that for systems in which the eqmlibrium line is straight, the overall mass transfer coefficients are related to each other by the equation... 

Overall Mass-Transfer Coejficient Tatterson (op. cit.) and Zlokarnik (op. cit.) have summarized the hterature covering overall mass-transfer coefficients. There is much scatter in the experimental data because the presence of surface-ac tive agents and electrolytes have a significant effect on the mass transfer. The correlation of Van t Riet [Ind. Eng Chem. Process Des. Dev., 18(3), 357 (1979)] is recommended ... 

Interfacial Phenomena These can significantly affect overall mass transfer. In fermentation reactors, small quantities of surface-active agents (especially antifoaming agents) can drastically reduce overall oxygen transfer (Aiba et al., op. cit., pp. 153, 154), and in aerobic... 

One cannot quantitatively predict the effect of the various interfacial phenomena thus, these phenomena will not be covered in detail here. The following literature gives a good general review of the effects of interfacial phenomena on mass transfer Goodridge and Robb, Ind. Eng. Chem. Fund., 4, 49 (1965) Calderbank, Chem. Eng. (London), CE 205 (1967) Gal-Or et al., Ind. Eng. Chem., 61(2), 22 (1969) Kintner, Adv. Chem. Eng., 4 (1963) Resnick and Gal-Or, op. cit., p. 295 Valentin, loc. cit. and Elenkov, loc. cit., and Ind. Eng. Chem. Ann. Rev. Mass Transfer, 60(1), 67 (1968) 60(12), 53 (1968) 62(2), 41 (1970). In the following outhne, the effects of the various interfacial phenomena on the factors that influence overall mass transfer are given. Possible effects of interfacial phenomena are tabulated below ... 

D Enhanced diffusivity mvs ft /ft K Overall mass-transfer kmol/(s-m ) (lb-mol)/(h-fF)... 

Overall Resistance With a linear isotherm (R = 1), the overall mass transfer resistance is the sum of intraparticle and extraparticle resistances. Thus, the overall LDF coefficient for use with a particle-side driving force (column 2 in Table 16-12) is ... 

Kqa = Gas film overall mass transfer coefficient, lb mols/hr (fP) (ATM)... 

Overall Mass Transfer Coefficient C02/Na0H System Metal Tower Packings... 

Overall Mass Transfer Coefficient COa/NaOH System ... 

Kp, = Overall mass transfer coefficient, g/m s a = Surface area per unit volume of adsorbent particle, mVm ... 

Equilibrium Considerations - Most of the adsorption data available from the literature are equilibrium data. Equilibrium data are useful in determining the maximum adsorbent loading which can be obtained for a specific adsorbate-adsorbent system under given operating conditions. However, equilibrium data by themselves are insufficient for design of an adsorption system. Overall mass transfer rate data are also necessary. 

The relationships between the local and overall mass transfer coefficients are ... 

The above expression indicates that the number of overall mass transfer units, Nqg, is only controlled by the concentrations of the solute in the inlet and outlet gas streams. 

This form is partieularly appropriate when the gas is of low solubility in the liquid and "liquid film resistanee" eontrols the rate of transfer. More eomplex forms whieh use an overall mass transfer eoeffieient whieh ineludes the effeets of gas film resistanee must be used otherwise. Also, if ehemieal reaetions are involved, they are not rate limiting. The approaeh given here, however, illustrates the required ealeulation steps. The nature of the mixing or agitation primarily affeets the interfaeial area per unit volume, a. The liquid phase mass transfer eoeffieient, kL, is primarily a funetion of the physieal properties of the fluid. The interfaeial 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, dj, whieh is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraetion of the total fluid volume (gas plus liquid) whieh is oeeupied by gas bubbles. 

Whenever die rich and the lean phases are not in equilibrium, an interphase concentration gradient and a mass-transfer driving force develop leading to a net transfer of the solute from the rich phase to the lean phase. A common method of describing the rates of interphase mass transfer involves the use of overall mass-transfer coefficients which are based on the difference between the bulk concentration of the solute in one phase and its equilibrium concentration in the other phase. Suppose that the bulk concentradons of a pollutant in the rich and the lean phases are yi and Xj, respectively. For die case of linear equilibrium, the pollutant concnetration in the lean phase which is in equilibrium with y is given by... 

Let us define two overall mass transfer coefficients one for the rich phase, Ky, and one for the lean phase, Kj,. Hence, the rate of interphase mass transfer for... 

Correlations for estimating overall mass-transfer coefficients can be found in McCabe et al. (1993), Perry and Green (1984), Geankoplis (1983), Henley and Seader (1981), King (1980) and Treybal (1980). 

Overall mass transfer coefficient based on liquid phase, lb mol/ (hr) (ft ) (lb mol/ft ) Overall mass transfer coefficient based on liquid film controlling, lb mol (hr) (ft ) (lb mol/ft3)... 

Given this evaporation rate, the overall mass transfer coefficient may then be calculated from Equation 4-391,... 

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