Prediction of Mass Transfer Coefficients

As mentioned in Section 11.1.2, fundamental theory is insufficient to predict mass transfer coefficients from first principles. However, existing results do provide a framework for interpreting and sometimes extrapolating experimental results. 

Surface Renewal Theory. The film model for interphase mass transfer envisions a stagnant film of liquid adjacent to the interface. A similar film may also exist on the gas side. These h5q othetical films act like membranes and cause diffu-sional resistances to mass transfer. The concentration on the gas side of the liquid film is a that on the bulk liquid side is af, and concentrations within the film are governed by one-dimensional, steady-state diffusion  

Equation (11.36) gives the central result of film theory and, as is discussed in any good text on mass transfer, happens to be wrong. Experimental measurements show that k, is proportional to rather than to 3 a, at least when the liquid phase is turbulent. 

Two rather similar models have been devised to remedy the problems of simple film theory. Both the penetration theory of Higbie and the surface renewal theory of Danckwerts replace the idea of steady-state diffusion across a film with transient diffusion into a semi-inhnite medium. We give here a brief account of surface renewal theory. 

Surface renewal theory envisions a continuous exchange of material between the bulk fluid and the interface. Eddy diffusion brings material of uniform composition ai to the interface and exposes it to the gas phase for a period of time t. The exposed fluid is then replaced with fresh fluid. Diffusion during the exposure 

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Experimental Mass Transfer Coefficients. Hundreds of papers have been pubHshed reporting mass transfer coefficients in packed columns. For some simple systems which have been studied quite extensively, mass transfer data may be obtained directiy from the Hterature (6). The situation with respect to the prediction of mass transfer coefficients for new systems is stiU poor. Despite the wealth of experimental and theoretical studies, no comprehensive theory has been developed, and most generalizations are based on empirical or semiempitical equations. 

Since the available correlations for prediction of mass transfer coefficients in trickle-beds do not lead to accurate... 

Correlation of Bravo, Rocha, and Fair for Structured Packings Bravo et al. (1985, 1992) developed correlations for the prediction of mass transfer coefficients for structured packing with the geometry shown in Figure 12.9. Bravo et al. (1985) use the correlation of Johnstone and Pigford (1942) to estimate the Sherwood (Shj/) number for the vapor phase... 

Danckwerts8 reasoned that some surfaces may remain in contact longer than other surfaces and generalized the penetration theory by introducing a probability function which expresses the fact that there exists a distribution of contact times lying between zero and infinity. In the resulting expression obtained for Na, the term 2 /D/nt is replaced by yJWs, where s is the fractional renewal rate. Since the unknown t is replaced by the unknown s, the model is not suitable for the prediction of mass transfer coefficients. 

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... 

Nedeltchev, S. (2003), Correction of the penetration theory applied for prediction of mass transfer coefficients in a high-pressure bubble column operated with gasoline and toluene, Journal of Chemical Engineering of Japan, 36(5) 630-633. 

Prediction of Mass-Transfer Coefficients. Predict the mass-transfer coefficients... 

Minnikanti, V S. De, S. et al. 1999. Prediction of mass transfer coefficient with suction for turbulent flow in cross flow ultrafiltration. Journal of Membrane Science 157 227-239. 

Maraqa, M. 2001. Prediction of mass-transfer coefficients for solute transport in porous media. Journal of Contaminant Hydrology 53 153-171. 

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