Point efficiency fundamentals

Point efficiency is usually discussed in terms of the two-film theory. The theory postulates resistances to mass transfer in both the vapor and liquid films near a vapor-liquid ihterface (Fig. 7.2a). The molar rate of diffusion, N (moles/s), is given by

N = ^'Pm.gCv, " y) = kLa'¡pM¿(* - = K0Ga'l(,Mfi(y* - y) (7.6)

The total interfacial area, a'¡, can be expressed in terms of the specific interfacial area and the froth volume

Combining Eqs. (7.6) and (7.7) and using a differential form over a froth element dhf gives dN = kaafiMfi(y, - y)AB dhfH2 = kLatfiMM(x - x,)AB dhf! 12

= KoGa^oiy* - y)AB dhfH2 A material balance for the differential element shown in Fig. 7.26 gives

Combining Eqs. (7.9) and (7.8), integrating, and defining transfer units Ng, Nl, and NOG gives a¡ - a¡Ashfi 12

Interface

Interface

Figure 7.2 Principles of point efficiency. (a) Concentration profiles of the more volatile component; (b) component balance in a froth element.

Figure 7.2 Principles of point efficiency. (a) Concentration profiles of the more volatile component; (b) component balance in a froth element.

J X ~ Xi dx kjflihf pJiX

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