13.9. SEPARATIONS IN PACKED TOWERS

Continuous changes in compositions of phases flowing in contact with each other are characteristic of packed towers, spray or wetted wall columns. The theory of mass transfer between phases and separation of mixtures under such conditions is based on a two-film theory. The concept is illustrated in Figure 13.14(a).

Figure 13.14: Mechanism, nomenclature, and constructions for absorption, stripping and distillation in packed towers (a) Two-film mechanism with equilibrium at the lnterface. (b) Sketch and nomenclature for countercurrent absorption or stripping in a packed tower (c) Equilibrium and material balance lines in absorption, showing how interfacial concentrations are found. (d) Equilibriurn and material balance lines in stripping, showing how interfacial concentrations are found. (e) Equilibrium and material balance lines in distillation showing how interfacial concentrations are found.

In its simplest form, the rate of mass transfer per unit area across these films is

(13.145)

Two special cases are commonly recognized.

1. Equimolar counterdiffusion between the phases, as in distillation with McCabe-Thiele approximations.

2. Unidirectional diffusion through a stagnant film or boundary layer, as in absorption or stripping processes involving transfer of a single component between liquid and vapor phases. Since there is a concentration gradient of the diffusing substance in the film or boundary layer, a correction is applied to the mass transfer coefficient. It is shown in texts on mass transfer (e.g., Hines and Maddox, 1985) that the effective coefficient for the film is

   (13.146)

   where

   (13.147)