Concentration profiles and heights of mass transfer columns

2 Concentration profiles and heights of mass transfer columns 

This type of calculation does not have to be carried out for a plate column because the two phases are well mixed on each plate. This means that on each individual plate a state of equilibrium can be presumed. Therefore a volume element is identical to an equilibrium stage, and the height of the column can be obtained from the number of equilibrium stages required for a particular separation. This is a thermodynamic rather then mass transfer problem. This explains why a mass transfer device, such as a distillation column can be sized without any knowledge of the laws of mass transfer. 

A packed column is filled with a packing material. The complex shape of the packing makes it difficult to ascertain the area of the phase interface where mass transfer takes place. Therefore only the product of the mass transfer coefficients and the interface area will be determined. The area of the interface A1 is related to the volume of the empty column VK, and the interface area per volume a is defined by 

We will first consider a control volume between two cross sections in an absorber, separated by a distance dz, Fig. 1.57. The amount of material transferred to the liquid over the interface area dAj 

The molar flux hA1 is given by (1.220), under the assumption that the amount of component A in the liquid and vapour phases is small, and so the values for the mole fractions yAm = Y and yAeq = Y can be replaced by mole ratios. It then follows from (1.228) that 

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