Intensity of countercurrent exchange time required

The hold-up is an essential factor in a countercurrent distillation and has an important influence on the time required for carrying it out (see chap. 4.10.5). Whilst the theoretical plate number and the reflux ratio increase in proportion to lAog , the time expended increases as the square of lf og tx. It is hence the time consumed that best characterizes the difficulty of a separation. If we calculate the quotient 

Its physical dimension is a reciprocal time, which is that of a frequency or — if the distillation is regarded from the aspect of labour economy — that of an investment return. 1 is independent of the scale and can be formulated for a volume element of arbitrary size in a column, having an arbitrary height and diameter. 

In the total time required we must include the period of equilibration during which the lowest-boiling component in the vapour is concentrating at the column head and distillate should not be taken off. According to von Weber [170] this time can be calculated by the formula 

The time for running-in is therefore roughly proportional to the square of the number of theoretical plates or to the column length [152], [169]. The equilibration time will be discussed more fuUy in connection with the separation of stable isotopes (section 

4) as it requires special attention when the number of theoretical separating stages exceeds 100. 

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