Crossflow of Stages

In Fig. 9.4-3 the three adsorbent streams are bronght together and mixed with the result that they have the loading X. This loading can be found by the rule of balances or the mixing rale This rale is at first applied on the mass streams 5ri and S,2 and then on the binary mixture (4i + r2) and S s. The approach to equilibrium in a stage can be expressed by a stage efficiency, compare the sections on absorption, extraction, and rectification. This efficiency is mainly dependent on the residence time in relation to a characteristic diffusion time, see later. 

a special problem will be discussed What is the minimum adsorbent mass in a two-stage unit for a given loading reduction from the loading Yq of the feed to the loading Y2 of the leaving fluid (Treybal 1968). 

It is assumed that the equilibrium can be described by the equation of Freundlich  

The total adsorbent mass flow based on the fluid stream Gr is 

The minimum mass flow of adsorbent (Sri + 2) can be found by differentiation and setting the derivative equal to zero  

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