Simplified Models of Fixed Beds

Integration of the differential equations presented in Table 9.5-1 leads to a description of the fields of concentration in the fixed bed and in the pellets. With respect to industrial adsorption the breakthrough curve of a fixed bed adsorber is most important because this curve is decisive for the capacity of the bed. 

Let us first assume that only one adsorbable component is present in a gas stream which is moving downward from the top to the bottom of a fixed bed. So potential fluidization can be avoided. The adsorptive enters the pores of adsorbent pellets in a thin layer of the fixed bed or in the mass transfer zone (mtz). When the equilibrium in this zone is established and the pellets are saturated the zone is moving downward. In such a mass transfer zone the concentration of the adsorptive decreases from the feed concentration to the small exit concentration at the bottom which tends to zero for a completely unloaded bed. After a certain operating time three zones in a fixed adsorber bed can be distinguished  

When the mass transfer zone arrives at the bottom and an allowable (product or environmental standard) adsorptive concentration is surpassed the raw gas stream must be switched to the second adsorber which has been regenerated. It is understandable that the mass transfer zone should be short to utilize a maximum of the adsorption capacity. Therefore, the shape of the breakthrough eurve is economically very important. 

The model presented in Table 9.5-1 is complex and calculatiorrs are time consuming. Therefore, many simplifications of the model are known and experimental breakthrongh curves have been compared with results obtained from simplified models. Most known is the linear driving force (LDF) model. As a rule the following assumptions are made  

The balance of the component i in a thin layer of a fixed bed without the dispersion term = 0) is with the pellet density = yC 3pp (see Table 9.5-1) 

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