Stage Efficiencies of Liquid-Solid Systems

Illustration 7.12 Stage Efficiencies of Liquid-Solid Systems 

We start by noting that the use of a solid-phase mass transfer coefficient calls for a driving force based on the internal concentration X (kg solute/kg solid). A solute mass balance, performed about a single particle assumed to be a sphere, leads to the expression 

Because X/X is by definition the fractional stage efficiency E, we obfain the following relation between E and the contact time t  

The success of Equation 7.29g in predicting stage efficiencies evidently hinges on how well we can estimate the solid-phase diffusivity Dg. Although the complex interior geometry of porous particles makes this a difficult task, reasonable first estimates of Dg can be made using a relation previously presented in Chapter 3, which is repeated here  

Here e is the interior pore volume fraction, typically of the order 0.3 to 0.4, while the tortuosity x is often given a representative value of 4. Thus, with diffusivities in liquids being of the order 10 m /s (see Chapter 3), we can expect (Dg) to have a typical value 10 m /s. We make use of these considerations in Practice Problem 7.10, which deals with the efficiency of a column adsorption process. In general, however, it is more fruitful to use Equation 7.29g to explore the effect of contact time t or particle radius R. 

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