Basic Equations for Adsorption

Although adsorbers are generally designed from laboratory data, the approximate performance can sometimes be predicted from equilibrium data and mass-transfer considerations. A mass balance on the solute for the flow of fluid through a differential adsorption-bed length, dz, over a differential-time duration, dt, gives 

The mechanism of solute transfer to the porous solid includes diffusion through the fluid film around the particle and diffusion inside the pores to internal adsorption sites. The actual process of adsorption is practically instantaneous and equilibrium is assumed to exist between the surface and the fluid at each point inside the particle. The transfer process is approximated using an overall volumetric mass-transfer coefficient (Kca) and an overall driving force  

The overall coefficient Kc depends on the external film coeffient, kc exl, and on an effective internal coefficient, kc int. The external film coefficient can be estimated from the correlations for packed beds given in Section 2.6.5. The internal coefficient may be estimated by (Vermeulen et al., 1973) 

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