Simplified Solution for a Single Pellet

In fixed or fluidized beds, in pneumatic or hydrauhc transport systems, or in a stirred vessel, adsorbent particles are surrounded by a fluid phase. If the nticropore diffusion (for instance in cages of zeolite crystals) can be neglected the adsorptive concentration in the macropores of a pellet with the radius R is given by 

Despite the fact that the effective diffusion coefficient is problematic the last equation is often applied on adsorption processes because simple solutions can be foimd in the literature. In the case of a constant initial concentration and a constant concentration at the particle surface the mean concentration, according to 

Here t/R is the Fourier number of mass transfer. If the ratio Cj /cj is smaller than 0.95 a further simplification of the last equation is valid  

The rate of adsorption is high when the pellets are small and the diffusion is fast (gaseous adsorptives at low pressure but high temperatures). In the case that after 

Since the expression is smaller than Is the last equation can be fur- 

---