Intra-particle diffusion in catalyst particles

1. The cumene (C₉H₁₂) (A) cracking reaction to form benzene C₆H₆ (B)is often used as a model reaction for determining the relative activities of cracking catalysts:

C₉H₁₂ → C₆H₆ + C₃H₆

A → B + C

The reaction takes place on silica-alumina catalyst in the temperature range of 300°C to 600°C. Calculate the combined diffusivity D_A’ and effective diffusivity D_eA of cumene in a mixture of benzene and cumene at 1 atm total pressure and 510°C within the pores of a TCC (thermal cracking catalyst) bed assuming equimolar counter diffusion applies. Report you answers in units of cm² /s

TCC catalyst data:

S_G = 342 m² /g

e_S = 0.51

eq. catalyst dia. D_p = 0.43 cm

ρ_p = 1.14 g/cm3

R = 8.314 J/mol·K

A narrow pore size distribution and tortuosity factor of 3 may be assumed. Use of methods by Poling _{et al}. suggest ordinary (molecular) diffusion D_AB = 0.150 cm² /s. Confirm the assumption of narrow pores such that the Knudsen diffusion term is dominant.