Mass Transfer in a Catalyst Particle

External (boundary layer) + Internal (Thiele · effectiveness factor)  |  1st-order A → products  |  CHE 461

Operating
Particle & Diffusion
Reaction
Bulk gas (Cb) flows past the particle. Reactant must diffuse across the boundary layer (thickness δ = dp/Sh) to reach the surface concentration Cs, then diffuse and react inside the particle. The Thiele modulus φ compares reaction rate to internal diffusion rate; the effectiveness factor η is the fraction of the catalyst that is actually used.
Inside the particle (Fogler Eq 15-27):  C(r)/Cs = (R/r)·sinh(φ·r/R)/sinh(φ)
Across the BL (stagnant film, Fogler Eq 14-28):  NA = kc(Cb − Cs)  →  linear drop from Cb to Cs. Steady state matches surface flux:  kc(Cb − Cs) = η·k(T)·R·Cs/3
Diagnostics
Key Equations (Fogler)
Frössling  Sh = 2 + 0.6·Re½·Sc⅓ 14-41
kc  = Sh·DAB/dp   δ = dp/Sh
Thiele φ  = (dp/2)·√(k/De) 15-23
η  = (3/φ²)(φ·coth φ − 1) 15-32
C(r)/Cs  = (R/r)·sinh(φr/R)/sinh(φ) 15-27
Cs/Cb  = 1 / (1 + η·k·R / (3·kc))
Ω  = η · Cs/Cb   (overall, → η as kc→∞)
Mears  η·k·(1−ε)·R / kc < 0.15 15-62
Weisz–Prater  η·φ² < 1 15-37
Computed Properties
Temperature scaling (Fogler-style)
DAB(T,P) = DAB,0 · (T/T0)1.75 · (P0/P)  (Fuller)
De(T) = De,0 · (T/T0)1.75
μ(T) = μ0 · (T/T0)0.67  (Sutherland-like)
ρf(T,P) = P·M̄ / (Rg·T)
k(T) = kref · exp(−Ea/Rg·(1/T − 1/Tref))
T0 = Tref = 573 K   P0 = 2 bar   M̄ = 12.5 g/mol   Ac = 1×10⁻⁵ m²