Mass Transfer Effects: Immobilized and Heterogeneous Reaction Systems - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 888

K= ∞

β = 0.4

β

10 2

E a
RT S

β = 0.3

γ =

= 20

β = 0.2

β = 0.1

β

= 0

10

= - 0.2

β

β = - 0.4

β = - 0.6

1

β = 0.8

= 0.6 β

10 -1

10 -2

10 -2 10 -1 1 10 10 2

φ β

= 0

FIGURE 17.8 Thermal effect on the effectiveness factor for spherical geometry.

reaction on the catalyst surface is thus virtually first order. The results of two experimental
runs made under identical conditions are as shown in Table E17-3.1 . Estimate the Thiele
modulus and effectiveness factor for each pellet. How small should the pellets be made to
virtually eliminate all internal diffusion effects on the overall reaction kinetics?

TABLE E17-3.1

Measured Rate,
mol-A/(g-cat$s) Pellet size, mm

Run 1 2.54 2.00

Run 2 0.254 10.5

Solution . When K A / N , the Thiele modulus is defined by Eqn (17.48) ,or

r

r max
D eA K A

d p
6

f ¼ (E17-3.1)

and the effectiveness factor is given by Eqn (17.52) ,

f cothð3 f Þ1=3

h ¼ (17.52)

f 2