Question

In petroleum catalytic cracking, silica-alumina microspheres with a diameter of 1.8 mm and a specific area of ??the pores of 3.2 cm².cm^-3 are used. Estimate the value of the effectiveness factor considering that the catalytic reaction, whose velocity is 6.9 cm.s^-1, is irreversible and of first order. The effective diffusion coefficient is 8.0x10^-4 cm².s^-1.

Answer 1

The given diameter = 1.8 mm

radius of sphere = 0.9 mm

specific crea of pore = 3.2 cm² /cm³

velocity = 6.9 cm/s

rate constant for first order reaction = 3.2 cm² /cm³  * 6.9 cm/s = 22.08 s^-1

effective diffusion coefficient is 8.0x10-4 cm2.s-1.

Thiele modules for sphere = (R/3) * (k/D)^0.5

=  (0.09 cm/3) * (22.08 /  8.0x10-4 )^0.5

= 14.95

Now, the expression for effectiveness factor is

n = (1/14.95) * ( 1/(tanh(3*14.95) - 1 / (3* 14.95) )

= 0.065