The effectiveness factor is calculated using the Thiele modulus (Ï), a dimensionless number that represents the ratio of reaction rate to diffusion rate within the porous catalyst. The mathematical relationship between the effectiveness factor and the Thiele modulus depends on the reaction order and the geometry of the pores. For a first-order reaction in a spherical catalyst particle, the relationship can be approximated by:
η = (1/Ï) * tanh(Ï)
where tanh is the hyperbolic tangent function. For other reaction orders and geometries, the relationship may vary.
