In
heterogeneous catalysis, understanding whether the reaction rate is controlled by
diffusion or intrinsic kinetics is crucial for the design and optimization of
catalytic reactors. If internal diffusion limitations are significant, the effective utilization of the catalyst is reduced, leading to inefficient processes. The Weisz-Prater criterion helps in identifying such limitations, allowing engineers to make informed decisions regarding catalyst design and reactor operation.
The Weisz-Prater criterion is given by the dimensionless number C_wp, expressed as:
C_wp = (r_obs * R^2) / (D_eff * C_s)
where:
r_obs is the observed reaction rate (mol/m3s)
R is the characteristic length of the catalyst particle (m)
D_eff is the effective diffusivity of the reactant in the catalyst (m2/s)
C_s is the concentration of the reactant at the external surface of the catalyst (mol/m3)
The value of C_wp provides insight into the extent of internal diffusion limitations:
If C_wp 1, internal diffusion limitations are significant, indicating that the reaction rate is controlled by the rate of diffusion of reactants into the catalyst particle.
To apply the Weisz-Prater criterion, one needs to measure or estimate the required parameters:
Determine the
observed reaction rate from experimental data.
Calculate the
characteristic length of the catalyst particle, which can be approximated by the particle radius for spherical particles.
Estimate the
effective diffusivity of the reactant within the catalyst, which may require empirical correlations or experimental determination.
Measure the
surface concentration of the reactant, which can be done using appropriate analytical techniques.
Once these parameters are known, the value of C_wp can be calculated to assess the presence of internal diffusion limitations.
Example Calculation
Consider a catalyst with the following parameters:
Observed reaction rate, r_obs = 0.01 mol/m3s
Particle radius, R = 0.001 m
Effective diffusivity, D_eff = 1 x 10-9 m2/s
Surface concentration, C_s = 1 mol/m3
The Weisz-Prater criterion is calculated as follows:
C_wp = (0.01 * (0.001)^2) / (1 x 10-9 * 1) = 0.01
Since C_wp = 0.01
