Calculator inputs
Enter observed kinetic and pellet transport values. Results appear above this form after calculation.
Example data table
| Case | Observed rate | Radius | Diffusivity | Surface concentration | Criterion | Interpretation |
|---|---|---|---|---|---|---|
| Lab screening A | 0.80 mol/m³·s | 1.50 mm | 5.0×10-6 m²/s | 2.00 mol/L | 0.000180 | Negligible internal diffusion limitation |
| Pilot pellet B | 120 mol/m³·s | 2.50 mm | 3.5×10-6 m²/s | 0.40 mol/L | 0.535714 | Moderate or transitional diffusion limitation |
| Scale-up check C | 450 mol/m³·s | 3.50 mm | 2.0×10-6 m²/s | 0.30 mol/L | 9.187500 | Strong internal diffusion limitation |
Formula used
Primary equation
CWP = (|robs| × Rp2) / (Cs × De)
Supporting design equations
Rmax = √[(Ctarget × Cs × De) / |robs|]
De,min = (|robs| × Rp2) / (Ctarget × Cs)
|r|max = (Ctarget × Cs × De) / Rp2
Here, robs is the observed rate per catalyst volume, Rp is pellet radius, De is effective diffusivity, and Cs is surface reactant concentration.
Values below roughly 0.30 usually indicate minor internal diffusion resistance. Values between 0.30 and 1.00 are cautionary. Values above 1.00 often show strong pore diffusion effects.
How to use this calculator
- Enter the observed reaction rate in the unit most convenient for your data source.
- Choose pellet radius and effective diffusivity with matching physical meaning for the catalyst pellet.
- Enter the reactant concentration at the pellet surface, not the bulk value unless they are essentially equal.
- Set a target criterion such as 0.30 for conservative screening or another project-specific limit.
- Press the calculate button to display the criterion above the form and review the transport interpretation.
- Download the CSV or PDF output if you need to document screening cases or compare multiple catalyst options.
FAQs
1. What does the Weisz-Prater criterion check?
It checks whether internal pore diffusion is distorting the observed catalyst rate. A low value suggests measured kinetics are close to intrinsic behavior within the pellet.
2. Why is 0.30 often used as a screening limit?
A value near 0.30 is a conservative threshold widely used for quick screening. Below it, diffusion limitations are often minor enough for preliminary kinetic interpretation.
3. What concentration should I enter?
Use the reactant concentration at the pellet surface. If only bulk concentration is known, apply caution because external mass transfer can make the surface value lower.
4. Can I use rates based on catalyst mass?
Yes. Select a mass-based unit and enter the catalyst apparent density. The calculator converts the rate to a catalyst-volume basis before evaluating the criterion.
5. Why does pellet size matter so strongly?
The criterion scales with the square of pellet radius. Even modest pellet growth can sharply increase diffusion resistance inside porous catalysts.
6. What does a value above 1.0 imply?
It usually indicates strong internal diffusion limitation. In that situation, the observed rate may no longer represent intrinsic chemistry alone.
7. Does this replace full pellet modeling?
No. It is a screening tool. Detailed catalyst assessment may still require effectiveness factors, Thiele modulus analysis, and coupled transport-reaction modeling.
8. When should I repeat the calculation?
Repeat it whenever pellet size, pore structure, temperature, concentration, or measured rate changes. Small transport changes can shift the diffusion regime quickly.