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Weisz-Prater Criterion for Pore Diffusion Calculator

In heterogeneous catalytic reactions, reactants must diffuse through catalyst pores before reaching active catalytic sites.

Reaction rate per unit catalyst volume measured experimentally.

Characteristic dimension / radius of catalyst pellet.

Knudsen/bulk effective pore diffusion coefficient.

Reactant concentration at outer pellet surface.

Calculated Result
0.200

Weisz-Prater Parameter (C_WP)

Result Summary

Weisz-Prater modulus C_WP = 0.200. Regime: Reaction Kinetics Controlled (No internal diffusion limitation).

Calculation Breakdown

  1. Step 1: Dimensionless Weisz-Prater FormulaC_WP = [ -r_A(obs) · R_p² ] / [ D_eff · C_As ] = [ 10 · (0.001)² ] / [ 0.000001 · 50 ] = 0.200
  2. Step 2: Regime DiagnosticC_WP = 0.200 < 0.3

What Is the Weisz-Prater Criterion for Pore Diffusion Calculator?

The Weisz-Prater criterion is a diagnostic tool in chemical reaction engineering to establish whether a catalyst pellet is operating under kinetic control or pore diffusion limitation.

How Does the Weisz-Prater Criterion for Pore Diffusion Calculator Work?

Computes the dimensionless parameter C_WP.

If C_WP < 0.3, internal concentration gradients are negligible (effectiveness factor η ≈ 1).

If C_WP > 1.0, severe pore diffusion limitation exists (η << 1).

Weisz-Prater Criterion for Pore Diffusion Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

C_WP = [ -r_A(obs) · R_p² ] / [ D_eff · C_As ]

Weisz-Prater dimensionless parameter comparing observed reaction rate to intraparticle diffusion rate.

How to Use the Weisz-Prater Criterion for Pore Diffusion Calculator

  1. Input experimental observed reaction rate and pellet radius.
  2. Enter effective diffusivity and external pellet surface concentration.

Step-by-Step Example Calculation

Porous Catalyst Pellet Diagnosis

Input Values:

observedRate:10
pelletRadius:0.001
diffusivity:0.000001
surfaceConcentration:50
Worked Steps: 1 mm pellet with D_eff = 10⁻⁶ m²/s and observed rate of 10 mol/(m³·s).

Understanding Your Result

Primary output indicates C_WP parameter.

Summary displays operating regime diagnostic.

Factors That Affect the Result

  • Pellet size (C_WP scales quadratically with pellet radius R_p²).
  • Pore tortuosity and porosity.

When Should You Use This Calculator?

  • Heterogeneous catalyst optimization, pellet sizing, and intrinsic kinetic studies.

Assumptions & Limitations

  • Assumes isothermal catalyst pellet.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard chemical reaction engineering diagnostic per Fogler and Weisz-Prater.

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