ThermoFluidCalc Report

Diffusion with Chemical Reaction โ€” 2026-08-21 15:24:45
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โš—๏ธ Diffusion with Chemical Reaction Calculator

Evaluate internal diffusion limitations in catalytic pellets using Thiele modulus, effectiveness factor and observable Weisz-Prater criterion.

๐Ÿงฌ Reaction-Diffusion Pellet Schematic

๐Ÿ“ Configuration

๐Ÿ“ Pellet Geometry
โš—๏ธ Reaction and Diffusion
First order: 1/s. Zero order: concentration units/s.
Key Equations:

First-order Thiele modulus: ฯ• = Lcโˆš(k/De)
Slab: ฮท = tanh(ฯ•)/ฯ•
Sphere: ฮท = 3/ฯ•ยฒ [ฯ• coth(ฯ•) โˆ’ 1]
Weisz-Prater: CWP = robsRยฒ/(CsDe)

๐Ÿ“Š Results & Visualization

Configure inputs and click Calculate to view results.

๐Ÿ“˜ Calculation Methodology

Mathematical Model

The calculator evaluates internal diffusion limitation for porous catalyst geometries. First-order kinetics use analytical effectiveness factors for slab, cylinder approximation, and sphere.

Worked Example

For a spherical pellet with R = 2 mm, De = 1ร—10โปโน mยฒ/s, and k = 0.01 sโปยน, ฯ• = Rโˆš(k/De). The engine computes ฮท and then estimates the observable Weisz-Prater criterion from the observed rate.

Assumptions

  • Isothermal porous pellet.
  • Constant effective diffusivity.
  • First-order analytical effectiveness factors are exact for standard geometries.
  • Zero-order mode is an engineering estimate based on a characteristic ฯ•.
  • External film resistance is not included.
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