⚗️ Diffusion with Chemical Reaction Calculator
Evaluate internal diffusion limitations in catalytic pellets using Thiele modulus, effectiveness factor and observable Weisz-Prater criterion.
🧬 Reaction-Diffusion Pellet Schematic
📝 Configuration
Key Equations:
First-order Thiele modulus: ϕ = Lc√(k/De)
Slab: η = tanh(ϕ)/ϕ
Sphere: η = 3/ϕ² [ϕ coth(ϕ) − 1]
Weisz-Prater: CWP = robsR²/(CsDe)
First-order Thiele modulus: ϕ = Lc√(k/De)
Slab: η = tanh(ϕ)/ϕ
Sphere: η = 3/ϕ² [ϕ coth(ϕ) − 1]
Weisz-Prater: CWP = robsR²/(CsDe)
📊 Results & Visualization
Configure inputs and click Calculate to view results.
📘 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 = 1×10⁻⁹ m²/s, and k = 0.01 s⁻¹, ϕ = R√(k/De). The engine computes η 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 ϕ.
- External film resistance is not included.