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Thiele Modulus (φ) & Catalyst Internal Pore Effectiveness Factor (η) Calculator

Easily calculate and compute thiele modulus (φ) & catalyst internal pore effectiveness factor (η) calculator with accurate equations, live formulas, and expert guidance.

Pellet volume divided by external surface area (V_p / S_p).

Intrinsic reaction rate per unit pellet volume.

Knudsen and molecular diffusion through pore network.

Pellet external geometry.

Calculated Result
0.02 factor

Effectiveness (η)

Effectiveness (η)

0.02 factor

Effectiveness Factor Eta

0.02

Thiele Modulus Phi

50

Effectiveness Percentage

2

Kinetic Regime Diagnosis

Strong Pore Diffusion Limitation (Catalyst Core Starved)

0.02 — factor

Calculation Breakdown

  1. Applied FormulaCalculates the Thiele modulus (φ) and internal effectiveness factor (η) for porous solid catalyst pellets, diagnosing whether reactions are hindered by internal pore diffusion.\phi = L_p \sqrt{\frac{k_v}{D_e}}, \quad \eta = \frac{3}{\phi_s} \left(\frac{1}{\tanh\phi_s} - \frac{1}{\phi_s}\right)

Thiele Modulus & Eta Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.30.50.81.0Effectiveness (η)

What Is the Thiele Modulus (φ) & Catalyst Internal Pore Effectiveness Factor (η) Calculator?

This tool computes thiele modulus (φ) & catalyst internal pore effectiveness factor (η) calculator with high precision arithmetic.

How Does the Thiele Modulus (φ) & Catalyst Internal Pore Effectiveness Factor (η) Calculator Work?

Calculates the Thiele modulus (φ) and internal effectiveness factor (η) for porous solid catalyst pellets, diagnosing whether reactions are hindered by internal pore diffusion.

Thiele Modulus (φ) & Catalyst Internal Pore Effectiveness Factor (η) Calculator Formula & Variables

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

ϕ=LpkvDe,η=3ϕs(1tanh⁡ϕs−1ϕs)\phi = L_p \sqrt{\frac{k_v}{D_e}}, \quad \eta = \frac{3}{\phi_s} \left(\frac{1}{\tanh\phi_s} - \frac{1}{\phi_s}\right)

Calculates the Thiele modulus (φ) and internal effectiveness factor (η) for porous solid catalyst pellets, diagnosing whether reactions are hindered by internal pore diffusion.

How to Use the Thiele Modulus (φ) & Catalyst Internal Pore Effectiveness Factor (η) Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Thiele Modulus (φ) & Catalyst Internal Pore Effectiveness Factor (η) Calculator Example

Input Values:

catalystCharacteristicLengthMm:2.5
firstOrderIntrinsicRateConstantK:18
effectiveDiffusivityM2PerS:4.5e-8
pelletGeometry:3
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required factor.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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