Thiele Modulus for Deactivation Calculator

Thiele Modulus Formula:

\[ MT_d = L \times \sqrt{\frac{k''' \times a}{D_e}} \]

Length of Catalyst Pore at Deactivation (L):

Rate Const. on Volume of Pellets (k'''):

1/s

Activity of Catalyst (a):

Diffusion Coefficient at Deactivation (Dₑ):

m²/s

Thiele Modulus for Deactivation (MTₑ):

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1. What is Thiele Modulus for Deactivation?

Definition: The Thiele Modulus for Deactivation is a dimensionless number that relates the reaction rate to the diffusion rate in a catalyst particle undergoing deactivation.

Purpose: It helps chemical engineers determine the effectiveness factor of a catalyst and predict how deactivation affects reaction performance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ MT_d = L \times \sqrt{\frac{k''' \times a}{D_e}} \]

Where:

\( MT_d \) — Thiele Modulus for Deactivation (dimensionless)
\( L \) — Length of catalyst pore at deactivation (m)
\( k''' \) — Rate constant on volume of pellets (1/s)
\( a \) — Activity of catalyst (dimensionless)
\( D_e \) — Diffusion coefficient at deactivation (m²/s)

Explanation: The formula compares the reaction rate (numerator) to the diffusion rate (denominator), scaled by the characteristic pore length.

3. Importance of Thiele Modulus Calculation

Details: Understanding the Thiele Modulus helps in catalyst design, predicting deactivation effects, and optimizing reactor performance.

4. Using the Calculator

Tips: Enter the pore length, rate constant, catalyst activity, and diffusion coefficient. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does a high Thiele Modulus indicate?
A: A high value suggests diffusion limitations are significant, meaning the reaction occurs primarily near the pore entrance.

Q2: How does deactivation affect the Thiele Modulus?
A: As the catalyst deactivates, the activity (a) decreases, which typically reduces the Thiele Modulus.

Q3: What's a typical range for catalyst activity?
A: Activity typically ranges from 0 (completely deactivated) to 1 (fully active), though values can exceed 1 for some promoted catalysts.

Q4: How do I determine the diffusion coefficient?
A: The diffusion coefficient can be measured experimentally or estimated from correlations based on temperature and molecular properties.

Q5: What's the relationship between Thiele Modulus and effectiveness factor?
A: The effectiveness factor can be calculated from the Thiele Modulus - for a first-order reaction, η = tanh(MT)/MT.