Initial Reactant Concentration of Reactant for Strong Pore Resistance in Catalyst Deactivation Calculator

Formula Used:

\[ C_{A0} = C_{A,SP} \times e^{\left(\frac{k' \times \tau'}{MT} \times e^{\left(\frac{-k_d \times t}{2}\right)}\right)} \]

Reactant Concentration for Strong Pore Diffusion (C_A,SP):

mol/m³

Rate Constant based on Weight of Catalyst (k'):

1/s

Space Time for 1st Order Catalyzed Reactions (τ'):

Thiele Modulus for Deactivation (MT):

Rate of Deactivation (k_d):

1/s

Time Interval (t):

Initial Reactant Concentration (C_A0):

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1. What is Initial Reactant Concentration for Strong Pore Resistance?

Definition: This calculator determines the initial concentration of reactant in catalytic reactions where strong pore diffusion resistance is present, accounting for catalyst deactivation over time.

Purpose: It helps chemical engineers design and analyze catalytic reactors by estimating initial reactant concentrations under conditions of pore diffusion limitations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_{A0} = C_{A,SP} \times e^{\left(\frac{k' \times \tau'}{MT} \times e^{\left(\frac{-k_d \times t}{2}\right)}\right)} \]

Where:

\( C_{A0} \) — Initial reactant concentration (mol/m³)
\( C_{A,SP} \) — Reactant concentration for strong pore diffusion (mol/m³)
\( k' \) — Rate constant based on weight of catalyst (1/s)
\( \tau' \) — Space time for 1st order catalyzed reactions (s)
\( MT \) — Thiele modulus for deactivation
\( k_d \) — Rate of deactivation (1/s)
\( t \) — Time interval (s)

Explanation: The formula accounts for both pore diffusion resistance and catalyst deactivation over time through nested exponential terms.

3. Importance of Initial Reactant Concentration Calculation

Details: Accurate calculation is crucial for reactor design, predicting reaction rates, and understanding catalyst performance under diffusion-limited conditions.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Default values are provided for typical conditions, but should be adjusted for specific catalysts and reactions.

5. Frequently Asked Questions (FAQ)

Q1: What is strong pore diffusion resistance?
A: It occurs when reactant diffusion into catalyst pores is slow compared to reaction rate, creating concentration gradients within the catalyst particle.

Q2: How is the Thiele modulus determined?
A: MT is calculated from catalyst properties and reaction kinetics, typically ranging from 0.1 to 10 for significant pore diffusion effects.

Q3: What affects the rate of deactivation?
A: Catalyst poisoning, sintering, coking, and thermal degradation can all contribute to deactivation rates.

Q4: When is this calculation most important?
A: For reactions with fast kinetics using porous catalysts, where diffusion limitations significantly impact overall reaction rates.

Q5: How does space time differ from residence time?
A: Space time is based on reactor volume and inlet flow rate, while residence time accounts for actual fluid dynamics within the reactor.