Volume of Reactor for Batch Solids and Batch Fluids Calculator

Volume of Reactor Formula:

\[ V = \frac{k' \times W_d}{e^{\ln(\ln(\frac{C_A}{C_{A∞}})) + k_d \times t} \times k_d} \]

Rate Constant based on Weight of Catalyst:

1/s

Weight of Catalyst in Deactivation:

Reactant Concentration:

mol/m³

Concentration at Infinite Time:

mol/m³

Rate of Deactivation:

1/s

Time Interval:

Volume of Reactor (m³):

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1. What is Volume of Reactor for Batch Solids and Batch Fluids?

Definition: This calculator determines the required reactor volume based on catalyst properties and reaction kinetics.

Purpose: It helps chemical engineers design appropriate reactor sizes for batch processes involving solids and fluids.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{k' \times W_d}{e^{\ln(\ln(\frac{C_A}{C_{A∞}})) + k_d \times t} \times k_d} \]

Where:

\( V \) — Volume of reactor (m³)
\( k' \) — Rate constant based on weight of catalyst (1/s)
\( W_d \) — Weight of catalyst in deactivation (kg)
\( C_A \) — Reactant concentration (mol/m³)
\( C_{A∞} \) — Concentration at infinite time (mol/m³)
\( k_d \) — Rate of deactivation (1/s)
\( t \) — Time interval (s)

Explanation: The formula accounts for catalyst deactivation over time and its effect on reaction kinetics.

3. Importance of Reactor Volume Calculation

Details: Proper reactor sizing ensures efficient chemical processing, safety, and cost-effectiveness in industrial applications.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is catalyst deactivation?
A: Catalyst deactivation is the process by which a catalyst loses its activity over time due to various factors like poisoning, sintering, or coking.

Q2: How is the rate constant determined?
A: The rate constant is typically determined experimentally from kinetic studies of the reaction.

Q3: What does concentration at infinite time represent?
A: This represents the reactant concentration when the reaction has proceeded for an infinitely long time (equilibrium concentration).

Q4: Can this calculator be used for continuous reactors?
A: No, this specific formula is designed for batch reactors with solids and batch fluids.

Q5: How does deactivation rate affect reactor volume?
A: Higher deactivation rates typically require larger reactor volumes to compensate for the loss of catalyst activity over time.