Space Time for Second Order Reaction using Recycle Ratio Calculator

Space Time Formula:

\[ \tau = \frac{(R+1) \times C_0 \times (C_0 - C_f)}{C_0 \times k'' \times C_f \times (C_0 + (R \times C_f))} \]

Recycle Ratio (R):

Initial Reactant Concentration (C₀):

mol/m³

Final Reactant Concentration (C_f):

mol/m³

Rate Constant (k''):

m³/(mol·s)

Space Time (τ):

seconds

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1. What is Space Time for Second Order Reaction with Recycle?

Definition: Space time (τ) is the time required to process one reactor volume of feed under specified conditions, accounting for reactant recycle in a second-order reaction system.

Purpose: This calculation helps chemical engineers design reactors with recycle streams for second-order reactions, optimizing reactor size and performance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \frac{(R+1) \times C_0 \times (C_0 - C_f)}{C_0 \times k'' \times C_f \times (C_0 + (R \times C_f))} \]

Where:

\( \tau \) — Space time (seconds)
\( R \) — Recycle ratio (dimensionless)
\( C_0 \) — Initial reactant concentration (mol/m³)
\( C_f \) — Final reactant concentration (mol/m³)
\( k'' \) — Rate constant for second-order reaction (m³/(mol·s))

Explanation: The formula accounts for the effect of reactant recycle on the reaction kinetics and the required residence time in the reactor.

3. Importance of Space Time Calculation

Details: Accurate space time calculation ensures proper reactor sizing, optimal conversion rates, and efficient use of recycled materials in chemical processes.

4. Using the Calculator

Tips: Enter the recycle ratio (R), initial concentration (C₀), final concentration (C_f), and rate constant (k''). All concentration values must be positive with C₀ > C_f.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical recycle ratio range?
A: Recycle ratios typically range from 0 (no recycle) to 5 or more, depending on process requirements.

Q2: Why is space time important in reactor design?
A: Space time directly relates to reactor volume needed for a given feed rate and desired conversion.

Q3: How does recycle affect space time?
A: Recycle generally increases required space time due to dilution of fresh feed with reacted material.

Q4: What units should be used for concentrations?
A: Use consistent molar concentration units (typically mol/m³) for all concentration values.

Q5: When is this calculation not applicable?
A: This formula is specific for second-order reactions with constant-density systems and perfect mixing.