Space Time for First Order Reaction using Rate Constant for Mixed Flow Calculator

Space Time Formula for MFR:

\[ \tau_{MFR} = \frac{1}{k_1} \times \frac{X_{MFR}(1 + \varepsilon X_{MFR})}{1 - X_{MFR}} \]

Space Time (τ_MFR):

Definition: Space Time (τ) is the time required to process one reactor volume of feed under specified conditions.

Purpose: It helps chemical engineers determine the residence time needed for a desired conversion in a continuously stirred tank reactor (CSTR).

The calculator uses the formula:

\[ \tau_{MFR} = \frac{1}{k_1} \times \frac{X_{MFR}(1 + \varepsilon X_{MFR})}{1 - X_{MFR}} \]

Where:

Explanation: The formula accounts for both the reaction kinetics and any volume change during the reaction.

Details: Proper space time calculation ensures optimal reactor design, efficient conversion, and cost-effective operation.

Tips: Enter the rate constant (positive value), conversion (0 to 0.999), and fractional volume change (can be negative, zero, or positive).

Q1: What does ε represent?
A: ε is the fractional volume change that would occur if the reaction went to completion (X=1).

Q2: When would ε be zero?
A: For reactions where the number of moles doesn't change (e.g., A → B with same stoichiometric coefficients).

Q3: What are typical k₁ values?
A: These vary widely but are typically between 0.001 to 100 1/s depending on temperature and reaction.

Q4: How does conversion affect space time?
A: Higher conversions require disproportionately larger space times, especially as X approaches 1.

Q5: Does this work for batch reactors?
A: No, this formula is specifically for continuous mixed flow reactors (CSTRs).