Exit Age Distribution Based On Dispersion Number Calculator

Exit Age Distribution Formula:

\[ E = \sqrt{\frac{u''^3}{4\pi D_p' l}} \times \exp\left(-\frac{(l - (u'' \Delta t))^2}{4(D_p' l)/u''}\right) \]

Velocity of Pulse Measuring Variance (u''):

m/s

Dispersion Coefficient at Dispersion Number > 100 (Dp'):

m²/s

Length of Spread (l):

Time Required for Change in Concentration (Δt):

Exit Age Distribution (E):

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1. What is Exit Age Distribution?

Exit Age Distribution is the Measure of the Stream of the Fluid Leaving Vessel. It provides information about how material or tracer particles exit a system over time, which is crucial for understanding residence time distributions in chemical reactors and other process systems.

2. How Does the Calculator Work?

The calculator uses the Exit Age Distribution formula:

\[ E = \sqrt{\frac{u''^3}{4\pi D_p' l}} \times \exp\left(-\frac{(l - (u'' \Delta t))^2}{4(D_p' l)/u''}\right) \]

Where:

\( E \) — Exit Age Distribution (1/s)
\( u'' \) — Velocity of Pulse Measuring Variance (m/s)
\( D_p' \) — Dispersion Coefficient at Dispersion Number > 100 (m²/s)
\( l \) — Length of Spread (m)
\( \Delta t \) — Time Required for Change in Concentration (s)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The equation describes how a pulse of tracer material spreads and exits a system, accounting for velocity, dispersion effects, and system geometry.

3. Importance of Exit Age Distribution Calculation

Details: Accurate calculation of exit age distribution is essential for reactor design, process optimization, and understanding mixing behavior in chemical processes. It helps in determining the residence time distribution, which affects conversion rates and product quality.

4. Using the Calculator

Tips: Enter all values in appropriate units (m/s for velocity, m²/s for dispersion coefficient, m for length, and s for time). All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of Dispersion Number > 100?
A: When dispersion number is greater than 100, it indicates significant dispersion effects in the system, meaning the formula accounts for substantial spreading of the tracer material.

Q2: How does velocity affect the exit age distribution?
A: Higher velocity generally results in narrower exit age distributions as the tracer moves through the system more quickly with less time for dispersion.

Q3: What are typical values for dispersion coefficient?
A: Dispersion coefficients vary widely depending on the system, ranging from 10⁻⁵ to 10⁻¹ m²/s for different processes and materials.

Q4: When is this formula most applicable?
A: This formula is particularly useful for systems with high dispersion numbers (>100) where dispersion effects dominate over convective transport.

Q5: How does length of spread impact the results?
A: Longer spread lengths generally result in broader exit age distributions as the tracer has more distance over which to disperse.