Question

Two reactors with average residence times \( t_1 \) and \( t_2 \) are placed in series. Reactor 1 has zero dispersion and reactor 2 has infinite dispersion. The E curve of the system is given by

• A. 0 for \( t \leq t_1 \), \( \frac{1}{t_2} \exp\left(\frac{t - t_1}{t_2}\right) \) for \( t>t_1 \)
• B. 0 for \( t \leq t_2 \), \( \frac{1}{t_1} \exp\left(\frac{t - t_2}{t_1}\right) \) for \( t>t_2 \)
• C. 0 for \( t \leq t_2 \), \( \frac{1}{t_1} \exp\left(\frac{t_1 - t_2}{t_2}\right) \) for \( t>t_2 \)
• D. 0 for \( t \leq t_1 \), \( \frac{1}{t_2} \exp\left(\frac{t_1 - t_2}{t_1}\right) \) for \( t>t_1 \)

Hint:

When analyzing reactor systems in series with different dispersion properties, the E curve is determined by the residence times and dispersion in each reactor.

Answer 1

The Correct Option is A

Step 1: Understanding the system.
The system consists of two reactors in series: Reactor 1 with zero dispersion and Reactor 2 with infinite dispersion. The E curve (exit age distribution curve) describes how the reactant concentration changes with time, which is influenced by the residence time and dispersion in each reactor.
Step 2: Analyzing the options.
(1) 0 for \( t \leq t_1 \), \( \frac{1}{t_2} \exp\left(\frac{t - t_1}{t_2}\right) \) for \( t>t_1 \): This is the correct answer. For Reactor 1 with zero dispersion, the reactant immediately exits at time \( t_1 \). For Reactor 2 with infinite dispersion, the E curve follows an exponential decay starting from \( t_1 \).
(2) 0 for \( t \leq t_2 \), \( \frac{1}{t_1} \exp\left(\frac{t - t_2}{t_1}\right) \) for \( t>t_2 \): This is incorrect because the dispersion and residence times are reversed.
(3) 0 for \( t \leq t_2 \), \( \frac{1}{t_1} \exp\left(\frac{t_1 - t_2}{t_2}\right) \) for \( t>t_2 \): This is incorrect as it incorrectly combines the times and dispersion effects.
(4) 0 for \( t \leq t_1 \), \( \frac{1}{t_2} \exp\left(\frac{t_1 - t_2}{t_1}\right) \) for \( t>t_1 \): This is incorrect as the exponential function does not properly represent the dispersion behavior.
Step 3: Conclusion.
The correct answer is option (1), which correctly describes the E curve behavior for the system of two reactors in series with the given dispersion characteristics.