Question

Choose the CORRECT statement that describes the dependence of the variance (\( \sigma^2_\Theta \)) of the residence time distribution (RTD) with respect to the number of tanks (\( n \)) in the Tanks-in-Series model of non-ideal reactors.

• A. \( \sigma^2_\Theta \) monotonically increases with \( n \)
• B. \( \sigma^2_\Theta \) first increases and then decreases with \( n \)
• C. \( \sigma^2_\Theta \) first decreases and then increases with \( n \)
• D. \( \sigma^2_\Theta \) monotonically decreases with \( n \)

Hint:

In process modeling, using multiple tanks in series can help approximate plug flow conditions, which are ideal for many steady-state continuous processes.

Answer 1

The Correct Option is D

Step 1: Understand the Tanks-in-Series Model.
In the Tanks-in-Series model, each tank is modeled as a completely mixed reactor, and increasing the number of tanks \( n \) leads to a more plug-flow-like behavior, reducing the spread of the RTD. 
Step 2: Analyze the Variance Trend.
As \( n \) increases, the variance of the residence time distribution (\( \sigma^2_\Theta \)) decreases due to the progressive narrowing of the RTD curve, reflecting less dispersion and more uniform residence times.