Question

The dispersion number for plug flow must be ______

• A. infinity
• B. < 2100
• C. Zero
• D. < 2

Hint:

Remember the limits of the dispersion number (\( D/uL \)):
\( D/uL = 0 \rightarrow \) Ideal Plug Flow Reactor (PFR).
\( D/uL \to \infty \rightarrow \) Ideal Continuous Stirred Tank Reactor (CSTR).
These limits are useful to keep in mind for reactor analysis.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the value of the vessel dispersion number for an ideal plug flow reactor (PFR).
This topic relates to non-ideal flow and the dispersion model in chemical reaction engineering.

Step 2: Key Formula or Approach:
The axial dispersion model uses an analogy to Fick's law of diffusion to describe back-mixing in real reactors.
The dimensionless group that characterizes this back-mixing is the vessel dispersion number:
\[ D^* = \frac{D}{u \cdot L} \]
where \( D \) is the axial dispersion coefficient, \( u \) is the fluid velocity, and \( L \) is the reactor length.
The reciprocal of the dispersion number is the axial Peclet number: \( Pe = \frac{u \cdot L}{D} \).

Step 3: Detailed Explanation:

• Ideal Plug Flow: In an ideal plug flow reactor, there is no mixing along the flow path (no axial mixing or back-mixing), and complete mixing occurs in the radial direction.
This means the axial dispersion coefficient \( D \) must be exactly zero.
\[ D = 0 \quad \implies \quad D^* = \frac{0}{u \cdot L} = 0 \]

• Ideal Mixed Flow (CSTR): For a completely back-mixed reactor (ideal CSTR), mixing is instantaneous and complete throughout the vessel.
This corresponds to infinite axial dispersion:
\[ D \to \infty \quad \implies \quad D^* \to \infty \]

• Real Reactors: Real, non-ideal reactors lie between these two extremes:
\[ 0 \lt \frac{D}{u \cdot L} \lt \infty \]


Step 4: Final Answer:
The dispersion number for an ideal plug flow reactor is Zero.