Question

Choose the correct option(s).
Permeability of a porous bed made of spherical particles is/are:

• A. Independent of particle size
• B. Increases with increase in particle size
• C. Decreases with increase in particle size
• D. Affected by particle size distribution

Hint:

Use the Kozeny-Carman/Ergun relation: permeability scales with particle diameter squared, and packing of mixed sizes reduces void space.

Answer 1

The Correct Option is B, D

Step 1: Recall the governing relation for flow through a packed bed.
For flow of a fluid through a bed of packed particles, the permeability is best understood through the Ergun equation or the Kozeny-Carman equation, both of which relate pressure drop to particle size, bed voidage, and fluid properties.
The Kozeny-Carman form for permeability \(k\) is
\[ k = \frac{d_p^2 \varepsilon^3}{180(1-\varepsilon)^2} \]
where \(d_p\) is the particle diameter and \(\varepsilon\) is the bed voidage (porosity).

Step 2: Analyze option (A).
Since permeability \(k\) depends directly on \(d_p^2\), it is clearly not independent of particle size.
So option (A) is incorrect.

Step 3: Analyze option (B).
From the relation \(k \propto d_p^2\), as the particle size increases, the void channels between particles become wider, so the fluid faces less resistance and permeability increases.
So option (B) is correct.

Step 4: Analyze option (C).
This says the opposite of what the formula shows. Permeability rises, not falls, with particle size, since larger particles leave larger open channels for flow.
So option (C) is incorrect.

Step 5: Analyze option (D).
A real bed rarely has particles of one single size. When the particle size distribution changes, smaller particles can settle into the gaps between larger ones, reducing the void space and lowering permeability, even if the average or largest particle size stays the same. This makes permeability sensitive to how spread out the particle sizes are, not just their average value.
So option (D) is correct.

Step 6: Final conclusion.
The correct statements are that permeability increases with particle size and that it is affected by particle size distribution.
\[ \boxed{\text{Options (B) and (D)}} \]
Hence, the correct answer is options (B) and (D), corresponding to choices 2 and 4.