Permeability tells us how easily a fluid can push through the gaps of a packed bed. Let's check each statement using the Ergun equation, which links pressure drop across a bed to particle size and void fraction.
Independent of particle size: The Ergun equation has particle diameter $d_p$ sitting in the denominator of both its viscous and inertial terms. Changing $d_p$ changes the resistance directly, so permeability cannot be independent of it. This statement is wrong.
Increases with increase in particle size: Bigger particles leave bigger gaps between them for the fluid to pass through. Wider flow channels mean less resistance per unit bed length, which is exactly what a higher permeability means. This statement is right.
Decreases with increase in particle size: This is the reverse of what actually happens. Larger particles open up the bed, they do not choke it, so permeability does not fall as particle size grows. This statement is wrong.
Affected by particle size distribution: A bed is almost never made of one exact particle size in practice. If small particles are mixed among large ones, the small ones can wedge into the pore spaces of the large ones, cutting down the void volume and the flow paths. So the spread of particle sizes, not just a single average size, changes the permeability. This statement is right.
So the correct choices are that permeability increases with particle size, and that it is affected by the particle size distribution.
Let's summarize:
Permeability rises as particle size rises, since larger particles create wider flow channels.
A wide spread of particle sizes lets small grains fill the gaps between large ones, which lowers permeability at a fixed average size.
The final answer is options (B) and (D), that is choices 2 and 4.
