Packed tower hydraulics (preloading region): How does pressure drop Δp vary with superficial gas mass velocity G?

Introduction:
Understanding how pressure drop scales with gas throughput in packed towers is crucial for capacity checks and energy estimates. In the preloading (non-flooding) regime with good liquid distribution, the pressure drop follows predictable correlations derived from momentum balance and empirical fits (e.g., generalized pressure drop correlations).

Given Data / Assumptions:

• Packed absorption/stripping tower operating below loading/flooding.
• Clean service; negligible fouling.
• Liquid rate held constant while gas rate varies.

Concept / Approach:
Inertial losses dominate in the preloading region, giving a quadratic dependence of pressure drop on gas mass velocity: Δp ∝ G^2. This mirrors frictional losses in many turbulent flows where dynamic pressure scales with velocity squared. As flooding is approached, the relationship becomes steeper due to interaction with liquid holdup and maldistribution.

Step-by-Step Solution:
Use generalized packed-bed correlation forms where friction factor and Re terms lead to Δp ∝ G^2 when other variables are fixed.Confirm that operation is below loading so liquid holdup changes are modest.Conclude that Δp varies approximately with the square of G.

Verification / Alternative check:
Packed-bed Ergun-type relations and vendor charts show nearly quadratic pressure-drop scaling in this region.

Why Other Options Are Wrong:

• Linear or square-root dependence understates the inertial contribution.
• Independence from G is physically incorrect.
• Inverse dependence contradicts frictional flow behavior.

Common Pitfalls:
Extrapolating the quadratic law into the loading/flooding regime without accounting for increased holdup and entrainment.

Final Answer:
Δp = G^2