Packed-tower design – relating HETP to HTU and absorption factor In a packed absorption column where both the equilibrium and operating lines are straight, how does the ratio HETP/HTU_OG vary with the absorption factor A (A = L/(mG))?

Introduction / Context:
For packed towers, designers often connect the concept of a theoretical plate (HETP, height equivalent to a theoretical plate) to transfer-unit methods (HTU–NTU). When the equilibrium and operating lines are linear, simple relationships exist between HETP, HTU, and the absorption factor A that guide performance estimates and packing selection.

Given Data / Assumptions:

• Linear equilibrium: y* = m x.
• Straight operating line with constant L and G.
• Absorption factor A = L/(mG).

Concept / Approach:
For straight lines, the number of transfer units NTU_OG reduces to a logarithmic function that mirrors the theoretical-stage expression. Under these conditions, an analytical link shows that HETP/HTU_OG is a function of A, becoming unity at A = 1 and increasing as A departs upward from 1 (absorption becomes easier with greater solvent rate relative to equilibrium slope). Thus statements about monotonic increase with A and equality to 1 at A = 1 are both true.

Step-by-Step Solution:

Verification / Alternative check:
Standard packed-column correlations and derivations in mass transfer texts show the equality at A = 1 and increasing ratio with A for systems with linear lines.

Why Other Options Are Wrong:

• “Neither” contradicts known analytical results for linear systems.

Common Pitfalls:
Applying the relationship outside its assumptions (strong curvature in equilibrium, variable L or G due to heat effects) can lead to errors; always check line linearity and constancy of flows.

Final Answer:
both (a) and (b)