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/HTUOG vary with the absorption factor A (A = L/(mG))?
-
Aincreases with increase in the absorption factor
-
Bequals 1 when the absorption factor equals unity
-
Cboth (a) and (b)
-
Dneither (a) nor (b)
Answer
Correct Answer: both (a) and (b)
Explanation
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 NTUOG reduces to a logarithmic function that mirrors the theoretical-stage expression. Under these conditions, an analytical link shows that HETP/HTUOG 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:
Define A = L/(mG).For linear lines, derive NTUOG with logarithmic integration.Relate theoretical stages to NTU to obtain HETP/HTUOG as a function of A.Evaluate at A = 1 → ratio = 1.Observe that increasing A increases HETP/HTUOG per the derived function.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)