Empirical design correlation: For many refinery distillation columns (relative volatility < 4; μ between 0.07 and 1.4 cP), which correlation reasonably estimates the overall column efficiency η (%) as a function of feed viscosity μ (cP)?

Introduction / Context:
Tray/overall efficiencies are needed to translate theoretical stages into actual plates or packed height equivalents. For refinery services with moderate relative volatility, empirical correlations that include feed viscosity provide quick estimates during early design and revamps.

Given Data / Assumptions:

• Hydrocarbon-type systems with relative volatility less than about 4.
• Molal-average feed viscosity μ in the range 0.07–1.4 cP.
• Nominal pressure drops per tray (Δp) are not explicitly included in the chosen simplified form.

Concept / Approach:
Higher viscosity generally reduces mass-transfer coefficients and tray efficiency. Log-viscosity forms capture this trend. The provided option η = 17 − 61.1 log μ is a commonly cited screening form that reflects decreasing efficiency as μ increases within the stated range.

Step-by-Step Solution:
Check limits: at μ ≈ 1 cP (log μ = 0) → η ≈ 17% (plausible for difficult, low-α services).At μ ≈ 0.1 cP (log μ = −1) → η ≈ 78% (higher mass transfer rates).Trend matches observed behavior: lower viscosity → higher efficiency.

Verification / Alternative check:
Plant data and design manuals present similar viscosity-based relationships for preliminary design; detailed rating later refines the estimate using hydrodynamics and property distributions.

Why Other Options Are Wrong:
Other expressions listed either do not yield realistic efficiencies over the stated μ range or lack the correct trend magnitude.

Common Pitfalls:

• Treating such correlations as universal; they are screening tools.
• Ignoring weeping, entrainment, and pressure effects that also impact efficiency.

Final Answer:
η = 17 − 61.1 log μ