Distillation Shortcut Design

Distillation Shortcut Design

Overview

Implements the classical shortcut suite:

• Fenske: minimum number of equilibrium stages from xD, xB, and an

averaged relative volatility alpha.

• Underwood: minimum reflux ratio for a multicomponent feed at a given

thermal condition q.

• Gilliland (Molokanov): actual stages from N/Nmin vs R/Rmin.
• McCabe-Thiele: stage stepping on a constant-alpha binary equilibrium

curve, with operating-line intersection from the feed q-line.

The methods are textbook (Seader/Henley, Sinnott, McCabe/Smith/Harriott) and implemented from first principles in engg_skills_common.separations.

Prerequisites

1. uv available.
2. On first use the script writes LICENSE_NOTIFICATION.txt listing the

library terms.

When to Use

• Sizing a new column (number of stages, reflux ratio, feed stage).
• Screening separation feasibility before committing to a rigorous simulation.
• Sanity-checking a rigorous result with an independent calculation path.

Don't use for

• Rigorous tray-by-tray rating or design — use an equilibrium-stage or

rate-based simulator.

• Azeotropic or extractive distillation — the alpha assumption breaks down.
• Reactive distillation, batch distillation, or columns with side draws and

multiple feeds.

• Sub-ambient cryogenic columns where K-values change strongly with stage T.

Utility Scripts

• uv run scripts/shortcut.py fenske --alpha 2.5 --xD 0.95 --xB 0.05 --output /tmp/fenske.json
• uv run scripts/shortcut.py underwood --alphas 4.0,2.0,1.0 --zs 0.4,0.4,0.2 --xds 0.95,0.04,0.01 --q 1.0 --output /tmp/underwood.json
• uv run scripts/shortcut.py gilliland --Nmin 12 --Rmin 1.3 --R 1.8 --output /tmp/gilliland.json
• uv run scripts/shortcut.py mccabe-thiele --alpha 2.5 --xD 0.95 --xB 0.05 --xF 0.40 --q 1.0 --R 2.0 --output /tmp/mt.json

Procedure

1. Decide on light key (LK) and heavy key (HK). Compute or look up the

average relative volatility alpha = K_LK / K_HK over the column.

1. Pick distillate (xD) and bottoms (xB) compositions for the LK from

product specs or recovery targets.

1. Compute Nmin with Fenske.
2. For multicomponent feed, compute Rmin with Underwood at the feed

thermal condition q (1.0 saturated liquid, 0.0 saturated vapor).

1. Pick operating reflux R = 1.2-1.5 × Rmin (industry rule of thumb;

higher gives fewer stages but more reboiler/condenser duty).

1. Use Gilliland to estimate N and the feed-stage ratio.
2. For binary screening with constant alpha, run mccabe-thiele to

sanity-check the integer stage count.

Pitfalls

• Using a feed-zone alpha instead of an averaged alpha across the column.

Fenske and Underwood need a representative value; averaging top and bottom K-values is the usual workaround.

• Underwood's theta is bracketed between successive component alphas;

picking the wrong root gives a useless Rmin. The script bisects only the first valid interval — if your system has multiple distributed components, inspect the theta value carefully.

• Treating R/Rmin of 1.05 or less as feasible; the Gilliland correlation

is increasingly inaccurate in that range and the resulting column would have many stages and small driving forces.

• Forgetting that Fenske returns total stages including the reboiler.
• Using McCabe-Thiele for a non-binary cut.
• Picking R = 1.5 × Rmin and reporting it as optimal without an

energy-vs-capex trade-off check.

• Assuming q = 1 for a partially vaporized feed; even ~10% vapor changes

Rmin noticeably.

• Reporting "10 actual trays" when Gilliland returns "10 equilibrium

stages" — actual tray count needs Murphree (or O'Connell-style) efficiency.

• Using the shortcut output for a tower-control or relief calculation.

Shortcut methods do not give per-stage T/P profiles.

Fallback Strategies

• If the system is too non-ideal for constant-alpha (e.g. methanol-water,

ethanol-water), Fenske/Gilliland gives misleading numbers; switch to a pseudo-binary basis (LK vs HK at top and bottom alphas averaged) and flag the deviation in your report.

• If Underwood's theta is not bracketed, the alphas are likely too closely

spaced (or the feed is too dilute in the keys). Pivot to a McCabe-Thiele treatment of LK/HK at constant average alpha and document the simplification.

Verification

• Run the listed script with representative inputs and an --output file when a deterministic calculation is available.
• Confirm the JSON result contains ok: true, expected units, and no unhandled warnings.
• Check result magnitudes against the stated assumptions, references, and a hand calculation or known operating range before reporting them.

References

• references/methods_summary.md — equations and assumptions for each

shortcut method.

• Seader, Henley, Roper, Separation Process Principles (any recent edition).
• McCabe, Smith, Harriott, Unit Operations of Chemical Engineering.

Anti-Patterns

• Reporting Gilliland stages as the actual tray count without efficiency

derating.

• Using shortcut methods to specify column internals (tray spacing, downcomer,

weir height); those require flooding/loading correlations not in this skill.

• Hiding the R/Rmin ratio in the final report — the optimization context

matters for the reader.

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: jskherman
• Source: jskherman/engg-skills
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.