What it does
A distillation column splits a mixture of two liquids by boiling. Each tray (a “stage”) lets rising vapour and falling liquid reach equilibrium, so the vapour gets a little richer in the more volatile, light component each step up. The McCabe-Thiele diagram is the classic way to count how many such stages a separation needs. You draw the equilibrium curve, the operating lines from the mass balances, and then step between them like a staircase from the top product down to the bottom product.
This tool draws the diagram and counts the stages for you. It also works out the minimum reflux, the minimum number of stages, the best feed stage, the number of real trays for a chosen efficiency, and the column flows.
How to use it
- Choose the equilibrium. With a constant relative volatility α, y = αx / (1 + (α − 1)x). That suits ideal mixtures such as benzene and toluene. For anything else, pick My x–y data and paste or open two columns: liquid mole fraction x and vapour mole fraction y of the light component. The tool adds (0, 0) and (1, 1) and draws a smooth, wiggle-free curve through your points.
- Enter the light-component mole fractions of the feed (xF), distillate (xD) and bottoms (xB).
- Set the feed condition q: 1 for a liquid at its boiling point, 0 for a saturated vapour, a fraction for a part-vapour feed, above 1 for a cold liquid, below 0 for a superheated vapour. It sets the slope of the q-line.
- Choose the reflux: a multiple of the minimum (1.2 to 1.5 is a common design choice), a reflux ratio L/D of your own, or total reflux to see the fewest stages possible.
- Optionally give a feed rate for the flows and an overall tray efficiency to turn theoretical stages into real trays.
What each result means
- Minimum reflux: the lowest reflux at which the separation is possible with endless stages. Usually the pinch is where the q-line meets the curve. With non-ideal data the curve may touch the top operating line above the feed first; the tool then reports a tangent pinch.
- Theoretical stages: counted from the total condenser at the top. The last stage is the partial reboiler. The stepped fraction shows how much of the last step was needed.
- Feed stage: the step that crosses where the operating lines meet. Feeding there gives the fewest stages.
- Minimum stages: from the Fenske equation with a constant α, or by stepping against y = x with data.
- Gilliland estimate: a quick shortcut correlation, useful as a cross-check.
- Flows: distillate D and bottoms B from the component balance, then the liquid and vapour flows above and below the feed.
Worked example
A saturated-liquid feed of 100 kmol/h has 50 % light component. The relative volatility is 2.5. The targets are 95 % in the distillate and 5 % in the bottoms.
The q-line is vertical at x = 0.5 and meets the curve at y = 0.714, so the minimum reflux is 1.100. At 1.5 times that, R = 1.65. Stepping gives 12 theoretical stages (11.67), with the feed on stage 6. Fenske gives at least 6.43 stages, and Gilliland estimates 12.3. At 70 % tray efficiency the column needs 16 real trays plus the reboiler. The flows are D = 50 and B = 50 kmol/h; L = 82.5 and V = 132.5 above the feed; L′ = 182.5 and V′ = 132.5 below it.
Good to know
- The method assumes constant molar overflow: the two components have similar molar heats of vaporisation, so flows stay the same within each section. For very different heats, use an enthalpy method or a process simulator.
- An azeotrope inside your range stops the separation; the tool says so.
- The real-tray count uses one overall efficiency. Real trays vary up the column.
FAQ
Why does the stage count shoot up near the minimum reflux? The operating line gets close to the equilibrium curve, so the steps become tiny near the pinch.
Should the reboiler count as a stage? It usually acts as one equilibrium stage, so the tool counts it. A total condenser does not change composition, so it is not a stage.
Where do I get x–y data? From a lab measurement, a handbook or a thermodynamic model. Check its licence before you share it.
Where the numbers come from
- McCabe-Thiele method (McCabe and Thiele, 1925), Fenske equation (1932) and Gilliland correlation in Eduljee's fitted form (1975): standard chemical engineering methods, written from the equations; no tables copied.
- Example equilibrium data on the page are made up by fibub for illustration; they are not measured values for any real mixture.
- Worked example written by fibub.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.