OpenSpecEngineering

Gives a first estimate of a binary distillation column: the minimum stages at total reflux, the minimum reflux ratio, and the theoretical stages at your operating reflux. Process engineers use it for screening before a rigorous simulation.

Equations

N_min = ln[(x_D/(1 − x_D))·((1 − x_B)/x_B)] / ln α

y* = αx / (1 + (α − 1)x)

R_min = (x_D − y′) / (y′ − x′)

X = (R − R_min)/(R + 1)

Y = 1 − exp[((1 + 54.4X)/(11 + 117.2X))·((X − 1)/√X)]

N = (Y + N_min)/(1 − Y)

The first line is the Fenske equation [1]. x_D, z_F and x_B are the mole fractions of the light component in the distillate, feed and bottoms. α is the relative volatility, taken as constant. y* is the vapor in equilibrium with liquid x. The pinch (x′, y′) is where the q-line crosses the equilibrium curve; for q = 1 it is at x′ = z_F. R_min is the reflux whose operating line just touches the pinch [2], [4]. Y is the Gilliland correlation in Molokanov’s equation form [3]. N_min and N both count the reboiler as a stage.

Inputs

• All compositions are mole fractions of the more volatile (light) component, not mass fractions.
• q is the heat needed to vaporize one mole of feed divided by its molar latent heat. It is 1 for a saturated liquid, 0 for a saturated vapor, above 1 when subcooled, and the liquid fraction when partly vaporized.

Limits and common mistakes

• Constant α and constant molar overflow are assumed. Azeotropes or a strongly varying α (such as ethanol–water) need a stage-by-stage construction or a simulator.
• The results are theoretical (equilibrium) stages. Divide by a tray efficiency, often 0.5 to 0.8, to get real trays.
• A partial condenser is also an equilibrium stage. If the column has one, subtract it as well as the reboiler.
• Gilliland is a fit to many columns. Expect about ±10 % on N, more when R is close to R_min.

Worked example

A benzene–toluene splitter takes a 40 mol% benzene feed at its bubble point. It must make 95 % benzene overhead and leave 5 % benzene in the bottoms, with a reflux ratio of 2. How many theoretical stages does it need?

1. Enter Distillate Mole Fraction 0.95, Feed Mole Fraction 0.4 and Bottoms Mole Fraction 0.05.
2. Enter Relative Volatility 2.5, a typical average for benzene–toluene.
3. Leave Feed Condition on Saturated liquid at its bubble point (q = 1).
4. Enter Operating Reflux Ratio 2 and press Solve. The Solution shows: Minimum stages Nmin (Fenske, incl. reboiler): 6.42687
   Pinch liquid composition x': 0.4
   Minimum reflux ratio Rmin: 1.44444
   R / Rmin: 1.38462
   Gilliland ordinate Y: 0.473319
   Theoretical stages N (incl. reboiler): 13.1013

So the column needs about 12.1 theoretical stages plus the reboiler. Check by hand: y′ = 2.5 × 0.4/(1 + 1.5 × 0.4) = 0.625, so R_min = (0.95 − 0.625)/(0.625 − 0.4) = 1.444. N_min = ln(19 × 19)/ln 2.5 = 5.889/0.9163 = 6.43. The rule of thumb N ≈ 2N_min at R of 1.2 to 1.5 times R_min gives about 12.9, close to 13.1.