Distillation Column Sizing Calculator

Distillation Column Sizing Calculator

Wiratama

11/16/20252 min read

1. Definition

A distillation column is a mass transfer device used to separate liquid mixtures based on differences in volatility. It achieves separation through repeated vapor–liquid equilibrium (VLE) stages, allowing more volatile components to rise and less volatile components to fall.

Distillation is one of the most widely used separation processes in chemical engineering, applied in petroleum refining, chemical production, pharmaceuticals, biofuels, and many other industries.

This calculator performs early-stage distillation column sizing, estimating the number of stages, reflux ratio, column height, and diameter based on simplified engineering correlations.

2. Background Theory

2.1 Minimum Number of Stages – Fenske Equation

The Fenske equation estimates the minimum number of theoretical stages required for a desired separation at total reflux (R → ∞):

Where:

  • xD: distillate mole fraction

  • xB bottoms mole fraction

  • α relative volatility

This gives the best possible stage requirement—actual columns need more stages.

2.2 Minimum Reflux Ratio – Underwood Equation

The Underwood equation estimates the minimum reflux ratio Rmin⁡:

(Here a typical light-key root θ≈0.5 is used as an engineering approximation.)

Actual reflux ratio usually lies in:

2.3 Actual Number of Stages – Gilliland Correlation

Using the minimum reflux ratio and minimum stages, the Gilliland correlation estimates actual stages.

2.4 Column Height

Column height depends on:

  • Number of stages

  • Tray spacing (typically 0.45–0.6 m for tray columns)

2.5 Column Diameter – Souders–Brown Equation

Column diameter is determined by allowable vapor velocity, preventing entrainment and flooding:

where:

  • K = Souders–Brown constant (~0.11 m/s for sieve trays)

  • ρL​, ρV: liquid & vapor density

Column vapor volumetric flowrate determines flow area:

3. How the Calculator Works

Step 1 — User Inputs

The calculator requires:

  • Feed composition

  • Distillate and bottoms purity

  • Relative volatility

  • Vapor & liquid density

  • Vapor flowrate (kmol/hr)

  • Tray spacing

Step 2 — Minimum Stages Calculation

The calculator applies the Fenske equation to estimate Nmin⁡​.

Step 3 — Minimum Reflux Ratio

It uses a simplified Underwood estimate for Rmin⁡​.

Step 4 — Actual Stages & Height

Using typical design ratios:

  • Nactual=1.8Nmin⁡

  • H=Nactual×tray spacing

Step 5 — Column Diameter

The calculator:

  1. Computes allowable vapor velocity (Souders–Brown)

  2. Converts vapor flowrate (kmol/hr → m³/s)

  3. Finds required cross-sectional area

  4. Computes the column diameter

4. Applications

This simplified design tool is perfect for:

  • Early feasibility studies

  • Preliminary process design

  • Educational and student calculations

  • Quick distillation sizing before full simulation

For detailed design, rigorous VLE data, hydraulics, Murphree efficiency, and tray design should be included.