Back to Documentation List

Distillation Calculator Documentation

Note: This documentation is based on standard chemical engineering principles for binary distillation. The actual implementation in the code may vary.

1. Objective

The Distillation Calculator is designed to solve preliminary design problems for binary distillation columns. It likely uses shortcut methods to estimate the number of theoretical stages and the required reflux ratio for a given separation.

2. Design Basis & Methodology

The calculator likely employs the Fenske-Underwood-Gilliland (FUG) shortcut method, which is a common approach for preliminary column design.

Key Formulas:

  1. Fenske Equation (Minimum Stages): Calculates the minimum number of theoretical stages (N_min) required at total reflux.

    N_min = log[ (x_D / (1-x_D)) * ((1-x_B) / x_B) ] / log(α_avg)

    Where x_D and x_B are the mole fractions of the light key component in the distillate and bottoms, and α_avg is the average relative volatility.

  2. Underwood Equation (Minimum Reflux): Calculates the minimum reflux ratio (R_min) required for the separation. This involves solving the Underwood equation for a root θ.

  3. Gilliland Correlation (Actual Stages vs. Reflux): An empirical correlation that relates the actual number of stages (N) and actual reflux ratio (R) to their minimum values.

    f( (N - N_min) / (N + 1) ) = g( (R - R_min) / (R + 1) )

3. Input Parameters

  • Feed Composition: Mole fraction of the light key component in the feed.
  • Feed Condition (q-value): Thermal condition of the feed (e.g., q=1 for saturated liquid, q=0 for saturated vapor).
  • Distillate & Bottoms Composition: Desired mole fractions of the light key component in the top and bottom products.
  • Relative Volatility (α): A measure of the separability of the two components.
  • Operating Reflux Ratio: The chosen reflux ratio, often expressed as a multiple of R_min (e.g., R = 1.2 * R_min).

4. Output Results

  • Minimum Number of Stages (N_min): The theoretical minimum stages required.
  • Minimum Reflux Ratio (R_min): The theoretical minimum reflux.
  • Actual Number of Theoretical Stages (N): The estimated number of stages for the specified reflux ratio.
  • Optimal Feed Stage Location: The estimated tray number where the feed should be introduced.

5. Limitations and Assumptions

  • Assumes constant molar overflow (CMO), meaning molar liquid and vapor flow rates are constant in each section of the column.
  • Assumes constant relative volatility.
  • Applies to binary (two-component) systems. For multi-component systems, more rigorous simulation is needed.

6. Example Calculation

Goal: Separate a Benzene-Toluene mixture.

Given:

  • Feed: 50% Benzene (z_F = 0.5), saturated liquid (q = 1).
  • Distillate: 95% Benzene (x_D = 0.95).
  • Bottoms: 5% Benzene (x_B = 0.05).
  • Relative Volatility (α): 2.5 (assumed constant).
  • Operating Reflux (R): 1.5 times the minimum reflux (R_min).

Calculation Steps:

  1. Calculate Minimum Stages (N_min) using Fenske Equation: N_min = log[ (x_D / (1-x_D)) * ((1-x_B) / x_B) ] / log(α) N_min = log[ (0.95/0.05) * (0.95/0.05) ] / log(2.5) = log(19 * 19) / log(2.5) = log(361) / 0.3979 ≈ 6.43

  2. Calculate Minimum Reflux (R_min) using Underwood Equation: First, find the Underwood root θ between 1 and α: (α * z_F) / (α - θ) + ((1-z_F) * 1) / (1 - θ) = 1 - q = 0 Solving (2.5 * 0.5) / (2.5 - θ) + 0.5 / (1 - θ) = 0 gives θ ≈ 1.428. Next, calculate R_min: R_min + 1 = (α * x_D) / (α - θ) + ((1-x_D) * 1) / (1 - θ) R_min + 1 = (2.5 * 0.95) / (2.5 - 1.428) + (0.05) / (1 - 1.428) ≈ 2.215 - 0.117 = 2.098 R_min ≈ 1.1

  3. Determine Actual Reflux (R) and Number of Stages (N): R = 1.5 * R_min = 1.5 * 1.1 = 1.65 Use the Gilliland Correlation. First, calculate the x-axis parameter: X = (R - R_min) / (R + 1) = (1.65 - 1.1) / (1.65 + 1) ≈ 0.208 From a Gilliland plot, X ≈ 0.208 corresponds to Y ≈ 0.4. Now, solve for N using the y-axis parameter: Y = (N - N_min) / (N + 1) => 0.4 = (N - 6.43) / (N + 1) 0.4N + 0.4 = N - 6.43 => 0.6N = 6.83 => N ≈ 11.4

Result: The design requires approximately 12 theoretical stages operating at a reflux ratio of 1.65.

Reference Standards

  • Perry's Chemical Engineers' Handbook: Distillation section correlations.
  • Kister, H.Z.: Distillation Design textbook guidelines (McGraw-Hill).
Go to the Distillation Column Calculator