1. Calculation Scope & Governing Equations
This module sizes continuous multi-component distillation columns using the classical Fenske-Underwood-Gilliland (FUG) shortcut methodology and Kirkbride feed stage correlation.
$$N_{\text{min}} = \frac{\ln\left[ \left(\frac{x_{LK}}{x_{HK}}\right)_D \cdot \left(\frac{x_{HK}}{x_{LK}}\right)_B \right]}{\ln(\alpha_{LK,HK})} \quad \text{(Fenske Equation)}$$
$$\sum_{i=1}^C \frac{\alpha_i z_{i,F}}{\alpha_i - \theta} = 1 - q, \quad R_{\text{min}} + 1 = \sum_{i=1}^C \frac{\alpha_i x_{i,D}}{\alpha_i - \theta} \quad \text{(Underwood Equations)}$$
$$\frac{N - N_{\text{min}}}{N + 1} = 1 - \exp\left[ \frac{1 + 54.4 X}{11 + 117.2 X} \left(\frac{X - 1}{X^{0.5}}\right) \right] \quad \text{where } X = \frac{R - R_{\text{min}}}{R + 1}$$
$$\frac{N_R}{N_S} = \left[ \left(\frac{z_{HK}}{z_{LK}}\right)_F \cdot \left(\frac{x_{LK,B}}{x_{HK,D}}\right)^2 \cdot \frac{B}{D} \right]^{0.206} \quad \text{(Kirkbride Feed Stage)}$$
2. Standard Parameters & Column Design Rules of Thumb
| Parameter | Recommended Industrial Rule | Engineering Rationale |
|---|---|---|
| Operating Reflux Ratio ($R$) | $1.15 \times R_{\text{min}}$ to $1.30 \times R_{\text{min}}$ | Minimizes lifecycle CAPEX + OPEX (reboiler utility cost). |
| Overall Tray Efficiency ($E_o$) | 60% – 80% (O'Connell Correlation) | Converts theoretical stages to actual mechanical trays. |
| Tray Spacing | 450 mm – 600 mm (18 – 24 in) | Allows internal maintenance access and downcomer foam disengagement. |
| Column Flooding Margin | 75% – 82% of flooding velocity | Souders-Brown vapor velocity limit to prevent jet entrainment. |
3. Engineering Assumptions & Boundary Limits
- Constant Molar Overflow (CMO): Assumes equimolar latent heats of vaporization throughout the rectifying and stripping sections.
- Key Components: Requires explicit designation of Light Key (LK) and Heavy Key (HK). Non-key components are assumed to distribute according to relative volatilities.