NGL Fractionation Train Architecture: Column Sizing (FUG Method), Internals & Product Specification Guide

Interactive Engineering Calculation Tool: Model column stages, minimum reflux ratios ($R_{min}$), hydraulic column diameters, and condenser/reboiler duties using the companion NGL Fractionation Train Sizer.

1. Executive Summary & Fractionation Train Configuration

Natural Gas Liquids (NGLs) extracted from cryogenic turboexpander plants or JT dew point units represent a mixed hydrocarbon stream ($\text{C}_2\text{--}\text{C}_6+$) with high commercial value. To convert this raw raw "Y-grade" NGL mix into fungible commodities, gas processing plants route the liquid through an NGL Fractionation Train composed of multi-stage distillation columns operating in series.

The commercial product specifications governing the fractionation train include: * Purity Ethane ($\text{C}_2\text{H}_6$): $\ge 90\text{--}95\ \text{mol}\%$ ethane; maximum $5\ \text{mol}\%$ methane/propane (used for petrochemical ethylene cracking). * Propane (HD-5 Spec): $\ge 90.0\ \text{vol}\%$ propane, $\le 5.0\ \text{vol}\%$ propylene, $\le 2.5\ \text{vol}\%$ butanes (commercial LPG fuel). * Commercial Butane Mix / Isobutane ($\text{i-C}_4$) & Normal Butane ($\text{n-C}_4$): Isobutane for refinery alkylation ($\ge 95\ \text{wt}\%$); Normal butane for gasoline blending ($RVP \le 7\text{--}15\ \text{psi}$). * Natural Gasoline / Pentanes Plus ($\text{C}_5+$): Motor gasoline blendstock or heavy oil diluent ($RVP \le 12\text{--}14\ \text{psia}$).

                  DIRECT SEQUENCE NGL FRACTIONATION TRAIN
Raw NGL Mix (Y-Grade: C2, C3, iC4, nC4, C5+)
  |
  v
+-----------------------+ Overhead: Ethane Gas / Liquid (C2)
|     DEETHANIZER       |-----------------------------------> Ethane Product
| (350 - 450 psig)      |
+-----------+-----------+
            | Bottoms (C3, iC4, nC4, C5+)
            v
  +-----------------------+ Overhead: Propane (C3)
  |     DEPROPANIZER      |-----------------------------------> HD-5 Propane
  | (200 - 250 psig)      |
  +-----------+-----------+
              | Bottoms (iC4, nC4, C5+)
              v
    +-----------------------+ Overhead: Mixed Butanes (iC4 + nC4)
    |     DEBUTANIZER       |-----------------------------------> Split to Deisobutanizer
    | (70 - 100 psig)       |                                     or Commercial LPG
    +-----------+-----------+
                | Bottoms: C5+ Pentanes Plus
                v
        Natural Gasoline (C5+)

2. Distillation Thermodynamics & The Classical FUG Shortcut Method

While commercial process simulators (e.g., Aspen HYSYS, PRO/II) perform rigorous tray-by-tray equilibrium flash iterations using the Peng-Robinson or SRK Equation of State, initial equipment scoping, debottlenecking, and optimization rely on the Fenske-Underwood-Gilliland (FUG) shortcut method.

2.1 Relative Volatility & Key Components

In multi-component fractionation, two components are chosen as the separation keys: * Light Key ($LK$): The lighter component whose recovery in the overhead distillate is strictly specified. * Heavy Key ($HK$): The heavier component whose recovery in the column bottoms is strictly specified.

The relative volatility of any component $i$ with respect to the heavy key is defined by:

$$\alpha_i = \frac{K_i}{K_{HK}} = \frac{y_i / x_i}{y_{HK} / x_{HK}}$$

2.2 Fenske Equation (Minimum Theoretical Stages at Total Reflux)

The minimum number of theoretical equilibrium stages ($N_{min}$) required to achieve the separation at infinite (total) reflux is given by Fenske's equation:

$$N_{min} = \frac{\ln \left[ \left( \frac{d_{LK}}{b_{LK}} \right) \left( \frac{b_{HK}}{d_{HK}} \right) \right]}{\ln(\alpha_{avg, LK})}$$

Where: * $d_{LK}, d_{HK}$ = Molar flow rates of light and heavy keys in the distillate ($\text{lbmol/h}$ or $\text{kmol/h}$) * $b_{LK}, b_{HK}$ = Molar flow rates of light and heavy keys in the bottoms * $\alpha_{avg, LK} = \sqrt{\alpha_{top} \cdot \alpha_{bottom}}$ = Geometric average relative volatility

2.3 Underwood Equations (Minimum Reflux Ratio, $R_{min}$)

For a multi-component feed with thermal quality $q$ (fraction of liquid in feed), the root $\theta$ lies between the relative volatilities of the keys ($\alpha_{HK} < \theta < \alpha_{LK}$) and satisfies:

$$\sum_{i=1}^{C} \frac{\alpha_i z_{i, feed}}{\alpha_i - \theta} = 1 - q$$

Once $\theta$ is determined via Newton-Raphson iteration, the minimum reflux ratio ($R_{min} = (L/D)_{min}$) is calculated from:

$$R_{min} + 1 = \sum_{i=1}^{C} \frac{\alpha_i x_{i, dist}}{\alpha_i - \theta}$$

2.4 Gilliland Correlation (Actual Theoretical Stages)

Industrial fractionation columns operate at an actual reflux ratio $R = 1.15\text{--}1.30 \times R_{min}$ to optimize the trade-off between capital cost (column height) and operating utility cost (reboiler steam/condenser cooling). The actual theoretical stages ($N$) are correlated via Molokanov’s algebraic fit of Gilliland's curve:

$$Y = 1 - \exp \left[ \left( \frac{1 + 54.4 X}{11 + 117.2 X} \right) \left( \frac{X - 1}{\sqrt{X}} \right) \right]$$

Where: $$X = \frac{R - R_{min}}{R + 1}, \quad Y = \frac{N - N_{min}}{N + 1}$$

2.5 Kirkbride Equation (Feed Tray Location)

The ratio of theoretical stages above the feed ($N_{rect}$) to theoretical stages below the feed ($N_{strip}$) is estimated by:

$$\frac{N_{rect}}{N_{strip}} = \left[ \left( \frac{z_{HK}}{z_{LK}} \right) \left( \frac{x_{LK, bot}}{x_{HK, dist}} \right)^2 \left( \frac{B}{D} \right) \right]^{0.206}$$

3. Column Hydraulics & Sizing via Fair's Flooding Method

3.1 Flooding Factor ($C_{sb}$) & Maximum Vapor Velocity

Distillation column diameter ($D_{col}$) is governed by the vapor flooding limit, above which liquid droplets are entrained upward into the tray above, destroying mass transfer efficiency. Fair's flooding correlation models maximum vapor capacity:

$$v_{flood} = C_{sb} \sqrt{\frac{\rho_L - \rho_V}{\rho_V}} \left( \frac{\sigma}{20} \right)^{0.2}$$

Where: * $v_{flood}$ = Flooding superficial vapor velocity ($\text{ft/s}$ or $\text{m/s}$) * $\sigma$ = Surface tension of the liquid ($\text{dynes/cm}$ or $\text{mN/m}$) * $C_{sb}$ = Capacity parameter determined from the Flow Parameter ($F_{lv}$): $$F_{lv} = \frac{L_{mass}}{V_{mass}} \sqrt{\frac{\rho_V}{\rho_L}}$$

For standard $24\text{-inch}$ tray spacing with valve trays: $$C_{sb} \approx 0.045 \times \log_{10}(1 / F_{lv}) + 0.35$$

3.2 Net Column Cross-Sectional Area

The operating superficial vapor velocity is set at $75\%\text{--}82\%$ of flood ($v_{op} = 0.80 \times v_{flood}$):

$$A_{net} = \frac{V_{vol}}{v_{op}} \implies D_{col} = \sqrt{\frac{4 A_{total}}{\pi}} \approx \sqrt{\frac{4 (A_{net} / (1 - A_{downcomer}))}{\pi}}$$

Where downcomer area $A_{downcomer}$ occupies $10\%\text{--}15\%$ of total column cross-section.

4. Sequence Architecture: Direct vs. Indirect vs. DWC

   DIRECT SEQUENCE (CONVENTIONAL)           DIVIDING WALL COLUMN (PETLYUK DWC)
   * Lightest component removed first       * Separates 3 pure cuts in 1 shell
   * Deethanizer -> Depropanizer -> Debutanizer  * 25-35% CapEx and OpEx energy savings

   [ Deethanizer ] -> C2                     +---------------------------+
         |                                   |         Vapor Space       |
         v                                   +=============+=============+
   [ Depropanizer ] -> C3                    | Ethane Cut  | Dividing    |
         |                                   |             | Wall        |
         v                                   |-------------|-------------|
   [ Debutanizer ]  -> C4                    | Propane Cut | Side-Draw   |
         |                                   |=============+=============|
         v C5+                               | C4 / C5+ Bottoms Product  |
                                             +---------------------------+

5. Quantitative Technology Selection Matrix

6. Step-by-Step Fractionation Sizing Workflow

   STEP 1: FEED CHARACTERIZATION & COMPONENT BALANCE
   * Establish raw NGL feed rate (BPD or lbmol/h), composition, and enthalpy.
   * Define sharp recovery specifications for Light Key and Heavy Key.
                         |
                         v
   STEP 2: SHORTCUT FENSKE-UNDERWOOD-GILLILAND (FUG)
   * Calculate minimum stages N_min at total reflux via Fenske.
   * Determine Underwood theta root and calculate R_min.
   * Set actual reflux ratio R = 1.20 * R_min; obtain actual theoretical stages N.
                         |
                         v
   STEP 3: TRAY HYDRAULIC SIZING (FAIR METHOD)
   * Calculate top and bottom vapor volumetric flow rates and densities.
   * Compute flow parameter F_lv, Fair flooding factor C_sb, and v_flood.
   * Size column internal diameter D_col at 80% flood.
                         |
                         v
   STEP 4: TRAY COUNT & COLUMN HEIGHT
   * Select overall tray efficiency E_o (typically 75% for Deethanizer, 85% for Depropanizer).
   * Calculate actual tray count N_actual = N / E_o.
   * Column Height H_col = N_actual * Spacing + Skirt + Vapor disengagement.
                         |
                         v
   STEP 5: HEAT EXCHANGER DUTIES
   * Condenser Duty Q_c = V_top * delta_H_vap.
   * Reboiler Duty Q_r = Q_c + Enthalpy_products - Enthalpy_feed.

7. Fully Worked Industrial Example

Problem Statement:

Design a commercial Depropanizer column processing a deethanized bottoms stream:

• Feed Flow Rate: $12{,}000\ \text{BPD}$ ($105{,}000\ \text{lb/h} = 1{,}850\ \text{lbmol/h}$)
• Feed Composition: Propane (LK) $52.0\ \text{mol}\%$, Isobutane (HK) $20.0\ \text{mol}\%$, Normal Butane $22.0\ \text{mol}\%$, Pentanes Plus $6.0\ \text{mol}\%$
• Operating Pressure: $240\ \text{psig}$ ($254.7\ \text{psia}$)
• Light Key (Propane) Recovery in Distillate: $98.5\%$
• Heavy Key (Isobutane) Recovery in Bottoms: $98.0\%$
• Average Relative Volatility ($\alpha_{LK/HK} = \alpha_{C3/iC4}$): $1.95$
• Feed Condition: Saturated liquid at bubble point ($q = 1.0$)
• Tray Spacing: $24\ \text{inches}$ ($0.61\ \text{m}$); Valve trays with overall efficiency $E_o = 80\%$

Step 1: Component Material Balance

• Propane in Feed: $1{,}850 \times 0.52 = 962.0\ \text{lbmol/h}$
• Isobutane in Feed: $1{,}850 \times 0.20 = 370.0\ \text{lbmol/h}$
• Propane in Distillate ($d_{LK}$): $962.0 \times 0.985 = 947.57\ \text{lbmol/h}$
• Propane in Bottoms ($b_{LK}$): $962.0 - 947.57 = 14.43\ \text{lbmol/h}$
• Isobutane in Bottoms ($b_{HK}$): $370.0 \times 0.980 = 362.60\ \text{lbmol/h}$
• Isobutane in Distillate ($d_{HK}$): $370.0 - 362.60 = 7.40\ \text{lbmol/h}$
• Total Distillate ($D$): $\approx 947.57 + 7.40 = 954.97\ \text{lbmol/h}$
• Total Bottoms ($B$): $\approx 1{,}850 - 955 = 895.0\ \text{lbmol/h}$

Step 2: Fenske Minimum Stages ($N_{min}$)

$$N_{min} = \frac{\ln \left[ \left( \frac{d_{LK}}{b_{LK}} \right) \left( \frac{b_{HK}}{d_{HK}} \right) \right]}{\ln(\alpha_{avg})} = \frac{\ln \left[ \left( \frac{947.57}{14.43} \right) \left( \frac{362.60}{7.40} \right) \right]}{\ln(1.95)}$$ $$\left( \frac{947.57}{14.43} \right) = 65.667; \quad \left( \frac{362.60}{7.40} \right) = 49.00$$ $$65.667 \times 49.00 = 3{,}217.7 \implies \ln(3{,}217.7) = 8.0764$$ $$\ln(1.95) = 0.6678$$ $$N_{min} = \frac{8.0764}{0.6678} = \mathbf{12.09\ \text{theoretical stages}}$$

Step 3: Underwood Minimum Reflux Ratio ($R_{min}$)

For saturated liquid feed ($q = 1.0$), $1 - q = 0$: $$\sum \frac{\alpha_i z_i}{\alpha_i - \theta} = 0 \implies \theta \approx 1.425$$ Using $\theta$ in the second Underwood equation gives: $$R_{min} = 1.34$$ Operating reflux ratio ($R = 1.25 \times R_{min}$): $$R = 1.25 \times 1.34 = \mathbf{1.675}$$

Step 4: Gilliland Theoretical Stages ($N$)

• $X = \frac{R - R_{min}}{R + 1} = \frac{1.675 - 1.34}{1.675 + 1} = \frac{0.335}{2.675} = 0.1252$
• Using Molokanov’s correlation: $Y \approx 0.525$
• $Y = \frac{N - N_{min}}{N + 1} \implies 0.525 (N + 1) = N - 12.09$
• $0.525 N + 0.525 = N - 12.09 \implies 0.475 N = 12.615 \implies N = \mathbf{26.6\ \text{stages}}$
• Actual Trays ($E_o = 0.80$): $$N_{actual} = \frac{26.6}{0.80} \approx \mathbf{34\ \text{actual trays}}$$

Step 5: Column Diameter via Fair's Flooding

At the top of the column ($T_{top} \approx 120^\circ\text{F} = 322\ \text{K}$, $P = 250\ \text{psia}$): * Vapor Density ($\rho_V$): $2.42\ \text{lb/ft}^3$; Liquid Density ($\rho_L$): $29.8\ \text{lb/ft}^3$ * Vapor Flow Rate ($V = D (R + 1)$): $$V = 955 \times (1.675 + 1) = 2{,}555\ \text{lbmol/h} \times 44.1\ \text{lb/lbmol} = 112{,}675\ \text{lb/h}$$ $$V_{vol} = \frac{112{,}675}{2.42 \times 3{,}600} = 12.93\ \text{ft}^3/\text{s}$$ * Flow Parameter ($F_{lv}$): $$L_{mass} = 955 \times 1.675 \times 44.1 = 70{,}545\ \text{lb/h}$$ $$F_{lv} = \left( \frac{70{,}545}{112{,}675} \right) \sqrt{\frac{2.42}{29.8}} = 0.626 \times 0.285 = 0.178$$ * Capacity Factor ($C_{sb}$): $$C_{sb} \approx 0.32\ \text{ft/s}$$ * Flooding Velocity ($v_{flood}$): $$v_{flood} = 0.32 \times \sqrt{\frac{29.8 - 2.42}{2.42}} = 0.32 \times \sqrt{11.31} = 0.32 \times 3.363 = 1.076\ \text{ft/s}$$ * Operating Velocity ($v_{op} = 0.80 \times 1.076 = 0.861\ \text{ft/s}$): $$A_{net} = \frac{12.93\ \text{ft}^3/\text{s}}{0.861\ \text{ft/s}} = 15.02\ \text{ft}^2$$ * Total Column Area ($A_{downcomer} \approx 12\%$): $$A_{total} = \frac{15.02}{1 - 0.12} = 17.07\ \text{ft}^2$$ $$D_{col} = \sqrt{\frac{4 \times 17.07}{\pi}} = \sqrt{21.73} = \mathbf{4.66\ \text{ft}} \implies \mathbf{5.0\ \text{ft (1.52 m) Inside Diameter}}$$

8. Diagnostic Troubleshooting & Failure Mode Matrix

Engineering Design Verification: To perform detailed FUG shortcut calculations, size column diameters across variable tray spacings, and evaluate reboiler/condenser thermal duties, use the NGL Fractionation Train Sizer.