Worked Example: Calculating NGL Recovery (GPM), Plant Gas Shrinkage & Condensate Stabilizer Sizing

Natural Gas Liquids (NGL)—comprising ethane ($\text{C}_2$), propane ($\text{C}_3$), butanes ($\text{iC}_4, \text{nC}_4$), and natural gasoline ($\text{C}_5+$)—represent high-value petrochemical feedstocks. Extracting NGL via cryogenic expansion or mechanical refrigeration captures substantial commercial revenue uplift. However, extracting liquid hydrocarbons causes Plant Volumetric Shrinkage (reduced sales gas volume) and Residue Gas Calorific Derating (lowered BTU content). Simultaneously, raw recovered liquids must be fractionated in a Condensate Stabilizer to hit Reid Vapor Pressure (RVP) limits safe for atmospheric storage.

This worked example details the complete process calculation for a $20.0\text{ MMSCFD}$ rich gas cryogenic turboexpander plant, evaluating component GPM potential, liquid barrel rates (BPD), plant gas shrinkage, sales gas Wobbe derating, and stabilizer column diameter and reboiler duty.

1. Design Basis & Raw Gas Chromatographic Composition

A gas processing facility treats $20.0\text{ MMSCFD}$ ($23,597\text{ Sm}^3/\text{h}$) of rich associated gas at $65.0\text{ barg}$ and $30.0^\circ\text{C}$:

2. Step 1: Hydrocarbon Liquid Potential (GPM)

The theoretical liquid content in Gallons per Thousand Standard Cubic Feet (GPM) is calculated via GPA Standard 2145:

$$\text{GPM}_i = y_i \times \frac{1,000\text{ SCF}}{379.482\text{ SCF/lbmol}} \times \left(\frac{\text{gal}}{\text{lbmol}}\right)_i$$

Component GPM Calculation:

• Ethane ($\text{C}_2$): $0.085 \times \frac{1,000}{379.482} \times 10.121 = \mathbf{2.267\text{ GPM}}$
• Propane ($\text{C}_3$): $0.045 \times \frac{1,000}{379.482} \times 10.437 = \mathbf{1.238\text{ GPM}}$
• i-Butane ($\text{iC}_4$): $0.012 \times \frac{1,000}{379.482} \times 12.396 = \mathbf{0.392\text{ GPM}}$
• n-Butane ($\text{nC}_4$): $0.018 \times \frac{1,000}{379.482} \times 11.945 = \mathbf{0.567\text{ GPM}}$
• i-Pentane ($\text{iC}_5$): $0.005 \times \frac{1,000}{379.482} \times 13.865 = \mathbf{0.183\text{ GPM}}$
• n-Pentane ($\text{nC}_5$): $0.005 \times \frac{1,000}{379.482} \times 13.722 = \mathbf{0.181\text{ GPM}}$
• Hexanes Plus ($\text{C}_6+$): $0.005 \times \frac{1,000}{379.482} \times 16.522 = \mathbf{0.218\text{ GPM}}$

Summary Liquid Potentials:

• Total $\text{C}_2+$ GPM Potential $= 2.267 + 1.238 + 0.392 + 0.567 + 0.183 + 0.181 + 0.218 = \mathbf{5.046\text{ GPM}}$
• Total $\text{C}_3+$ GPM Potential $= \mathbf{2.779\text{ GPM}}$

3. Step 2: Cryogenic Turboexpander Recovery Yields & Production (BPD)

A cryogenic turboexpander plant chilling gas to $-85^\circ\text{C}$ achieves deep extraction: * $\text{C}_1$ Recovery: $0.0\%$ * $\text{C}_2$ Recovery: $85.0\%$ * $\text{C}_3$ Recovery: $98.0\%$ * $\text{i-C}_4, \text{n-C}_4$ Recovery: $99.5\%$ * $\text{C}_5+$ Recovery: $100.0\%$

Recovered Liquid GPM:

$$\text{GPM}_{rec} = (2.267 \times 0.85) + (1.238 \times 0.98) + (0.959 \times 0.995) + (0.582 \times 1.0)$$ $$\text{GPM}_{rec} = 1.927 + 1.213 + 0.954 + 0.582 = \mathbf{4.676\text{ GPM Recovered}}$$

Daily Liquid Barrels per Day (BPD):

For a $20.0\text{ MMSCFD}$ feed rate ($20,000\text{ MSCF/day}$):

$$\text{Liquid Production} = \frac{20,000\text{ MSCF} \times 4.676\text{ GPM}}{42\text{ gal/bbl}} = \mathbf{2,226.7\text{ BPD}} \quad (\mathbf{354.0\text{ m}^3/\text{d}})$$

Mass rate of NGL product: $\mathbf{8,740\text{ kg/h}}$ ($209.8\text{ tonnes/day}$).

4. Step 3: Plant Volumetric Gas Shrinkage

Every gallon of extracted liquid represents hydrocarbon vapor removed from the sales gas stream. The vapor equivalent factor for the recovered NGL mix averages $36.8\text{ SCF of gas per gallon of liquid}$:

Gas Equivalent Shrinkage:

$$Q_{shrink} = \frac{20,000\text{ MSCF} \times 4.676\text{ GPM} \times 36.8\text{ SCF/gal}}{1,000,000} = \mathbf{3.44\text{ MMSCFD}}$$

Residue Sales Gas Flow Rate:

$$Q_{residue} = Q_{inlet} - Q_{shrink} = 20.00 - 3.44 = \mathbf{16.56\text{ MMSCFD}} \quad (\mathbf{19,539\text{ Sm}^3/\text{h}})$$

Volumetric Shrinkage Factor:

$$S_f = \frac{Q_{residue}}{Q_{inlet}} = \frac{16.56}{20.00} = \mathbf{0.828} \quad (\mathbf{17.20\%\text{ Volumetric Shrinkage}})$$

5. Step 4: Residue Gas Energy & Wobbe Index Derating

Recovering ethane, propane, and butane removes the highest-heating-value molecules:

Gross Heating Value (HHV) Comparison:

• Raw Inlet Gas: $\mathbf{1,228.4\text{ BTU/SCF}}$ ($45.76\text{ MJ/m}^3$)
• Residue Sales Gas: $\mathbf{1,028.5\text{ BTU/SCF}}$ ($38.31\text{ MJ/m}^3$)
• Calorific Derate: $\frac{1,228.4 - 1,028.5}{1,228.4} \times 100\% = \mathbf{16.27\%}$

Wobbe Index Evaluation:

• Inlet Wobbe Index: $\mathbf{50.84\text{ MJ/m}^3}$
• Residue Wobbe Index: $\mathbf{47.88\text{ MJ/m}^3}$
• (Interstate pipeline tariff compliant: $47 - 52\text{ MJ/m}^3$)

6. Step 5: Condensate Stabilizer Column Design (RVP Control)

Unstabilized raw liquids from the high-pressure cryogenic cold separator are saturated with dissolved light ends. A condensate stabilizer strips these lights to produce an ASTM D323 Reid Vapor Pressure of $10.0\text{ psia}$ safe for floating-roof tanks:

Stabilizer Column Parameters:

• Operating Column Pressure: $7.0\text{ barg}$ ($8.01\text{ bar(a)} = 116.3\text{ psia}$)
• Number of Valve Trays: 20 Trays (Feed at Tray 5)
• Reboiler Temperature: $\mathbf{188.5^\circ\text{C}}$ ($371.3^\circ\text{F}$)
• Condenser Temperature: $\mathbf{49.0^\circ\text{C}}$ ($120.2^\circ\text{F}$)
• Stabilizer Inside Diameter: 24 inches ($0.61\text{ m}$)
• Reboiler Thermal Duty: $\mathbf{355.0\text{ kW}}$ ($1.21\text{ MMBtu/h}$)

7. Complete Performance & Yield Dashboard