1. Overview & Applications
A turboexpander is a centrifugal or axial flow turbine that recovers energy from high-pressure gas by expanding it through a pressure reduction. The expansion process cools the gas (Joule-Thomson effect plus work extraction), making turboexpanders essential for cryogenic NGL recovery and refrigeration.
NGL recovery plants
Cryogenic processing
Expand sales gas from 600–1200 psia to 200–400 psia, cooling to −40°F to −100°F for ethane+ recovery.
Power generation
Energy recovery
Expander drives compressor (residue gas recompression) or electric generator (1–5 MW typical).
Liquefaction cycles
LNG/NGL plants
Nitrogen or methane expanders provide refrigeration for LNG liquefaction cycles.
Pressure letdown
Energy efficiency
Replace JT valves with expanders to recover energy from pipeline pressure reductions.
Key Concepts
- Isentropic efficiency: Ratio of actual enthalpy drop to ideal (isentropic) enthalpy drop
- Expansion ratio: Inlet pressure divided by outlet pressure (typical 2:1 to 4:1)
- Brake power: Actual shaft power delivered by expander to compressor or generator
- Polytropic efficiency: Path efficiency independent of pressure ratio (85–90% typical)
Why efficiency matters: A 5% increase in expander efficiency (e.g., 80% to 85%) results in 10–15°F additional cooling, which can increase ethane recovery by 2–5% and propane+ recovery by 1–3%, worth millions in annual revenue for large plants.
2. Expander Thermodynamics
The expansion process in a turboexpander is approximately isentropic (constant entropy) in ideal case, but real processes have friction, heat leak, and aerodynamic losses that reduce efficiency.
Isentropic (Ideal) Expansion
Ideal Expansion Process:
For isentropic expansion (s₁ = s₂):
ΔH_isentropic = H₁ - H₂s
Where:
H₁ = Inlet enthalpy (Btu/lb or kJ/kg)
H₂s = Outlet enthalpy at constant entropy (Btu/lb or kJ/kg)
s₁ = s₂ (entropy constant for ideal expansion)
Temperature drop for ideal gas approximation:
T₂s / T₁ = (P₂ / P₁)^((k-1)/k)
Where:
k = Cp/Cv (specific heat ratio ≈ 1.27 for natural gas)
P₁, P₂ = Inlet and outlet pressures (psia)
T₁, T₂s = Inlet and isentropic outlet temperatures (°R)
Actual Expansion with Efficiency
Real Expansion Process:
Actual enthalpy drop:
ΔH_actual = η_isentropic × ΔH_isentropic
ΔH_actual = H₁ - H₂
Actual outlet enthalpy:
H₂ = H₁ - (η × (H₁ - H₂s))
Actual temperature:
T₂ > T₂s (less cooling than ideal due to inefficiency)
Brake power:
W = ṁ × ΔH_actual × η_mechanical
Where:
ṁ = Mass flow rate (lb/hr or kg/s)
η_mechanical = Mechanical efficiency (0.95–0.98)
W = Shaft power (HP or kW)
Expansion Ratio Selection
| Expansion Ratio (P₁/P₂) | Temperature Drop (approx) | Application | Typical Efficiency |
|---|---|---|---|
| 1.5:1 to 2:1 | 40–60°F | Shallow propane+ recovery | 78–82% |
| 2:1 to 3:1 | 60–100°F | Ethane recovery, GSP plants | 82–86% |
| 3:1 to 4:1 | 100–140°F | Deep ethane recovery | 84–88% |
| 4:1 to 6:1 | 140–180°F | LNG, nitrogen cycles | 80–85% (multi-stage) |
Example Calculation
Calculate outlet temperature for gas expansion from 1000 psia, 80°F to 250 psia with 85% efficiency:
Given:
P₁ = 1000 psia, T₁ = 80°F = 539.67°R
P₂ = 250 psia
η = 0.85, k = 1.27
Step 1: Calculate isentropic outlet temperature
T₂s / 539.67 = (250 / 1000)^((1.27-1)/1.27)
T₂s / 539.67 = (0.25)^(0.2126)
T₂s / 539.67 = 0.6594
T₂s = 355.8°R = −103.9°F
Step 2: Calculate actual enthalpy drop (from EOS or charts)
Using Peng-Robinson EOS for natural gas (SG=0.6):
H₁ = 280 Btu/lb, H₂s = 190 Btu/lb
ΔH_isentropic = 280 - 190 = 90 Btu/lb
Step 3: Calculate actual enthalpy drop
ΔH_actual = 0.85 × 90 = 76.5 Btu/lb
H₂ = 280 - 76.5 = 203.5 Btu/lb
Step 4: Find actual outlet temperature (from EOS)
T₂ ≈ −85°F (18.9°F warmer than isentropic due to 85% efficiency)
Temperature drop: 80 - (−85) = 165°F actual vs. 184°F ideal
Power Generation
Brake Power Calculation:
W_brake = ṁ × ΔH_actual × η_mechanical / 2545
Where:
ṁ = Mass flow rate (lb/hr)
ΔH_actual = Actual enthalpy drop (Btu/lb)
η_mechanical = 0.96 typical
2545 = Conversion factor (Btu/hr to HP)
Example:
ṁ = 100,000 lb/hr (≈ 50 MMscfd)
ΔH_actual = 76.5 Btu/lb
η_mechanical = 0.96
W_brake = 100,000 × 76.5 × 0.96 / 2545
W_brake = 2885 HP (2.15 MW)
This power drives the residue gas compressor or generator.
3. Isentropic Efficiency Calculations
Isentropic efficiency quantifies how closely the real expansion approaches the ideal isentropic process. It accounts for aerodynamic losses, mechanical friction, and heat transfer.
Isentropic Efficiency Definition
Isentropic Efficiency:
η_isentropic = ΔH_actual / ΔH_isentropic
η_isentropic = (H₁ - H₂) / (H₁ - H₂s)
Or in terms of temperature (approximate for ideal gas):
η_isentropic ≈ (T₁ - T₂) / (T₁ - T₂s)
Where:
H₁ = Inlet enthalpy
H₂ = Actual outlet enthalpy
H₂s = Isentropic outlet enthalpy (at same P₂, s₂ = s₁)
T₁, T₂, T₂s = Temperatures (absolute)
Typical values:
- Modern expanders: 82–88%
- Older designs: 75–82%
- Small expanders (<500 HP): 70–80%
- Large expanders (>2000 HP): 85–88%
Polytropic Efficiency
Polytropic efficiency is path-independent and better for comparing expanders at different pressure ratios:
Polytropic Efficiency:
η_polytropic = ln(P₁/P₂) / ln(T₁/T₂) × (k-1)/k
Relationship to isentropic efficiency:
η_isentropic = [(P₂/P₁)^((k-1)/k × η_poly) - 1] / [(P₂/P₁)^((k-1)/k) - 1]
Polytropic efficiency is typically 2–4% higher than isentropic:
- Polytropic: 85–90%
- Isentropic: 82–88%
Use polytropic efficiency for:
- Comparing expanders at different pressure ratios
- Multi-stage expander design
- Performance trending over time
Efficiency Loss Mechanisms
| Loss Mechanism | Typical Impact | Mitigation Strategy |
|---|---|---|
| Aerodynamic losses (blade friction) | 4–8% | Optimized blade design, smooth surfaces |
| Tip clearance leakage | 2–4% | Tight clearances, labyrinth seals |
| Mechanical friction (bearings) | 2–4% | Magnetic bearings, low-friction seals |
| Inlet flow distortion | 1–3% | Inlet guide vanes, flow straighteners |
| Off-design operation | 2–6% | Variable nozzles, proper sizing |
| Heat leak (ambient) | 1–2% | Insulation, cold box enclosure |
Measuring Expander Efficiency
In operating plants, efficiency is determined from measurements:
Field Efficiency Measurement:
Method 1: Using enthalpies (requires composition + P/T)
η = (H₁_measured - H₂_measured) / (H₁_measured - H₂s_calculated)
Required measurements:
- Inlet P, T, composition → H₁ from EOS
- Outlet P, T, composition → H₂ from EOS
- Calculate H₂s from inlet entropy at outlet pressure
Method 2: Using power output (if driving compressor)
W_measured = Compressor power + mechanical losses
ΔH_actual = W_measured / (ṁ × η_mechanical)
η = ΔH_actual / ΔH_isentropic
Method 3: Using temperature (approximate)
η ≈ (T₁ - T₂_measured) / (T₁ - T₂s_calculated)
Accuracy: ±2–5% typical for field measurements
Efficiency degradation: Expander efficiency decreases 0.5–1% per year due to erosion, fouling, and seal wear. Performance testing every 1–2 years identifies when overhaul is needed (typically every 3–5 years or 30,000–50,000 operating hours).
Efficiency Correction Factors
- Molecular weight effect: Higher MW gas → lower efficiency (heavy hydrocarbons increase losses)
- Reynolds number: Low flow rates → lower Re → increased viscous losses
- Pressure ratio: Efficiency peaks at design pressure ratio (±10% off-design reduces efficiency 2–3%)
- Inlet temperature: Cold inlet (e.g., after chilling) → higher density → improved efficiency
- Wet gas operation: Liquid carryover → erosion and efficiency loss (install upstream separator)
4. NGL Recovery Integration
In cryogenic NGL recovery plants, the turboexpander is the heart of the process. It provides the deep cooling needed to condense ethane, propane, and heavier hydrocarbons while recovering energy.
Typical Expander Process Flow
Cryogenic Turboexpander Process:
1. Feed gas conditioning:
- Dehydration to <1 ppmv H₂O (prevent hydrates/ice)
- Mercury removal (protect aluminum exchangers)
- CO₂ removal if >2% (prevent dry ice formation)
2. Pre-cooling:
- Propane refrigeration to 0°F to +20°F
- Or cold residue gas heat exchange
3. Turboexpander:
Inlet: 600–1200 psia, +10°F to +40°F
Outlet: 200–400 psia, −40°F to −100°F
Power: 500–5000 HP drives residue compressor
4. Cold separator (demethanizer feed):
- Separate vapor (methane-rich) from liquid (NGL)
- Vapor to demethanizer overhead
- Liquid to demethanizer feed tray
5. Residue gas recompression:
- Compressor driven by expander
- Compress to pipeline pressure 800–1200 psia
- Aftercooling before sales
NGL Recovery vs. Temperature
| Outlet Temperature | Ethane Recovery | Propane+ Recovery | Plant Type |
|---|---|---|---|
| +20°F to 0°F | < 20% | 85–92% | Propane recovery only |
| 0°F to −20°F | 20–40% | 92–96% | Shallow ethane rejection |
| −20°F to −40°F | 40–70% | 96–98% | Moderate ethane recovery |
| −40°F to −80°F | 70–90% | 98–99.5% | High ethane recovery |
| −80°F to −110°F | > 90% | > 99.5% | Maximum ethane recovery |
Optimization of Recovery vs. Power
The trade-off between NGL recovery and power generation is a key economic decision:
Recovery-Power Trade-off:
Higher expansion ratio → Lower temperature → More NGL recovery
BUT: Higher pressure ratio → More power to recompress residue gas
Economic balance:
Value of incremental NGL vs. Cost of recompression power
Example calculation:
Increase expansion from 3:1 to 4:1:
- Ethane recovery increases 65% → 80% (+15%)
- Outlet P decreases 300 psia → 225 psia
- Compressor discharge P must increase to same sales pressure
- Additional compressor power: +400 HP (+$200k/year fuel)
Incremental ethane revenue:
15% × 1000 bbl/day × 365 days × $25/bbl = $1.37 million/year
Net benefit: $1.37M - $0.20M = $1.17M/year → Optimize for recovery
But if ethane price < $15/bbl, may optimize for rejection (less compression).
Hydrate and Ice Formation Prevention
Critical concern in expander operation at cryogenic temperatures:
- Dehydration requirement: <1 ppmv H₂O to prevent ice formation at −40°F and below
- TEG dehydration: Typical method, achieves 1–7 ppmv (use TEG stripping for <1 ppmv)
- Molecular sieve: Achieves <0.1 ppmv for very low temperatures (−80°F to −110°F)
- Methanol injection: Emergency measure only; avoid liquid methanol in expander (erosion risk)
- CO₂ limit: Keep <50 ppm to prevent dry ice at −100°F; <2% at −40°F
Dehydration criticality: Ice formation in the expander wheel causes immediate catastrophic failure. A single hydrate particle can destroy $2–5 million in equipment in seconds. Continuous online moisture analyzers with automatic shutdown at 5 ppmv are standard practice.
5. Compressor-Expander Matching
Most turboexpanders drive a centrifugal compressor on the same shaft (expander-compressor or E-C unit). Proper matching ensures stable operation across the full operating range.
Mechanical Coupling Options
Three Coupling Configurations:
1. Direct drive (common shaft):
Expander → Compressor (same speed, no gearbox)
Advantages: Simple, reliable, no gear losses
Disadvantages: Fixed speed ratio, limited turndown
2. Geared drive:
Expander → Gearbox → Compressor (different speeds)
Advantages: Optimize each machine independently
Disadvantages: Gear losses (2–3%), maintenance
3. Electric motor assist/generator:
Expander + Motor/Generator → Compressor
Advantages: Variable power, grid export, startup flexibility
Disadvantages: Cost, complexity, electrical infrastructure
Most NGL plants: Direct drive (85% of installations)
Large plants (>200 MMscfd): Geared or motor-assisted (15%)
Power Balance Matching
Power Balance Equation:
W_expander = W_compressor + W_losses
W_expander = ṁ_exp × ΔH_exp × η_exp
W_compressor = ṁ_comp × ΔH_comp / η_comp
W_losses = Bearing friction + windage + seal leakage (2–4% of total)
For stable operation:
W_expander ≥ W_compressor + W_losses
Startup requirement:
Motor provides initial power until expander develops sufficient power.
Typical startup sequence:
1. Motor starts compressor (no expander flow)
2. Feed gas admitted to expander
3. Expander accelerates, power increases
4. At 80% speed, motor load transfers to expander
5. Motor shifts to helper/generator mode
Operating Range Matching
| Operating Condition | Expander Power | Compressor Power | Balance Strategy |
|---|---|---|---|
| Design point (100%) | 3000 HP | 2850 HP | 5% margin for losses/variation |
| Maximum rate (110%) | 3450 HP | 3400 HP | Motor absorbs excess or exports |
| Minimum rate (60%) | 1650 HP | 1550 HP | Both machines at reduced efficiency |
| Startup (0–60%) | 0–1650 HP | Motor provides power | Variable frequency drive on motor |
Speed Matching Considerations
Rotational Speed Compatibility:
Expander optimal speed: f(P_ratio, flow, wheel diameter)
Compressor optimal speed: f(compression_ratio, flow, impeller diameter)
Typical speeds:
- Small units (500–1500 HP): 15,000–25,000 RPM
- Medium units (1500–3500 HP): 10,000–18,000 RPM
- Large units (>3500 HP): 8,000–14,000 RPM
Speed ratio for geared systems:
SR = N_compressor / N_expander = 0.8 to 1.5
Design process:
1. Select expander for required expansion duty
2. Calculate expander power output at design speed
3. Design compressor to absorb that power at compatible speed
4. If direct drive: Iterate to find common optimal speed
5. If geared: Select gear ratio to optimize both independently
Vendor iterates through multiple impeller/wheel designs to achieve match.
Turndown and Capacity Control
Methods to maintain stable operation at reduced rates:
- Inlet guide vanes (IGV): Vary expander inlet flow angle, maintains efficiency at 60–110% design flow
- Expander bypass: Route gas around expander through JT valve (loses power recovery, emergency only)
- Compressor recycle: Recirculate compressed gas to prevent surge at low rates
- Variable speed (motor assist): Slow down entire shaft to match reduced flow (60–105% speed typical)
- Multiple trains: Run 1, 2, or 3 trains to match plant throughput (50%, 75%, 100% capacity)
Example Matching Calculation
Expander-Compressor Sizing Example:
Given:
Plant capacity: 100 MMscfd (50,000 lb/hr gas, MW = 19)
Expander inlet: 1000 psia, 40°F
Expander outlet: 250 psia (4:1 expansion)
Compressor inlet: 250 psia, −70°F (expander outlet + separator)
Compressor outlet: 1000 psia (sales gas pressure)
Step 1: Calculate expander power
Using Peng-Robinson EOS:
H₁ = 295 Btu/lb, H₂s = 198 Btu/lb, ΔH_isen = 97 Btu/lb
η_exp = 0.86
ΔH_actual = 0.86 × 97 = 83.4 Btu/lb
W_exp = 50,000 × 83.4 / 2545 = 1638 HP
Step 2: Calculate compressor power required
Residue gas: 48,000 lb/hr (2000 lb/hr NGL extracted)
Using compressor curves for 4:1 compression at −70°F inlet:
ΔH_comp = 115 Btu/lb (polytropic head)
η_comp = 0.78
W_comp = 48,000 × 115 / (0.78 × 2545) = 2781 HP required
Step 3: Power shortfall
W_exp = 1638 HP, W_comp = 2781 HP
Shortfall = 1143 HP → Requires motor assist or higher expansion ratio
Step 4: Increase expansion ratio to 5:1 (200 psia outlet)
New expander power: ΔH_actual = 105 Btu/lb (higher expansion)
W_exp = 50,000 × 105 / 2545 = 2062 HP
New compressor requirement: 5:1 compression → 3150 HP
Still short → Use 600 HP motor assist + optimize both machines.
Final design: 2100 HP expander + 600 HP motor = 2700 HP total
Compressor designed for 2700 HP at 12,500 RPM (common shaft)
Matching flexibility: A well-matched expander-compressor operates efficiently from 60–110% of design rate. Poor matching results in compressor surge at low rates or motor overload at high rates. Expect $500k–$1M cost premium for proper matching engineering, but payback in 6–12 months through avoided shutdowns and improved efficiency.
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