Turboexpander Efficiency
Engineering fundamentals for cryogenic gas processing
1. Operating Principles
Turboexpanders extract work from high-pressure gas while producing significant cooling through isentropic expansion. This process is more efficient than throttling (J-T valve) for cryogenic NGL recovery.
How It Works
- Expansion: High-pressure gas enters radial inflow turbine wheel
- Work extraction: Gas does work on turbine blades, losing enthalpy
- Cooling: Work extraction produces lower outlet temperature than J-T valve
- Power recovery: Shaft drives compressor (booster) or generator
Comparison to J-T Valve
| Parameter |
J-T Valve |
Turboexpander |
| Process |
Isenthalpic (h = constant) |
Isentropic (s = constant) |
| Temperature drop |
5-7°F per 100 psi |
10-15°F per 100 psi |
| Work produced |
None |
Recovered as compression/power |
| Ethane recovery |
60-70% |
85-95% |
| Capital cost |
Low |
Higher |
Key advantage: Turboexpanders produce 40-60% more cooling than J-T valves for the same pressure drop, enabling deeper NGL recovery.
2. Efficiency Calculations
Turboexpander efficiency is measured as the ratio of actual work output to ideal (isentropic) work output.
Isentropic Efficiency
Isentropic (adiabatic) efficiency:
η_s = (h₁ - h₂) / (h₁ - h₂s) × 100%
Where:
h₁ = Inlet enthalpy (BTU/lb)
h₂ = Actual outlet enthalpy
h₂s = Isentropic outlet enthalpy (at s₁ and P₂)
Temperature-based approximation:
η_s ≈ (T₁ - T₂) / (T₁ - T₂s)
Valid when Cp is relatively constant
Polytropic Efficiency
Polytropic efficiency:
η_p = [(k-1)/k] / [(n-1)/n]
Where:
k = Cp/Cv (isentropic exponent)
n = Polytropic exponent (from actual P-V relationship)
Relationship:
η_p is always higher than η_s for expansion
Difference increases with pressure ratio
Typical Efficiency Ranges
| Application |
Flow Range |
Typical η_s |
| Small cryogenic plants |
5-25 MMSCFD |
78-82% |
| Medium NGL plants |
25-100 MMSCFD |
82-86% |
| Large NGL plants |
100-500 MMSCFD |
85-88% |
| Very large plants |
>500 MMSCFD |
86-90% |
3. Temperature Calculations
Outlet temperature determines NGL recovery capability and is the key design parameter.
Isentropic Temperature Drop
Ideal (isentropic) outlet temperature:
T₂s = T₁ × (P₂/P₁)^[(k-1)/k]
Where:
T₁, T₂s = Absolute temperatures (°R)
P₁, P₂ = Absolute pressures (psia)
k = Cp/Cv ≈ 1.28 for natural gas
Ideal temperature drop:
ΔT_ideal = T₁ × [1 - (P₂/P₁)^((k-1)/k)]
Actual Temperature Drop
Actual outlet temperature:
T₂ = T₁ - η_s × (T₁ - T₂s)
Actual temperature drop:
ΔT_actual = η_s × ΔT_ideal
Example calculation:
T₁ = 0°F (460°R), P₁ = 900 psia, P₂ = 300 psia
k = 1.28, η_s = 85%
T₂s = 460 × (300/900)^(0.28/1.28) = 460 × 0.734 = 338°R = -122°F
ΔT_actual = 0.85 × (0 - (-122)) = 104°F
T₂ = 0 - 104 = -104°F
Effect of Efficiency on Recovery
| Expander η_s |
Outlet Temp (typical) |
Ethane Recovery |
| 75% |
-85°F |
~80% |
| 80% |
-95°F |
~85% |
| 85% |
-105°F |
~90% |
| 88% |
-115°F |
~93% |
4. NGL Recovery Applications
Turboexpanders are the heart of modern cryogenic NGL recovery plants.
Process Configurations
- GSP (Gas Subcooled Process): Traditional design, 85-90% C₂ recovery
- RSV (Recycle Split Vapor): Enhanced recovery, 90-95% C₂
- SCORE (Single Column Overhead Recycle): High efficiency, >95% C₂
- CRR (Cold Residue Recycle): Very high recovery with recycle stream
Power Recovery
Expander power output:
W = ṁ × (h₁ - h₂) / 2,545
Where:
W = Power (HP)
ṁ = Mass flow (lb/hr)
h₁ - h₂ = Enthalpy drop (BTU/lb)
2,545 = BTU/hr per HP
Approximate formula:
W (HP) ≈ Q × ΔP × η_s / 20
Where:
Q = Flow (MMSCFD)
ΔP = Pressure drop (psi)
Typical Operating Conditions
| Parameter |
Typical Range |
| Inlet pressure |
600-1,200 psia |
| Outlet pressure |
200-450 psia |
| Pressure ratio |
2.5:1 to 4:1 |
| Inlet temperature |
-20°F to +20°F |
| Outlet temperature |
-120°F to -80°F |
| Wheel speed |
15,000-50,000 RPM |
5. Design Considerations
Factors Affecting Efficiency
- Size: Larger units have higher efficiency (less tip leakage)
- Speed: Optimal tip speed ~800-1,000 ft/s
- Pressure ratio: Best efficiency at design PR
- Liquid formation: Two-phase flow reduces efficiency
- Bearings: Magnetic bearings reduce losses vs. oil bearings
Materials
| Component |
Material |
Reason |
| Expander wheel |
Aluminum alloy (7075-T6) |
Low temp toughness, light weight |
| Housing |
Stainless steel (304/316) |
Cryogenic service |
| Shaft |
Alloy steel or Inconel |
Strength at temperature extremes |
| Seals |
Labyrinth or dry gas seals |
Minimize leakage |
⚠ Two-phase operation: If liquid forms in the expander (typically >10% by weight), efficiency drops significantly and erosion risk increases. Inlet conditions must ensure mostly vapor phase.
References
- GPSA Engineering Data Book, Section 16 (Hydrocarbon Recovery)
- API 617 – Axial and Centrifugal Compressors (turboexpander sections)
- Gas Processors Association Technical Publications