Compressor Design Theory
Gas compression is a fundamental unit operation in process engineering for increasing gas pressure for transport, storage, or reaction.
Thermodynamic Processes
Gas compression can be modeled as different thermodynamic processes:
Isothermal (PV = constant)
Ideal case with continuous heat removal. Minimum work required but impractical.
Isentropic (PVk = constant)
Adiabatic and reversible. No heat transfer, theoretical maximum work.
Polytropic (PVn = constant)
Real process with some heat transfer. Most practical for design.
Polytropic Head
The polytropic head represents the work done per unit mass of gas:
Hp = (Z·R·T1/MW) × (n/(n-1)) × [(P2/P1)(n-1)/n - 1]
Where:
- Hp = Polytropic head (kJ/kg)
- Z = Gas compressibility factor
- R = Gas constant (8.314 kJ/kmol·K)
- T1 = Inlet temperature (K)
- MW = Molecular weight (kg/kmol)
- n = Polytropic exponent
- P1, P2 = Inlet and discharge pressure
Polytropic Efficiency
The polytropic efficiency relates the isentropic and polytropic exponents:
ηp = [(k-1)/k] / [(n-1)/n]
Rearranging to find n:
n/(n-1) = k·ηp/(k-1)
Discharge Temperature
The discharge temperature for polytropic compression:
T2 = T1 × (P2/P1)(n-1)/n
High discharge temperatures (>150°C) may require intercooling between stages.
Power Requirements
Gas horsepower (GHP) and shaft power calculations:
GHP = ṁ × Hp
Shaft Power = GHP / ηmech
Where ṁ is mass flow rate (kg/s) and ηmech is mechanical efficiency (typically 96-99%).
Compressor Types
| Type | Flow Range | Pressure Ratio | Efficiency |
|---|---|---|---|
| Centrifugal | 1,000 - 200,000 m³/h | 2-10 per stage | 70-85% |
| Axial | 50,000 - 1,000,000 m³/h | 1.1-1.5 per stage | 85-92% |
| Reciprocating | 10 - 10,000 m³/h | 2-6 per stage | 75-90% |
| Screw | 100 - 50,000 m³/h | 3-15 | 70-85% |
Staging Considerations
Multiple stages with intercooling are used when:
- Compression ratio exceeds practical single-stage limits
- Discharge temperature would exceed material limits (~150°C)
- Energy savings justify the additional equipment cost
Optimal staging: For minimum power, use equal pressure ratios per stage with intercooling back to inlet temperature.
References
- Brown, R.N. (2005). Compressors: Selection and Sizing. Gulf Professional Publishing.
- Bloch, H.P. (2006). A Practical Guide to Compressor Technology. Wiley.
- Ludwig, E.E. (1997). Applied Process Design. Gulf Professional Publishing.
- API Standard 617: Axial and Centrifugal Compressors.