1. Introduction
Accurate gas property determination is fundamental to reliable compressor calculations. Small errors in gas properties can lead to significant errors in head, power, and temperature predictions. This guide covers the key gas properties and methods for determining them.
Why Gas Properties Matter
A 5% error in Z-factor can result in 5-10% error in head calculation, potentially leading to an undersized or oversized compressor selection. Similarly, incorrect k-value leads to wrong discharge temperature predictions, affecting equipment design and safety.
2. Compressibility Factor (Z)
Definition and Physical Meaning
The compressibility factor Z accounts for the deviation of real gas behavior from ideal gas behavior. It's defined as the ratio of actual molar volume to ideal molar volume:
Real Gas Equation of State
PV = ZnRT
Z = PV / (nRT)
P = pressure, V = volume, n = moles
R = universal gas constant, T = absolute temperature
Interpreting Z Values
- Z = 1: Ideal gas behavior (low pressure, high temperature)
- Z < 1: Attractive forces dominate; gas is more compressible than ideal
- Z > 1: Repulsive forces dominate; gas is less compressible than ideal
Reduced Properties
Z depends on reduced pressure and temperature:
Pᵣ = P / Pᶜ (Reduced Pressure)
Tᵣ = T / Tᶜ (Reduced Temperature)
Pᶜ and Tᶜ are pseudo-critical pressure and temperature for mixtures
Methods for Calculating Z
Method
Standing-Katz
Classic correlation, ±1-2% accuracy for natural gas
Method
DAK Correlation
Mathematical fit for computer calculations
Method
SRK/PR EOS
Rigorous for complex mixtures
Z-Factor in Compressor Calculations
For centrifugal compressors, Z is needed at multiple conditions:
- Z₁: At suction conditions (density calculation)
- Z₂: At discharge conditions (density calculation)
- Zₐᵥg: Average Z for head calculation = (Z₁ + Z₂) / 2
Iteration Required
Since Z₂ depends on discharge temperature, which depends on head, which depends on Zₐᵥg, an iterative solution is required. Start with an assumed Z₂, calculate T₂, recalculate Z₂, and repeat until converged.
3. Specific Heat Ratio (k)
Definition
The specific heat ratio (also called the isentropic exponent or gamma) is the ratio of heat capacity at constant pressure to heat capacity at constant volume:
k = Cₚ / Cᵥ
Cₚ = specific heat at constant pressure
Cᵥ = specific heat at constant volume
Importance in Compressor Calculations
The k-value appears in:
- Head calculation: (k-1)/k term in polytropic head equation
- Temperature rise: Discharge temperature prediction
- Efficiency conversion: Between polytropic and isentropic
- Speed of sound: c = √(kZRT/MW)
Typical Values
| Gas | k-Value | Notes |
|---|---|---|
| Methane (CH₄) | 1.31 | Primary natural gas component |
| Natural Gas | 1.26-1.32 | Depends on composition |
| Nitrogen (N₂) | 1.40 | Diatomic gas |
| Carbon Dioxide (CO₂) | 1.29 | Triatomic, more complex |
| Hydrogen (H₂) | 1.41 | Light diatomic gas |
| Rich Gas (C₂+) | 1.15-1.25 | Heavier components lower k |
Temperature and Pressure Effects
Unlike ideal gases where k is constant, real gas k varies with:
- Temperature: k generally decreases with increasing temperature
- Pressure: k changes significantly near critical conditions
- Composition: Heavier components decrease k
Don't Use Ideal Gas k
Using ideal gas k values at high pressures can introduce significant errors. Always calculate real gas Cₚ and Cᵥ from equations of state for accurate results.
4. Molecular Weight (MW)
Calculation for Gas Mixtures
For a gas mixture, the apparent molecular weight is the mole-fraction weighted average:
MW = Σ(yᵢ × MWᵢ)
yᵢ = mole fraction of component i
Relationship to Specific Gravity
Specific gravity relates molecular weight to air:
SG = MW / 28.97
28.97 is the molecular weight of air
Impact on Compressor Performance
- Head requirement: Head is inversely proportional to MW for the same pressure ratio
- Number of stages: Lighter gases require more head (more stages) per unit pressure ratio
- Impeller tip speed: Limited by MW (Mach number concerns)
- Power: MW cancels from the power equation at the same volumetric flow and pressure ratio; power depends primarily on k-value, not MW directly
Heavy vs. Light Gas
A compressor designed for natural gas (MW ≈ 18) will achieve a much lower pressure ratio on hydrogen (MW = 2) at the same head, since lighter gases require far more head to achieve the same compression. Conversely, on propane (MW = 44), the same head produces a higher pressure ratio.
5. Critical Properties
Pseudo-Critical Properties for Mixtures
For gas mixtures, pseudo-critical properties are calculated using mixing rules:
Kay's Mixing Rules
Pₚc = Σ(yᵢ × Pcᵢ)
Tₚc = Σ(yᵢ × Tcᵢ)
Simple mole-fraction weighted averages
Acid Gas Corrections
For gases containing H₂S or CO₂, corrections to pseudo-critical properties are required:
Wichert-Aziz Correction
ε = 120(A^0.9 - A^1.6) + 15(B^0.5 - B^4)
Tₚc' = Tₚc - ε
Pₚc' = Pₚc × Tₚc' / (Tₚc + B(1-B)ε)
A = mol fraction CO₂ + mol fraction H₂S
B = mol fraction H₂S
6. Gas Density
Calculation
Gas density at any condition is calculated from the equation of state:
ρ = P × MW / (Z × R × T)
R = 10.7316 psia·ft³/(lbmol·°R)
T in °R, P in psia, ρ in lbm/ft³
Importance in Compressor Applications
- ACFM calculation: Mass flow / density = volumetric flow
- Surge prediction: Surge flow is a function of inlet density
- Power calculation: Mass flow is density × volume flow
7. Equations of State
When to Use EOS
Equations of state provide more rigorous property calculations for:
- Complex multi-component mixtures
- Near-critical conditions
- High H₂S or CO₂ content
- Liquid phase present (phase envelope concerns)
Common Equations of State
Soave-Redlich-Kwong (SRK)
P = RT/(V-b) - a(T)/(V(V+b))
Good for vapor phase calculations, widely used in process simulation.
Peng-Robinson (PR)
P = RT/(V-b) - a(T)/(V²+2bV-b²)
Better liquid density predictions, commonly used in reservoir applications.
EOS Outputs
A properly tuned EOS provides all necessary properties:
- Compressibility factor (Z)
- Density (ρ)
- Enthalpy (H)
- Entropy (S)
- Heat capacities (Cₚ, Cᵥ, k)
- Speed of sound (c)
- Joule-Thomson coefficient
8. Practical Guidance
When Detailed Analysis is Required
- High pressure ratio (>3:1 per stage)
- Near critical conditions (Tᵣ < 1.2)
- Acid gas content >5%
- Variable gas composition expected
- Detailed performance guarantee
Quick Estimation Methods
- Use standing charts for natural gas at moderate conditions
- Assume k = 1.28 for natural gas screening
- Use MW = 28.97 × SG for quick estimates
Sensitivity Analysis
Always perform sensitivity analysis on gas properties for critical applications. Test ±10% variation in MW, k, and Z to understand impact on compressor selection and performance.
References
- GPSA, Section 23 - Physical Properties
- API 617 - Axial and Centrifugal Compressors
- Campbell, J.M. - Gas Conditioning and Processing
- Standing, M.B. and Katz, D.L. - Density of Natural Gases (1942)
- Dranchuk, P.M. and Abou-Kassem, J.H. - Calculation of Z Factors