What is the Z-factor in natural gas calculations?

The Z-factor (gas compressibility factor) is a dimensionless correction that accounts for the deviation of real gas behavior from the ideal gas law. Z = 1.0 for an ideal gas. For natural gas at typical pipeline pressures (500-1500 psia), Z ranges from 0.65 to 0.92, meaning the gas is 8-35% denser than ideal gas predictions.

How is the Z-factor calculated?

The Z-factor is calculated in two steps: (1) determine pseudo-critical properties (Tpc, Ppc) from gas specific gravity using Sutton correlations, then calculate pseudo-reduced temperature and pressure; (2) solve the Dranchuk-Abou-Kassem or Hall-Yarborough equation iteratively using Newton-Raphson method. For sour gas, Wichert-Aziz correction adjusts pseudo-critical properties before step 2.

When should I use Z-factor correction instead of ideal gas assumptions?

Always use Z-factor correction when pressure exceeds 100 psia. At low pressure (< 50 psia), Z is approximately 1.0 and ideal gas is adequate. For custody transfer, pipeline hydraulics, compressor sizing, and relief valve calculations, accurate Z-factor is essential. At 1000 psia, ignoring Z can introduce 15-25% error in density and flow calculations.

What is the difference between DAK and Hall-Yarborough methods?

Both methods are mathematical fits of the Standing-Katz Z-factor chart. Dranchuk-Abou-Kassem (DAK) uses an 11-coefficient equation solved for reduced density, while Hall-Yarborough uses the Starling-Carnahan equation of state. Both are accurate to within 1% for typical natural gas conditions. DAK is more widely used in the gas industry; HY sometimes converges better at extreme conditions.

Z-Factor Calculator | Gas Compressibility Factor (Standing-Katz)

Operating Conditions

Pressure

Temperature

°F

Gas Properties

Gas Specific Gravity (Air = 1.0)

Typical: 0.55-0.70 (sweet gas), 0.70-0.90 (rich gas)

Gas Type

Acid Gas / Impurity Content

H₂S Content

mol%

CO₂ Content

mol%

N₂ Content

mol%

Sour gas: Uses Piper-McCain-Corredor (1993) pseudo-critical correlations with Wichert-Aziz (1972) acid gas correction.

Calculation Method

Z-Factor Correlation

DAK: Most widely used, 11-coefficient Standing-Katz fit
HY: Starling-Carnahan equation, better at some extremes
Both: Compare methods for quality assurance

Understanding the Z-Factor

What is Z-Factor?
The compressibility factor (Z) corrects ideal gas behavior for real gas intermolecular forces. Z = PV/(nRT). At Z = 1.0, gas follows ideal behavior; Z < 1.0 means gas is denser than ideal prediction.

Typical Ranges:
Low pressure (<100 psia): Z = 0.98-1.00
Pipeline (500-1500 psia): Z = 0.65-0.92
High pressure (>3000 psia): Z = 0.80-1.20

Where Z-Factor is Used:
Gas density (ρ = PMW/ZRT), pipeline hydraulics, compressor sizing, orifice meter calculations, relief valve sizing, gas inventory (line pack), custody transfer volume correction.

📚 Learn the Theory

Understand real gas behavior, Standing-Katz chart, pseudo-critical correlations, and equations of state

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Results

Z-Factor

dimensionless

Pseudo-Reduced Temperature (Tr) -

Pseudo-Reduced Pressure (Pr) -

Pseudo-Critical Temp (Tpc) -

Pseudo-Critical Pressure (Ppc) -

Ideal Gas Deviation -

Gas Density -

Z-Factor Method -

Pseudo-Critical Method -

Formula

Z = f(Pr, Tr)

Z = Compressibility factor (dimensionless)

Pr = P / Ppc (pseudo-reduced pressure)

Tr = T / Tpc (pseudo-reduced temperature)

Tpc = 168 + 325·SG - 12.5·SG² (Sutton)

Ppc = 677 + 15.0·SG - 37.5·SG² (Sutton)

Standards & References

GPSA Engineering Data Book
Section 23: Physical Properties
AGA Report No. 8
Compressibility Factors for Natural Gas
Dranchuk & Abou-Kassem (1975)
JCPT 14(3):83-92 — Standing-Katz Z-factor correlation
Hall & Yarborough (1973)
Oil & Gas Journal — Equation of state Z-factor
Sutton (1985)
SPE 14265 — Pseudo-critical property correlations
Wichert & Aziz (1972)
Hydrocarbon Processing — Sour gas correction

Engineering Notes

Accuracy: ±1% for sweet gas at Tr 1.05-3.0, Pr 0.2-15
Sour gas: Switch to "Sour/Impure Gas" for H₂S or CO₂ > 1 mol%
AGA-8 DETAIL: For custody transfer, use full compositional AGA-8 DETAIL method (not gravity-based)
Low pressure: Z → 1.0 as P → 0. Below 50 psia, Z ≈ 0.99-1.00
Minimum Z: Typically occurs near Tr = 1.1-1.3, Pr = 2-5 (pipeline conditions)
Z > 1.0: Possible at very high pressure where molecular repulsion dominates

Quick Reference — Typical Z Values

500 psig, 80°F, SG 0.65 → Z ≈ 0.87
1000 psig, 100°F, SG 0.65 → Z ≈ 0.78
1500 psig, 120°F, SG 0.65 → Z ≈ 0.76
2000 psig, 100°F, SG 0.65 → Z ≈ 0.74
3000 psig, 150°F, SG 0.65 → Z ≈ 0.82

Z-Factor Calculator

Operating Conditions

Gas Properties

Acid Gas / Impurity Content

Calculation Method

Understanding the Z-Factor

📚 Learn the Theory

Results

Formula

Standards & References

Engineering Notes

Quick Reference — Typical Z Values

Related Calculators

Gas Density

Ideal Gas Law

Fixed Pressure Factor

Compressor HP