Gas compressibility factor (Z-factor)

Dranchuk

The Dranchuk correlation (1975) is one of the most accurate analytical models for calculating the compressibility factor (Z-factor) of natural gases. The method is based on a modification of the Starling-Carnahan equation of state. It delivers high accuracy across a wide range of reduced pressures and temperatures. A notable feature is the use of a large number of constants, calibrated to match the Standing-Katz generalized chart. 
Recommended applicability range:

• Reduced pressure: 0.2 – 30
• Reduced temperature: 1.05 – 3
• CO ₂ content: < 15%
• H ₂ S content: < 10%
• N ₂ content: < 20%

Papay

The Papay correlation (1985) is one of the simplest and most convenient methods for quick estimation of the gas compressibility factor (Z-factor). It was developed based on data from European gas fields. The model performs especially well for typical natural gases under moderate pressures and temperatures. The formula expresses the compressibility factor as a function of reduced pressure and temperature. 
Recommended applicability range:

• Reduced pressure: 0.2 – 15
• Reduced temperature: 1.05 – 3
• CO ₂ content: < 5%
• H ₂ S content: < 5%

Standing

The Standing correlation for gas compressibility factor (Z-factor) is one of the earliest practical methods developed for engineering calculations. The model is based on the principle of corresponding states. It uses reduced pressure and temperature and demonstrates good accuracy for standard natural gases with moderate non-hydrocarbon content. The method is especially useful for quick estimates due to its simplicity. However, the author notes the unreliability of the correlation outside the recommended applicability range—particularly for reduced temperature. 
Recommended applicability range:

• Reduced pressure: 0.2 – 15
• Reduced temperature: 0.92 – 2.4
• CO ₂ content: < 10%
• H ₂ S content: < 5%

Redlich & Kwong

The Redlich & Kwong correlation (1949) is a cubic equation of state widely used to calculate the compressibility factor (Z-factor) of natural and process gases. As one of the first practical modifications of the Van der Waals equation, it combines relative simplicity with acceptable accuracy. The method is particularly useful for preliminary engineering calculations. 
Recommended applicability range:

• Reduced pressure: 0.2 – 10
• Reduced temperature: 0.7 – 5 (optimal accuracy for 1 – 2)
• CO ₂ content: < 20%

Hall & Yarborough

The Hall & Yarborough correlation (1973) is an analytical approximation of the Standing-Katz chart, specifically developed for calculating the compressibility factor (Z-factor) of natural gases. The method is based on the Starling-Carnahan equation of state and provides high accuracy without requiring iterative calculations. A key advantage is the use of an explicit formulation, making it computationally efficient. 
Recommended applicability range:

• Reduced pressure: 0.2 – 20
• Reduced temperature: 1.2 – 3 (optimal accuracy for 1.4 – 2.8)
• CO ₂ content: < 15%
• H ₂ S content: < 10%

Beggs & Brill

The Beggs & Brill correlation (1973) offers a convenient analytical approximation of the classic Standing-Katz chart for calculating the gas compressibility factor (Z-factor). The model combines good accuracy with computational simplicity and is especially popular in gas pipeline flow modeling. For reduced temperatures below 1.5, it is recommended to use an alternative method. 
Recommended applicability range:

• Reduced pressure: 0.2 – 15
• Reduced temperature: 1.2 – 3
• Gas specific gravity (air = 1): 0.55 – 0.9
• CO ₂ content: < 5%