A3.1. 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
- CO₂ content: < 15%
- H₂S content: < 10%
- N₂ 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
- CO₂ content: < 5%
- H₂S 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
- CO₂ content: < 10%
- H₂S 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)
- CO₂ 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)
- CO₂ content: < 15%
- H₂S 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
- CO₂ content: < 5%
A3.2. Viscosity
Carr
The classical Carr correlation provides an estimate of natural gas viscosity at atmospheric and reservoir conditions. The method includes two steps:
- Calculation of viscosity at atmospheric pressure.
- Correction for reservoir pressure and temperature.
This approach is simple and reliable but may show deviations when hydrogen sulfide (H₂S) is present.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 1.55
- Temperature: 100 – 400 °F
- Pressure: < 10,000 psi
Lee
The Lee correlation is one of the most widely used methods for calculating natural gas viscosity. It combines ease of use with good accuracy across a broad range of conditions. The formula accounts for the effects of temperature, gas density, and molecular weight through dimensionless parameters. It is well-suited for gases containing a low proportion of non-hydrocarbon components.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 1.5
- Temperature: 100 – 340 °F
- Methane content (CH₄): > 70%
- Pressure: 100 – 8000 psi
Dean & Stiel
The Dean & Stiel method is designed for calculating gas viscosity using reduced parameters and is particularly accurate at high pressures and for non-standard gas compositions (e.g., gases containing H₂S and CO₂). The method is based on the principle of corresponding states.
Recommended applicability range:
- Reduced pressure: 0.1 – 15
- Reduced temperature: 1 – 3
- Gas specific gravity (air = 1): 0.5 – 2
- Gas composition: no limitations
A3.3. Pseudocritical Pressure and Temperature of Pure Hydrocarbon Gas
A3.3.1. Dry Gas
Brown
The Brown correlation is a classical method for estimating pseudocritical pressure and temperature. The model is widely used in the oil and gas industry due to its simplicity and acceptable accuracy under standard conditions. The correlation is applicable only for calculating properties of dry gas.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 1
- C₇⁺ content: < 1%
Dùn & Oriji
The Dùn & Oriji correlation was developed for more accurate calculation of the pseudocritical pressure of dry natural gases, based on modern datasets. The method is derived from statistical analysis of an extensive PVT database from African and Middle Eastern fields. The correlation does not account for the influence of heavy hydrocarbons.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 0.8
Golan & Whitson
The Golan & Whitson method offers an improved approach for determining the pseudocritical pressure and temperature of dry natural gases. The correlation is based on a modification of the classic Standing-Katz method, incorporating the molecular weight of the gas. It shows better accuracy compared to traditional methods when applied to gases containing minor non-hydrocarbon impurities.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 0.8
Thomas, Hankinson & Phillips
The Thomas, Hankinson & Phillips correlation estimates pseudocritical pressure and temperature values for dry natural gases. It is suitable for typical natural gases without significant concentrations of non-hydrocarbon components. It is not applicable to gases with a specific gravity (air = 1) greater than 0.8.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 0.8
- C₄+ content: > 90%
Joshi
The Joshi correlation offers a modernized approach to calculating pseudocritical pressure and temperature for dry and slightly sour gases. The method is based on a comprehensive global dataset. Its key advantage is high accuracy for gases with atypical compositions, without requiring complex corrections.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 0.8
Lee & Wattenbarger
The Lee & Wattenbarger correlation was developed for accurate calculation of pseudocritical pressure and temperature for dry natural gases. The method is a modification of classical approaches, incorporating gas thermodynamics. It is based on research from reservoirs around the world. A key feature is the use of separate calculation formulas for different gas specific gravity ranges.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 1.1
Golan & Whitson
The Golan & Whitson correlation is designed to calculate the pseudocritical pressure and temperature of wet hydrocarbon gases containing significant amounts of heavy fractions. The method is based on gas mixing rules, accounting for the influence of molecular weight and gas composition, which ensures high accuracy for gas-condensate systems.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.6 – 1.2
- C₇⁺ content: 1 – 20%
A3.4. Pseudocritical Pressure and Temperature of Non-Hydrocarbon Impurities
Carr
The Carr correlation allows correction of the pseudocritical pressure and temperature of natural gas in the presence of non-hydrocarbon impurities. The method is especially useful for fields with high concentrations of acid gases, where standard methods produce significant errors.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 1.2
- CO₂ content: < 20%
- H₂S content: < 25%
- N₂ content: < 5%
Piper & McCain
The Piper & McCain correlation is an advanced method for determining pseudocritical properties of gas-condensate mixtures containing non-hydrocarbon components. It was developed based on an extensive database from North Sea fields. The model provides high accuracy for complex multicomponent systems.
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 1.2
- CO₂ content: < 20%
- H₂S content: < 30%
- N₂ content: < 10%
Wichert & Aziz
The Wichert & Aziz correlation is a fundamental method for adjusting pseudocritical properties of natural gases with elevated levels of acid gases. The method accounts for the non-ideal behavior of such mixtures and ensures accuracy in the calculation of the gas compressibility factor. It is not applicable to gases with a high content of heavy hydrocarbons (C₇⁺ > 5%).
Recommended applicability range:
- Gas specific gravity (air = 1): 0.55 – 1.0
- CO₂ content: < 40%
- H₂S content: < 40%
A3.5. Surface Tension
A3.5.1. Gas-Water
Sutton
The Sutton correlation is a modern method for calculating interfacial tension between natural gas and water, accounting for the effects of pressure, temperature, and water salinity. Unlike classical approaches, this correlation was specifically developed for high-pressure and wide-temperature conditions, making it especially useful for deep-water fields and unconventional reservoirs.
Recommended applicability range:
- CO₂ content: < 15%
- Water salinity: 0 – 300,000 ppm
- Temperature: 100 – 400 °F
- Pressure: < 30,000 psi (optimal: 500 – 15,000 psi)
A3.5.2. Gas-Oil
Abdul-Majid
The Abdul-Majid correlation is a specialized method for calculating interfacial tension between oil and natural gas, taking into account oil density, temperature, pressure, and gas properties. The method is based on experimental data from Middle Eastern oils. It demonstrates particular accuracy for light and medium oils under high-pressure conditions.
Recommended applicability range:
- Oil density (API Gravity): 25 – 45 °API
- Gas–oil ratio: 200 – 2500 SCF/STB
- Temperature: 100 – 300 °F
- Pressure: < 10,000 psi (optimal: 1,000 – 8,000 psi)