Appendix A: PVT Correlations

A1.1 Bubble Point Pressure and Gas Solubility

Al-Marhoun

The Al-Marhoun correlation (1988) was developed to calculate the bubble point pressure of crude oil based on data from Middle Eastern oilfields. It takes into account temperature, gas-oil ratio, gas density, and oil density. It was specifically designed for Middle Eastern crude oils. The correlation provides good accuracy for high-sulfur oils and serves as an alternative to the Standing and Vasquez & Beggs correlations for certain regions. 
Recommended applicability range:

• Oil density (API Gravity): 20 – 55 °API
• Gas-oil ratio: 25 – 1600 SCF/STB
• Temperature: 75 – 240 °F
• Pressure: 130 – 3500 psi

De Ghetto et al.

The De Ghetto et al. correlation (1995) provides several specialized formulas for calculating bubble point pressure based on oil density. The method is derived from data from Mediterranean and Venezuelan oilfields. The correlation offers high accuracy for heavy and medium crudes, where traditional correlations (Standing, Vasquez & Beggs) often produce significant errors. For extra-heavy oils (<10 °API), it is the only correlation that delivers acceptable accuracy. 
Recommended applicability range:

• Oil density (API Gravity): 5 – 40 °API
• Gas-oil ratio: 20 – 1500 SCF/STB
• Temperature: 100 – 280 °F

Glaso

The Glaso correlation was developed based on an extensive database of crude oils from the North Sea and other regions. It accounts for the influence of gas-oil ratio, temperature, oil density, and gas specific gravity, making it applicable to various types of fluids. The method uses logarithmic transformations and polynomial relationships, providing high accuracy, especially for light and medium oils. Unlike earlier correlations (e.g., Standing), the Glaso correlation performs better for oils containing dissolved gas over a wide pressure range. 
Recommended applicability range:

• Oil density (API Gravity): 22 – 48 °API
• Gas-oil ratio: 90 – 2500 SCF/STB
• Temperature: 80 – 280 °F
• Pressure: 100 – 5000 psi

Lasater

The Lasater correlation is one of the earliest reliable methods for calculating the bubble point pressure of crude oil. The calculation is based on the mole fraction of dissolved gas. It shows particular accuracy for medium and heavy oils (< 40 °API). The method uses empirical relationships derived from the analysis of oils from Canada and the United States. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Gas-oil ratio: 50 – 3500 SCF/STB
• Temperature: 100 – 300 °F
• Pressure: 100 – 5000 psi

Petrosky

The Petrosky correlation was developed for crude oils from the Gulf of Mexico. It demonstrates improved accuracy for this region compared to traditional methods. The correlation accounts for the thermodynamic properties of offshore shelf crudes and serves as an alternative to the Standing and Vasquez & Beggs correlations for offshore fields. The average error is ±6.5% compared to laboratory data. 
Recommended applicability range:

• Oil density (API Gravity): 16 – 45 °API
• Gas-oil ratio: 200 – 1500 SCF/STB
• Temperature: 110 – 300 °F
• Pressure: 1500 – 4000 psi

Standing

The Standing correlation is used to calculate the bubble point pressure of crude oil based on the gas-oil ratio, gas specific gravity, oil gravity, and temperature. Originally developed for California crude oils, it has since been widely applied to other regions. The correlation is known for its simplicity, minimal input requirements, and good accuracy for light oils (25–40 °API). However, it tends to overestimate results for heavy oils (<20 °API). 
Recommended applicability range:

• Oil density (API Gravity): 16 – 45 °API
• Gas-oil ratio: 20 – 1500 SCF/STB
• Temperature: 100 – 300 °F

Vasquez & Beggs

The Vasquez & Beggs correlation improves the calculation of bubble point pressure by: normalizing gas specific gravity to a reference pressure of 100 psi; dividing oils into three groups based on API gravity; and accounting for temperature and gas-oil ratio. It was developed using a global database of 600 PVT analyses. The correlation also considers separation conditions. It is less accurate for heavy oils (<20 °API). 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Gas-oil ratio: 20 – 2070 SCF/STB
• Temperature: 75 – 295 °F

Kartoatmodjo & Schmidt

The Kartoatmodjo & Schmidt correlation provides two separate formulas: one for oils with API ≤ 30 and another for API > 30, allowing for higher accuracy across different fluid types. The method accounts for the influence of gas-oil ratio, temperature, oil gravity, and separator gas properties. A key feature is the use of a correction factor to account for gas separation conditions. It is particularly effective for Southeast Asian crudes and other regions with similar characteristics. 
Recommended applicability range:

• Oil density (API Gravity): 14 – 45 °API
• Gas-oil ratio: 20 – 2500 SCF/STB
• Temperature: 100 – 300 °F

A1.2 Saturated Oil Formation Volume Factor

Al-Marhoun

The Al-Marhoun correlation (1988) was specifically developed for Middle Eastern crude oils based on an extensive PVT database. The method takes into account the effects of gas-oil ratio, oil and gas specific gravity, and temperature, offering improved accuracy compared to classical correlations such as Standing and Glaso. A key feature is the use of a power-law relationship optimized for Middle Eastern reservoir conditions. The formula is not applicable to oils with abnormal composition (e.g., high content of harmful components). 
Recommended applicability range:

• Oil density (API Gravity): 20 – 45 °API
• Gas-oil ratio: 100 – 2500 SCF/STB
• Gas specific gravity: 0.65 – 1.2
• Temperature: 100 – 300 °F

De Ghetto et al.

The De Ghetto et al. correlation represents an advanced method for calculating the formation volume factor of saturated oil, specifically designed for use with heavy and highly viscous oils (API < 25°). Unlike classical methods (e.g., Standing, Vasquez & Beggs), this correlation applies separate calculation approaches for light and heavy fluids, resulting in improved prediction accuracy. The formula incorporates the combined effects of gas-oil ratio, temperature, oil and gas densities through a system of power-law relationships. 
Recommended applicability range: 

• Oil density (API Gravity): 10 – 45 °API
• Gas-oil ratio: 50 – 3000 SCF/STB
• Temperature: 100 – 300 °F

Glaso

The Glaso correlation allows calculation of the formation volume factor of saturated oil based on the gas-oil ratio, gas and oil density, and temperature. It was developed for North Sea crude oils but is also applicable to other regions. The method is known for its high accuracy with light and medium oils but tends to be less precise for heavy fluids. 

Recommended applicability range:

• Oil density (API Gravity): 22 – 48 °API
• Gas-oil ratio: 90 – 2500 SCF/STB
• Temperature: 80 – 280 °F

Lasater

The Lasater correlation (1958) is based on the analysis of North American crude oils with a focus on the effect of gas solubility. The method uses the mole fraction of gas in the system for calculation, which makes it particularly accurate for gas-saturated oils. The approach is physically based but requires knowledge of the oil’s molecular weight. It tends to overestimate values for heavy oils. It does not account for sulfur or paraffin content. 
Recommended applicability range: 

• Oil density (API Gravity): 15 – 40 °API
• Gas-oil ratio: 50 – 3500 SCF/STB
• Temperature: 100 – 220 °F

Petrosky

The Petrosky correlation is used to estimate the formation volume factor of saturated oil based on reservoir oil parameters such as gas-oil ratio, gas and oil density, and temperature. It was developed for crude oils from the Gulf of Mexico, but the correlation also shows good accuracy for similar reservoirs. The formula takes into account the influence of dissolved gas. 
Recommended applicability range: 

• Oil density (API Gravity): 15 – 40 °API
• Gas-oil ratio: 90 – 3000 SCF/STB
• Pressure: up to 7000 psi
• Temperature: 120 – 300 °F

Standing

The Standing correlation is one of the most widely used empirical models for estimating the formation volume factor of saturated oil. It is based on data from California oilfields and takes into account the gas-oil ratio, specific gravity of oil and gas, and reservoir temperature. Simple to apply, this correlation delivers acceptable accuracy for "black oil" models. 
Recommended applicability range:

• Oil density (API Gravity): 22 – 58 °API
• Gas-oil ratio: 20 – 2100 SCF/STB
• Pressure: up to 5000 psi
• Temperature: 100 – 260 °F

Vasquez & Beggs

The Vasquez & Beggs correlation is one of the most versatile and widely used models for calculating the formation volume factor of saturated oil. It was developed based on an extensive database of over 600 oil samples. The formula categorizes oils into several groups based on API gravity. A distinguishing feature of the correlation is the normalization of gas parameters to standard separation conditions, which enhances its accuracy. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 55 °API
• Gas-oil ratio: 0 – 3000 SCF/STB
• Gas specific gravity (air = 1): 0.58 – 1.18
• Temperature: 70 – 295 °F

Ahmed

The Ahmed correlation was developed as a modification of existing models to provide more accurate predictions of the saturated oil formation volume factor. It performs particularly well for heavy oils and considers the relationship between gas-oil ratio, fluid properties, and reservoir conditions. The model demonstrates good accuracy for Middle Eastern fields and yields reliable results for both heavy and medium crude oils. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 50 °API
• Gas-oil ratio: 50 – 3500 SCF/STB
• Gas specific gravity (air = 1): 0.65 – 1.2
• Temperature: 100 – 300 °F

Arps

The Arps correlation is a simplified linear formula used to estimate the formation volume factor of saturated oil. It relates the volume factor directly to the gas-oil ratio. The model is suitable for quick approximation calculations; however, it does not account for the effects of temperature, oil gravity, or gas gravity. This oversimplification limits its accuracy. 
Recommended applicability range (exact boundaries are not defined; model is applicable within the “Black Oil” model):

• Oil density (API Gravity): 20 – 35 °API
• Gas-oil ratio: 100 – 1000 SCF/STB
• Gas specific gravity (air = 1): 0.65 – 1.0
• Temperature: 100 – 200 °F

Kartoatmodjo & Schmidt

The Kartoatmodjo & Schmidt correlation was developed based on an extensive database of over 740 crude oil samples. It is considered one of the most versatile models available. The correlation demonstrates good accuracy across a wide range of crude types—from light to heavy oils. A distinguishing feature of the method is its use of power-law relationships to account for the effects of temperature, gas-oil ratio, and fluid properties. 
Recommended applicability range:

• Oil density (API Gravity): 14 – 59 °API
• Gas-oil ratio: 20 – 2900 SCF/STB
• Gas specific gravity (air = 1): 0.56 – 1.18
• Temperature: 75 – 320 °F

A1.3 Undersaturated Oil Formation Volume Factor

Al-Marhoun

The Al-Marhoun correlation was specifically developed to calculate the oil formation volume factor above the bubble point pressure. The model is based on data from Middle Eastern oilfields. It accounts for the effects of pressure, temperature, and fluid properties through a power-law relationship. The correlation demonstrates good accuracy over a wide range of conditions but is most accurate for medium and heavy crude oils. 
Recommended applicability range:

• Oil density (API Gravity): 19 – 45 °API
• Gas-oil ratio: 25 – 1600 SCF/STB
• Pressure: < 10,000 psi
• Gas specific gravity (air = 1): 0.75 – 1.35
• Temperature: 75 – 240 °F

De Ghetto et al.

The De Ghetto et al. correlation was developed to calculate the oil formation volume factor above the bubble point pressure. It is based on the analysis of data from heavy (<22.3 °API), medium (22.3–31.1 °API), and light (>31.1 °API) crude oils, making it suitable for a wide range of reservoir types. The model accounts for the effects of pressure, temperature, gas-oil ratio, and fluid properties. It is also suitable for reservoirs with abnormal oil characteristics. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Gas-oil ratio: 15 – 1500 SCF/STB
• Pressure: < 8000 psi
• Gas specific gravity (air = 1): 0.65 – 1.3
• Temperature: 120 – 320 °F

Glaso

The Glaso correlation is considered one of the most reliable models for calculating the oil formation volume factor in the undersaturated zone. It was developed based on North Sea crude oils. The model incorporates the effects of pressure, temperature, and fluid properties through logarithmic relationships. A key feature of the method is its high accuracy across a wide range of crude oils—from light to heavy. However, it is less accurate for oils with extreme properties (very light or very heavy). 
Recommended applicability range:

• Oil density (API Gravity): 22 – 48 °API
• Gas-oil ratio: 90 – 2600 SCF/STB
• Pressure: < 8000 psi
• Gas specific gravity (air = 1): 0.65 – 1.27
• Temperature: 80 – 280 °F

Petrosky

The Petrosky correlation was specifically developed for crude oils from the Gulf of Mexico. It provides high accuracy in calculating the oil formation volume factor in the undersaturated zone. The model incorporates the effects of pressure, temperature, and fluid properties using power-law relationships. A distinctive feature of the method is its adaptability to different oil types within the defined limits. The average error is ±3–5% within the recommended applicability range. It performs especially well for reservoirs with high gas-oil ratios. 
Recommended applicability range:

• Oil density (API Gravity): 16 – 45 °API
• Gas-oil ratio: 90 – 3000 SCF/STB
• Pressure: < 10,000 psi
• Gas specific gravity (air = 1): 0.6 – 0.9
• Temperature: 120 – 300 °F

Standing

The Standing correlation is a classical method for calculating the oil formation volume factor in the undersaturated zone. It was developed based on data from California oilfields and is widely used in the petroleum industry due to its simplicity and reliability. The model accounts for oil compressibility through an exponential dependence on pressure. The average error is ±5–8% within the recommended applicability range. 
Recommended applicability range:

• Oil density (API Gravity): 22 – 58 °API
• Gas-oil ratio: 20 – 2100 SCF/STB
• Pressure: < 5000 psi
• Gas specific gravity (air = 1): 0.63 – 1.05
• Temperature: 100 – 250 °F

Vasquez & Beggs

The Vasquez & Beggs correlation is one of the most versatile and accurate models for calculating the oil formation volume factor in the undersaturated zone. It was developed using an extensive database of more than 600 crude oil samples. The correlation accounts for separation conditions and categorizes oils into several groups based on density, which enables high accuracy across different reservoir types. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 55 °API
• Gas-oil ratio: 0 – 3000 SCF/STB
• Pressure: < 10,000 psi
• Gas specific gravity (air = 1): 0.56 – 1.18
• Temperature: 70 – 295 °F

Lasater

The Lasater correlation offers an alternative approach for calculating the oil formation volume factor in the undersaturated zone, based on the mole fraction of dissolved gas. It was developed using data from Canadian and U.S. oilfields. The model performs particularly well for oils with high gas-oil ratios. However, the correlation is less accurate for heavy oils (<25 °API). 
Recommended applicability range:

• Oil density (API Gravity): 20 – 48 °API
• Gas-oil ratio: 100 – 3500 SCF/STB
• Pressure: < 5000 psi
• Gas specific gravity (air = 1): 0.65 – 1.2
• Temperature: 100 – 250 °F

Ahmed

The Ahmed correlation is a modern model for calculating the oil formation volume factor in the undersaturated zone. It was developed based on a wide dataset from Middle Eastern and North African oilfields. A distinctive feature of this formula is its non-traditional approach to modeling oil compressibility through a double exponential relationship, which more accurately reflects the behavior of oils with a nonlinear volume factor dependence on pressure. 
Recommended applicability range:

• Oil density (API Gravity): 25 – 40 °API
• Gas-oil ratio: 50 – 2000 SCF/STB
• Pressure: < 10,000 psi
• Temperature: 100 – 250 °F

Arps

The Arps correlation is one of the earliest practical models for estimating oil volume changes in the undersaturated zone. It was developed based on empirical data from U.S. oilfields. The method uses a linear approximation of the relationship between formation volume factor and pressure, making it simple to apply but limited in accuracy under complex reservoir conditions. At elevated pressures (> 2000 psi), the error can reach up to 10%. 
Recommended applicability range:

• Oil density (API Gravity): 20 – 40 °API
• Gas-oil ratio: 100 – 1500 SCF/STB
• Pressure: < 3000 psi
• Temperature: 100 – 220 °F

Kartoatmodjo & Schmidt

The Kartoatmodjo & Schmidt correlation (1994) was developed based on an expanded global database that includes crude oil samples from various regions around the world. The method provides an advanced approach for calculating formation volume factor in the undersaturated zone, accounting for the nonlinear dependence on pressure and fluid properties. A key feature is the use of a power function to more accurately describe oil volume changes. 
Recommended applicability range:

• Oil density (API Gravity): 14 – 45 °API
• Gas-oil ratio: 20 – 2500 SCF/STB
• Pressure: < 8000 psi
• Temperature: 100 – 300 °F

A1.4 Compressibility

Standing

The Standing correlation, developed in 1947, is one of the earliest and most widely used methods for estimating oil compressibility. Standing proposed an empirical relationship that links compressibility with pressure, temperature, gas-oil ratio, and the specific gravities of oil and gas. The method performs particularly well for conventional crude oils with moderate gas content. 
Recommended applicability range:

• Oil density (API Gravity): 20 – 45 °API
• Gas-oil ratio: 50 – 800 SCF/STB
• Temperature: 100 – 220 °F

Vasquez & Beggs

The Vasquez & Beggs correlation is an enhanced method for calculating oil compressibility, developed from an extensive PVT database. Unlike earlier models (such as Standing), this correlation explicitly accounts for the effects of pressure, temperature, gas-oil ratio, and other oil properties through a set of empirical coefficients. The method provides good accuracy across a wide range of crude oils—from light to medium. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Pressure: < 10,000 psi
• Gas-oil ratio: 50 – 3500 SCF/STB
• Temperature: 100 – 300 °F

Glaso

The Glaso (1980) correlation for oil compressibility is based on generalized data from North Sea oilfields. The method incorporates the effects of pressure, temperature, gas-oil ratio, and oil density, offering more accurate estimates compared to classical approaches (e.g., Vasquez & Beggs). A notable feature of this model is the separation of calculation formulas for different pressure ranges—above and below the bubble point. 
Recommended applicability range:

• Oil density (API Gravity): 18 – 52 °API
• Pressure: 500 – 8000 psi
• Gas-oil ratio: 50 – 3000 SCF/STB
• Temperature: 100 – 300 °F

De Ghetto et al.

This correlation was developed based on a large volume of experimental PVT data for heavy and extra-heavy crude oils, as earlier models (e.g., Standing, Vasquez & Beggs) produced significant errors for oils with API gravity below 25. The key feature of the model is the classification of fluids into multiple categories based on density, with a separate compressibility formula provided for each class. Its main limitation is that it is not universal—it performs best within the scope of the original data set. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 45 °API
• Pressure: < 5000 psi
• Gas-oil ratio: 0 – 2000 SCF/STB
• Temperature: 80 – 260 °F

De Ghetto et al.

This correlation was developed based on a large set of experimental PVT data for heavy and extra-heavy crude oils, as previously existing models (such as Standing and Vasquez & Beggs) produced significant errors when API gravity was below 25. The key feature of the method is the classification of fluids into several categories based on oil density. Each class has its own dedicated oil compressibility correlation. The main limitation is its lack of universality—it performs best within the bounds of the original dataset. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 45 °API
• Pressure: < 5000 psi
• Gas-oil ratio: 0 – 2000 SCF/STB
• Temperature: 80 – 260 °F

Petrosky

The Petrosky correlation was specifically developed for crude oils from the Gulf of Mexico, but it is also applicable to other regions. Key features of the model include consideration of gas-oil ratio, gas specific gravity, oil density, and temperature. It is optimized for light and medium crude oils. Compared to the Standing correlation, it yields more accurate results under high-temperature conditions. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Pressure: < 8000 psi
• Gas-oil ratio: 100 – 2500 SCF/STB
• Temperature: 100 – 300 °F

Al-Marhoun

The Al-Marhoun (2003) correlation was developed to provide a more accurate estimation of oil compressibility, based on a comprehensive dataset from Middle Eastern reservoirs. The method accounts for the effects of pressure, temperature, gas-oil ratio, and fluid properties, offering improved accuracy compared to classical correlations. A distinctive feature is the use of power-law relationships optimized for various thermobaric (temperature-pressure) conditions. 
Recommended applicability range:

• Oil density (API Gravity): 18 – 44 °API
• Pressure: 500 – 8000 psi
• Gas-oil ratio: 50 – 3000 SCF/STB
• Temperature: 100 – 300 °F

Lasater

The Lasater (1958) correlation was developed based on the analysis of crude oils from Canadian and U.S. fields. The method uses an empirical relationship linking oil compressibility with pressure, gas-oil ratio, and fluid properties. A key feature of this approach is its emphasis on the influence of gas solubility, making it particularly useful for oils with high gas content. At pressures above 3000 psi, the correlation may underestimate compressibility—other models are recommended for such conditions. 
Recommended applicability range:

• Oil density (API Gravity): 20 – 45 °API
• Pressure: 100 – 3000 psi
• Gas-oil ratio: 50 – 1500 SCF/STB
• Temperature: 100 – 250 °F

Ahmed

The empirical correlation proposed by Tarek Ahmed is used to estimate the isothermal compressibility of crude oil. It is based on the analysis of PVT data for light and medium crude oils and is applicable when laboratory measurements are not available. The model accounts for the effects of pressure, dissolved gas, temperature, and oil density. It is known for its simplicity and reliable results under typical reservoir conditions. The correlation is well-suited for early-stage design or reservoir simulators where a quick property estimation is needed. 
Recommended applicability range:

• Oil density (API Gravity): 20 – 45 °API
• Pressure: < 5000 psi
• Gas-oil ratio: 0 – 2000 SCF/STB
• Temperature: 100 – 300 °F

Kartoatmodjo & Schmidt

This correlation is a modern method for calculating oil compressibility, developed using an extensive database of PVT analyses. Unlike classical approaches (e.g., Standing, Vasquez & Beggs), this method is specifically optimized for heavy and highly viscous crude oils, showing particular accuracy under challenging conditions. The formula captures the combined influence of pressure, temperature, gas-oil ratio, and oil density through a system of power-law relationships. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 50 °API
• Pressure: < 8000 psi
• Gas-oil ratio: 20 – 2500 SCF/STB
• Temperature: 80 – 320 °F

A1.5 Heat Capacity

Wright

The Wright (1991) correlation was developed to calculate the isobaric heat capacity of crude oils over a wide range of temperatures and pressures. The method is based on generalized experimental data for various types of crude, including heavy and bituminous oils. A distinguishing feature of the model is its consideration of oil density, temperature, and pressure through polynomial relationships. 
Recommended applicability range: 

• Oil density (API Gravity): 10 – 50 °API
• Pressure: < 5000 psi
• Temperature: 50 – 350 °F

A1.6 Oil Density

McCain

The McCain (1990) correlation is one of the most reliable methods for calculating the density of reservoir oil. It was developed using an extensive PVT database from U.S. oilfields. A key feature of this method is its consideration of the effects of dissolved gas, pressure, and temperature on oil density. The correlation is widely used in engineering calculations due to its strong accuracy and physical relevance. 
Recommended applicability range:

• Temperature: 100 – 300 °F
• Oil density (API Gravity): 18 – 45 °API
• Gas-oil ratio: 50 – 3000 SCF/STB
• Pressure: 500 – 10,000 psi

Ahmed

This correlation was developed by Tarek Ahmed and published in his classic work Reservoir Engineering Handbook (1989). It is intended for estimating the density of gas-saturated crude oil under standard conditions. The correlation is widely used in PVT analysis when laboratory data is unavailable. It expresses oil density as a function of gas-oil ratio, oil specific gravity, and gas specific gravity. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 50 °API
• Gas-oil ratio: 0 – 2000 SCF/STB
• Gas specific gravity (air = 1): 0.6 – 1.3

Katz

The Katz (1942) correlation is one of the earliest and most well-known empirical models for estimating reservoir oil density, accounting for the effect of dissolved gas. It is based on extensive experimental data. This correlation was widely used before the development of more advanced models such as Standing and Vasquez & Beggs. 
Recommended applicability range:

• Temperature: 60 – 220 °F
• Oil density (API Gravity): 15 – 45 °API
• Gas-oil ratio: 20 – 1000 SCF/STB
• Pressure: 100 – 5000 psi

Standing

The Standing (1947) correlation is a classical method for calculating oil density under reservoir conditions. It accounts for the effects of dissolved gas, pressure, temperature, and the properties of both oil and gas. Based on experimental data from California oilfields, the correlation remains widely used today in black oil models. 
Recommended applicability range:

• Temperature: 60 – 250 °F
• Oil density (API Gravity): 15 – 45 °API
• Gas-oil ratio: 20 – 1500 SCF/STB
• Pressure: 50 – 5000 psi

A2.1 Formation Volume Factor

McCain

The McCain (1990) correlation is a classical method for calculating the formation water volume factor. The method accounts for the effects of pressure, temperature, salinity (TDS), and dissolved gas, offering a physically grounded model with high accuracy. A key feature is the separate treatment of water compressibility and thermal expansion. For formation waters with TDS > 50,000 ppm, a salinity correction is required. 
Recommended applicability range:

• Temperature: 100 – 400 °F
• Salinity (TDS): 0 – 200,000 ppm
• Gas content: 0 – 50 SCF/STB
• Pressure: 14.7 – 10,000 psi

A2.2 Viscosity

McCain

The McCain (1991) correlation estimates the viscosity of formation water based on temperature, pressure, and salinity. It accounts for the effect of dissolved salts, making it more accurate than simple correlations for pure water. The model is based on experimental data and is widely used in the oil and gas industry. It provides good accuracy for moderately to highly saline waters, but for highly mineralized water (near the applicability limits), comparison with laboratory data is recommended. 
Recommended applicability range:

• Salinity: up to 200,000 ppm
• Temperature: 30 – 300 °F
• Pressure: < 10,000 psi

Beggs & Brill

The Beggs & Brill (1973) correlation was developed to calculate water viscosity in oil production processes. It is especially applicable to multiphase flow in wells. The formula accounts for the effects of temperature and pressure but does not include a correction for salinity, making it more suitable for relatively fresh formation waters. 
Recommended applicability range:

• Salinity: not considered; suitable for low-salinity water
• Temperature: 60 – 300 °F
• Pressure: < 10,000 psi

Matthews & Russell

The Matthews & Russell (1967) correlation allows for estimating the viscosity of formation water by considering temperature, pressure, and salinity. It is based on experimental data and is suitable for engineering calculations in the oil and gas industry. Unlike McCain's method, this correlation uses a simpler model but remains popular due to its reliability under standard conditions. 
Recommended applicability range:

• Salinity: up to 200,000 ppm
• Temperature: 60 – 400 °F
• Pressure: < 10,000 psi

HP Petroleum

HP Petroleum is a modern commercial software package for modeling PVT properties, incorporating advanced correlations for calculating water viscosity. Unlike classical correlations, HPPFP uses more sophisticated models that account for:

• Temperature effects (from cryogenic to high-temperature conditions),
• Pressure (including ultra-high pressures),
• Salinity (including complex salt compositions),
• Dissolved gases (H ₂ S, CO ₂ ).

Recommended applicability range:

• Temperature: 30 – 500 °F
• Salinity: up to 300,000 ppm
• Pressure: < 10,000 psi

A2.3 Oil Viscosity

A2.3.1 Dead Oil Viscosity

Beal

The Beal correlation is one of the earliest but still widely used empirical models for estimating the viscosity of dead (degassed) oil. It is based on experimental data from North American crude oils. The correlation links viscosity with oil density and temperature. 
Recommended applicability range:

• Oil density (API Gravity): 14 – 40 °API
• Temperature: 100 – 220 °F
• Viscosity: 1 – 1000 cP (accuracy decreases for values > 100 cP)

Beggs & Robinson 

The Beggs & Robinson correlation estimates the viscosity of dead (degassed) oil based on oil density and temperature. It performs well for light and medium crude oils (above 22°API) but is less accurate for heavy oils (below 16°API) and highly viscous fluids. 
Recommended applicability range:

• Oil density (API Gravity): 16 – 58 °API
• Temperature: 70 – 295 °F
• Viscosity: 0.5 – 50 cP

Bergman

The Bergman correlation (2004) was developed specifically for heavy and bituminous crude oils, where classical models (such as Beggs & Robinson) often produce significant errors. This model is based on an extensive database that includes high-viscosity oil samples and provides more accurate predictions under complex conditions. 
Recommended applicability range:

• Oil density (API Gravity): 5 – 30 °API
• Temperature: 60 – 300 °F
• Viscosity: 10 – 20,000 cP

De Ghetto

The De Ghetto correlation was developed to estimate the viscosity of dead oil based on data from Mediterranean and Middle Eastern crude oils. It is particularly useful for medium and heavy oils, where many classical correlations (such as Beggs & Robinson) yield significant errors. The correlation is well-suited for high-sulfur crude oils. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 45 °API
• Temperature: 80 – 300 °F
• Viscosity: 1 – 500 cP

De Ghetto (Agip)

The De Ghetto et al. correlation (developed for Agip) is designed to estimate the viscosity of dead oil, with a focus on heavy and bituminous crudes. It is based on a comprehensive database including samples from various regions and provides two separate formulas for heavy and light oils. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 48 °API
• Temperature: 60 – 300 °F
• Viscosity: 1 – 50,000 cP

Petrosky

The Petrosky (1990) correlation was developed based on the analysis of PVT properties of crude oils from Gulf of Mexico fields. A key feature of the model is its adaptation to high-temperature conditions and oils with elevated gas content, which are typical for the region. The correlation performs well for paraffinic oils. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Temperature: 80 – 320 °F
• Viscosity: 0.5 – 200 cP

Egbogah

The Egbogah correlation was specifically developed for accurate prediction of dead oil viscosity, especially under high-temperature conditions and for heavy fluids. Unlike classical methods (Beal, Beggs & Robinson), this correlation incorporates an enhanced temperature dependence and modified coefficients, providing better accuracy for oils with API < 25°. The formula is based on statistical analysis of data from Canadian oil fields, making it particularly useful for oils with atypical properties. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 45 °API
• Temperature: 50 – 300 °F
• Viscosity: 1 – 100,000 cP

Kartohadiprodjo & Schmidt

This correlation was developed based on an extensive database comprising over 4,500 crude oil samples from around the world. It is considered one of the most universal and accurate methods for estimating dead oil viscosity, especially across a wide range of oil densities. Additionally, it accounts for the nonlinear dependence of viscosity on both temperature and oil gravity. It is claimed to outperform Beggs & Robinson and Glaso correlations in terms of accuracy, particularly for heavy oils. 
Recommended applicability range:

• Oil density (API Gravity): 6 – 50 °API
• Temperature: 70 – 295 °F
• Viscosity: 1 – 10,000 cP (highest accuracy in the range of 10 – 1,000 cP)

Khan

The Khan correlation is a modified version of the classical Beggs & Robinson method, specifically developed for accurate prediction of dead oil viscosity across a wide range of temperatures and oil gravities. The method introduces additional correction factors that enhance accuracy for heavy oils and high-temperature conditions. The formula is based on statistical analysis of data from Pakistani oil fields but has demonstrated good applicability to other regions. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 45 °API
• Temperature: 70 – 300 °F
• Viscosity: 1 – 10,000 cP (highest accuracy in the range of 10 – 1,000 cP)

Glaso

The Glaso correlation was developed based on PVT data analysis for North Sea crude oils. It estimates dead oil viscosity at atmospheric pressure using oil density and temperature. Compared to the Beal and other early correlations, Glaso offers a wider temperature applicability range. It is particularly suitable for North Sea oils but has been validated on fields in other regions as well. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 50 °API
• Temperature: 50 – 300 °F
• Viscosity: 0.5 – 50 cP

A2.3.2 Saturated Oil Viscosity

Beggs & Robinson

The Beggs & Robinson correlation estimates the viscosity of saturated oil containing dissolved gas. It is based on data from North American crude oils and involves two steps: calculating the viscosity of dead oil, and then applying a correction for the presence of dissolved gas. The correlation is known for its simplicity and reliable accuracy for light and medium oils (20–45 °API). 
Recommended applicability range:

• Oil density (API Gravity): 16 – 58 °API
• Temperature: 70 – 295 °F
• Viscosity: 0.5 – 50 cP
• Solution gas–oil ratio (GOR): 20 – 2000 SCF/STB

Beal

The Beal correlation is one of the earliest fundamental methods for calculating the viscosity of saturated oil. It was developed based on experimental data from North American crude oils. The method defines viscosity as a function of bubble point pressure, temperature, and oil density using a set of empirical coefficients. Its key feature is simplicity and reliability under standard conditions, although additional adjustments may be required for heavy oils or extreme conditions. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Temperature: 100 – 220 °F
• Viscosity: 0.5 – 50 cP

Bergman

The Bergman correlation (2004) is designed to estimate the viscosity of saturated oil based on the viscosity of dead oil and solution gas-oil ratio. It is most suitable for medium-density oils with moderate gas content but may introduce errors for heavy oils, condensates, or extreme gas-oil ratios. The formula is simple to apply but should not replace laboratory measurements when working with non-standard fluids. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Temperature: 70 – 300 °F
• Viscosity: 0.5 – 50 cP
• Gas-oil ratio: 50 – 2000 SCF/STB

De Ghetto

The De Ghetto empirical correlation was developed based on an extensive analysis of experimental data for saturated oil. It was primarily designed for application to Brazilian oilfield conditions but has demonstrated good versatility and applicability beyond this region. 
Recommended applicability range:

• Oil density (API Gravity): 16 – 45 °API
• Temperature: 20 – 260 °F
• Viscosity: 0.1 – 1000 cP
• Gas-oil ratio: 10 – 2000 SCF/STB

De Ghetto Agip

The De Ghetto correlation, developed by Agip, is designed to estimate the viscosity of saturated oil based on its density, gas-oil ratio, and temperature. It is derived from a statistical analysis of various oil types, including heavy and highly viscous oils, making it more versatile than many other methods. The formula includes correction factors to account for the influence of oil density and dissolved gas content, allowing for application across a wide range of conditions. 
Recommended applicability range:

• Oil density (API Gravity): 6 – 50 °API
• Temperature: 80 – 300 °F
• Viscosity: 0.5 – 1000 cP
• Gas-oil ratio: 50 – 2000 SCF/STB

Petrosky

The Petrosky correlation was specifically developed for Gulf of Mexico crude oils, considering the high temperatures and pressures typical of deepwater reservoirs. It provides high accuracy for light to medium oils (20–40 °API) and includes a correction for gas-oil ratio. Compared to Beggs & Robinson, it demonstrates 10–15% better accuracy for Gulf of Mexico conditions. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Temperature: 80 – 320 °F
• Viscosity: 0.5 – 50 cP
• Gas-oil ratio: 100 – 2500 SCF/STB

Egbogah

The Egbogah correlation was specifically developed for heavy and bituminous oils (5–25 °API). It accounts for the effects of gas-oil ratio, dead oil viscosity, and temperature. This model is especially useful for "cold" reservoirs and crudes with high asphaltene content. It is not applicable to light oils. 
Recommended applicability range:

• Oil density (API Gravity): 5 – 25 °API
• Temperature: 60 – 250 °F
• Viscosity: 50 – 50,000 cP
• Gas-oil ratio: 20 – 800 SCF/STB

Chu & Connally

The Chu & Connally correlation estimates the viscosity of saturated oil based on dead oil viscosity and gas-oil ratio. It is especially useful for light and medium oils and is widely used in engineering calculations. The model accounts for the nonlinear effect of dissolved gas on oil viscosity, but it is less accurate for heavy oils (API < 20) and highly viscous fluids (>50 cP). 
Recommended applicability range:

• Oil density (API Gravity): 15 – 50 °API
• Temperature: 70 – 295 °F
• Viscosity: 0.5 – 50 cP
• Gas-oil ratio: 50 – 3500 SCF/STB

Standing

Standing proposed an empirical correlation to estimate the viscosity of saturated oil based on data from California oil fields. The method relates viscosity to pressure, temperature, gas-oil ratio, and oil density. The correlation is simple to apply and suitable for "Black oil" models without significant amounts of non-hydrocarbon components. At high gas-oil ratios, it may overestimate viscosity. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Temperature: 100 – 250 °F
• Pressure: < 5000 psi
• Gas-oil ratio: 90 – 1500 SCF/STB

Kartotomojo & Schmidt

The early version of the Kartotomojo & Schmidt (1991) correlation was developed as an improvement over the Standing and Beggs & Robinson models. It provides more accurate viscosity predictions for a wide range of crude oils, especially for fields in Southeast Asia. This version of the correlation uses a power-law dependency on gas-oil ratio and dead oil viscosity, delivering better accuracy for heavy and high-viscosity oils. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 45 °API
• Temperature: 100 – 300 °F
• Viscosity: 1 – 5000 cP
• Gas-oil ratio: 50 – 2500 SCF/STB

Khan

The Khan correlation was developed for predicting saturated oil viscosity by accounting for the effects of gas-oil ratio, temperature, and oil density. It is particularly useful across a wide range of oil properties, including heavy fluids. Its main advantage is versatility, as it is applicable to light, medium, and heavy crude oils. Additionally, the model accounts for the significant impact of high gas-oil ratios on viscosity. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Temperature: 100 – 300 °F
• Viscosity: 1 – 1000 cP
• Gas-oil ratio: 200 – 2500 SCF/STB

Glaso

Glaso (1980) proposed a generalized correlation for estimating oil viscosity, taking into account gas-oil ratio, oil and gas density, and temperature. It is better suited for light and medium crude oils than Standing’s method, especially under high gas-oil ratios. The correlation offers improved accuracy compared to older models due to the generalization of a large dataset. However, it is not recommended for heavy oils (API < 15°). 
Recommended applicability range:

• Oil density (API Gravity): 15 – 55 °API
• Temperature: 70 – 295 °F
• Gas-oil ratio: 50 – 3500 SCF/STB

A2.3.3 Undersaturated Oil Viscosity

Beal 

The Beal correlation (1946) is one of the earliest and most well-known methods for estimating undersaturated oil viscosity. It is based on empirical data from North American crude oils and uses a power-law relationship linking viscosity at bubble-point pressure to viscosity at higher pressures. The formula accounts for the effects of pressure, temperature, and oil density, but does not explicitly include gas-oil ratio. Due to its simplicity and age, the correlation is not suitable for oils with unusual properties. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Temperature: 100 – 220 °F
• Viscosity: 0.5 – 50 cP
• Pressure: P_b – 5000 psi

Beggs & Robinson

The Beggs & Robinson correlation (1975) was developed based on a large dataset of laboratory measurements for North American crude oils. It estimates the increase in oil viscosity at pressures above the bubble point. The method accounts for the effects of pressure, saturated oil properties, and temperature. Due to its simplicity and satisfactory accuracy for most oil types, this correlation has become widely used in petroleum engineering. 
Recommended applicability range:

• Oil density (API Gravity): 16 – 58 °API
• Temperature: 70 – 295 °F
• Gas-oil ratio: 20 – 2100 SCF/STB
• Pressure: P_b – 8000 psi

Bergman

The Bergman correlation (2004) is designed to calculate the viscosity of undersaturated oil at pressures above the bubble point, particularly for heavy and bituminous fluids (5–25 °API). It employs an exponential relationship with pressure difference and includes a correction factor that accounts for gas-oil ratio and saturated oil viscosity. The model demonstrates good accuracy for high-viscosity oils and is recommended for use in "cold" reservoirs with typical formation conditions. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 40 °API
• Temperature: 100 – 300 °F
• Gas-oil ratio: 20 – 1500 SCF/STB
• Pressure: P_b – 5000 psi

De Ghetto

The De Ghetto correlation was developed to predict the viscosity of undersaturated oil, with a particular focus on heavy and bituminous crudes. The method provides separate calculation approaches for light and heavy fluids, ensuring high accuracy across a broad range of conditions. 
Recommended applicability range:

• Oil density (API Gravity): 10 – 45 °API
• Temperature: 100 – 250 °F
• Gas-oil ratio: 50 – 2500 SCF/STB
• Pressure: P_b – 8000 psi

De Ghetto Agip

The De Ghetto correlation, developed by Agip, is designed to predict oil viscosity at pressures above the bubble point. It accounts for overpressure, saturated oil viscosity, and gas-oil ratio, delivering high accuracy for medium to heavy crudes (10–35 °API). 
Recommended applicability range:

• Oil density (API Gravity): 10 – 35 °API
• Gas-oil ratio: 50 – 1500 SCF/STB
• Pressure: P_b – 8000 psi

Petrosky

The Petrosky correlation was specifically developed for Gulf of Mexico crude oils. It demonstrates good accuracy in predicting undersaturated oil viscosity under high-pressure conditions. The method is based on a modification of the classical Beal approach, incorporating regional fluid characteristics. The formula employs a power-law relationship linking viscosity at bubble point pressure to viscosity at higher pressures. 
Recommended applicability range:

• Oil density (API Gravity): 16 – 45 °API
• Gas-oil ratio: 100 – 3500 SCF/STB
• Viscosity: 0.5 – 50 cP
• Pressure: P_b – 10,000 psi

Shilov

The Shilov correlation was developed to address modern field development conditions, particularly considering the characteristics of Russian crude oils. It is based on machine learning and the analysis of an extensive PVT database. The method delivers high accuracy for oils with anomalous properties and under high-pressure conditions. It accounts for thermobaric conditions, oil composition, and gas-oil ratio. 
Recommended applicability range:

• Oil density (API Gravity): 12 – 45 °API
• Gas-oil ratio: 50 – 2500 SCF/STB
• Temperature: 100 – 350 °F
• Pressure: P_b – 10,000 psi

Gimatutdinov

The Gimatutdinov correlation was developed based on studies of oil fields in the former USSR. It is widely used in field development practices across CIS countries. The method incorporates the effect of pressure above the bubble point on oil viscosity through a logarithmic relationship. A distinctive feature of this correlation is its adaptation to the conditions of Western Siberia and other traditional oil-producing regions of the USSR/Russia. 
Recommended applicability range:

• Oil density (API Gravity): 18 – 40 °API
• Gas-oil ratio: 200 – 4500 SCF/STB
• Temperature: 65 – 250 °F
• Pressure: P_b – 6,000 psi

Mishchenko

The Mishchenko correlation was developed to estimate oil viscosity under high-pressure conditions typical of deep reservoirs. The method is based on a modified exponential approach that incorporates thermodynamic parameters. A key feature of this correlation is its high accuracy for oils with elevated dissolved gas content and under abnormal reservoir conditions. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 48 °API
• Gas-oil ratio: 100 – 3000 SCF/STB
• Temperature: 140 – 400 °F
• Pressure: < 12,000 psi

Chu & Connally

The Chu & Connally correlation (1959) is one of the earliest and most widely used models for estimating oil viscosity at pressures above the bubble point. It is based on experimental data from U.S. oilfields and uses a power-law relationship to account for the effect of pressure on viscosity. The method is especially popular due to its simplicity and reliability under standard reservoir conditions. 
Recommended applicability range:

• Oil density (API Gravity): 20 – 45 °API
• Gas-oil ratio: 50 – 1500 SCF/STB
• Temperature: 100 – 250 °F
• Pressure: < 5000 psi

Standing

Standing (1947) proposed one of the earliest practical correlations for estimating changes in oil viscosity at pressures above the bubble point. The method is based on data from California oilfields and uses a linear relationship between the logarithm of viscosity and pressure. Although considered outdated, this correlation is still used for preliminary calculations due to its simplicity. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Gas-oil ratio: 90 – 1500 SCF/STB
• Temperature: 100 – 250 °F
• Pressure: < 5000 psi

Kartoatmodjo & Schmidt

The Kartoatmodjo & Schmidt (1991) correlation was developed to predict the viscosity of undersaturated oil with high accuracy, especially for heavy and bituminous crudes. It is based on an extensive database of more than 1,500 analyzed samples. The correlation accounts for the effects of pressure, temperature, gas-oil ratio, and oil density. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 40 °API
• Temperature: 100 – 250 °F
• Gas-oil ratio: 20 – 2500 SCF/STB
• Pressure: P_b – 5000 psi

Khan

The Khan correlation was developed to predict the viscosity of undersaturated oil, with particular emphasis on accounting for the effects of pressure, temperature, and fluid composition. Unlike many other methods, this correlation explicitly incorporates temperature dependence, making it especially useful in wide temperature range conditions. The formula is based on data from Pakistani oil fields but has shown good accuracy for other regions as well. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 45 °API
• Temperature: 100 – 300 °F
• Gas-oil ratio: 100 – 2500 SCF/STB
• Viscosity: 0.5 – 50 cP
• Pressure: P_b – 10,000 psi

Glaso

The Glaso correlation (1980) is an advanced method for calculating oil viscosity at pressures above the bubble point. It was developed based on an extensive database from North Sea oil fields. A key feature of this method is the use of a logarithmic relationship that captures the nonlinear behavior of viscosity as pressure increases. 
Recommended applicability range:

• Oil density (API Gravity): 18 – 52 °API
• Temperature: 100 – 300 °F
• Gas-oil ratio: 100 – 3000 SCF/STB
• Pressure: Pb – 8000 psi

Vazquez & Beggs

The Vazquez & Beggs correlation is designed to estimate oil viscosity in the undersaturated region. It accounts for the effects of pressure, temperature, and oil properties using a power-law relationship based on extensive laboratory data. The formula relates oil viscosity at the bubble point pressure to its value at higher pressures. It is most suitable for light and medium oils (API > 20°), where the correlation provides the highest accuracy. 
Recommended applicability range:

• Oil density (API Gravity): 15 – 50 °API
• Temperature: 100 – 300 °F
• Viscosity: 0.5 – 50 cP
• Pressure: Pb – 10000 psi

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
• 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%

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:

1. Calculation of viscosity at atmospheric pressure.
2. Correction for reservoir pressure and temperature. 
   This approach is simple and reliable but may show deviations when hydrogen sulfide (H ₂ S) 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 (CH ₄ ): > 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 H ₂ S and CO ₂ ). 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
• C ₇⁺ 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
• C ₄ + 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
• C ₇⁺ 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
• CO ₂ content: < 20%
• H ₂ S content: < 25%
• N ₂ 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
• CO ₂ content: < 20%
• H ₂ S content: < 30%
• N ₂ 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 (C ₇⁺ > 5%). 
Recommended applicability range:

• Gas specific gravity (air = 1): 0.55 – 1.0
• CO ₂ content: < 40%
• H ₂ S 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:

• CO ₂ 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)