Gas PVT Properties

Overview

Accurate prediction of natural gas properties is fundamental to:

• Reservoir simulation — Material balance, GIIP calculations
• Well deliverability — Backpressure equations, AOF determination
• Pipeline design — Pressure drop, compression requirements
• Gas lift optimization — Injection rate and pressure design
• Gas processing — Separation, dehydration, compression

This document covers correlations for essential gas PVT properties:

• Compressibility factor (Z) — Real gas deviation from ideal behavior
• Gas formation volume factor (Bg) — Volume change from standard to reservoir conditions
• Gas compressibility (Cg) — Pressure-volume relationship
• Gas viscosity (μg) — Flow resistance
• Gas density (ρg) — Mass per unit volume
• Pseudo-critical properties — Ppc, Tpc for correlations

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Real Gas Behavior and Z-Factor

The Gas Compressibility Factor

Real gases deviate from ideal gas law ($pV = nRT$) due to:

1. Molecular volume — Gas molecules occupy space
2. Intermolecular forces — Attraction and repulsion between molecules

The compressibility factor (Z) corrects for this deviation:

$$pV = Z n RT$$

Where:

• $Z$ = gas compressibility factor (dimensionless)
• $Z = 1$ for ideal gas
• $Z < 1$ at low P, high T (attraction dominates)
• $Z > 1$ at high P (molecular volume dominates)

Corresponding States Principle

The principle of corresponding states allows prediction of Z using reduced properties:

$$Z = f(p_r, T_r)$$

Where:

• $p_r = p / p_{pc}$ = reduced pressure
• $T_r = T / T_{pc}$ = reduced temperature
• $p_{pc}$, $T_{pc}$ = pseudo-critical pressure and temperature

Physical basis: All fluids behave similarly when compared at same reduced conditions (same distance from critical point).

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Pseudo-Critical Properties

Standing Correlations (1977)

Standing developed correlations for sweet natural gases (no H₂S or CO₂) based on gas specific gravity:

$$p_{pc} = 756.8 - 131.0 \gamma_g - 3.6 \gamma_g^2$$$$T_{pc} = 169.2 + 349.5 \gamma_g - 74.0 \gamma_g^2$$

Where:

• $p_{pc}$ = pseudo-critical pressure, psia
• $T_{pc}$ = pseudo-critical temperature, °R
• $\gamma_g$ = gas specific gravity (air = 1.0)

Applicability:

• Gas gravity: 0.55 to 1.60
• Temperatures: to 360°F
• Pressures: to 12,500 psia
• Accuracy: Z-factor within ±2% of experimental
• Sweet gases only (minimal H₂S, CO₂)

Physical trends:

• Heavier gases (high γg) → Lower Tpc, lower Ppc
• Methane (γg ≈ 0.55): Tpc ≈ 343°R, Ppc ≈ 667 psia
• Heavy gas (γg ≈ 1.0): Tpc ≈ 393°R, Ppc ≈ 623 psia

Sutton Correlations (1985)

Sutton improved Standing's correlations for better accuracy with separator gas:

$$p_{pc} = 787 - 147 \gamma_g - 7.5 \gamma_g^2$$$$T_{pc} = 169 + 314 \gamma_g - 71.3 \gamma_g^2$$

Advantages over Standing:

• Better for separator gas compositions
• Accounts for presence of intermediate hydrocarbons (C₂-C₆)
• Slightly better accuracy for condensate gases

When to use:

• Standing — Standard choice for most applications
• Sutton — When dealing with separator gas from high-GOR wells
• Either gives acceptable results within typical engineering accuracy

Acid Gas Corrections

For sour gases containing H₂S and CO₂, apply Wichert-Aziz corrections:

$$T_{pc}' = T_{pc} - \epsilon$$$$p_{pc}' = \frac{p_{pc} T_{pc}'}{T_{pc} + y_{H_2S}(1 - y_{H_2S})\epsilon}$$

Where:

$$\epsilon = 120(f_{acid}^{0.9} + f_{acid}^{1.6}) + (f_{H_2S}^{0.5} - f_{H_2S}^4)$$

And:

• $f_{acid} = y_{H_2S} + y_{CO_2}$ (total acid gas fraction)
• $y_{H_2S}$, $y_{CO_2}$ = mole fractions of H₂S and CO₂

Applicability:

• CO₂ to 55 mol%
• H₂S to 74 mol%
• Temperatures to 300°F
• Pressures to 7,000 psia
• Z-factor accuracy within ±5%

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Z-Factor Correlations

Dranchuk-Abou-Kassem (DAK) Correlation (1975)

The DAK correlation is the industry standard for Z-factor calculation. It fits the Standing-Katz chart using an 11-coefficient equation of state:

$$Z = 1 + \left(A_1 + \frac{A_2}{T_r} + \frac{A_3}{T_r^3} + \frac{A_4}{T_r^4} + \frac{A_5}{T_r^5}\right)\rho_r$$$$+ \left(A_6 + \frac{A_7}{T_r} + \frac{A_8}{T_r^2}\right)\rho_r^2 - A_9\left(\frac{A_7}{T_r} + \frac{A_8}{T_r^2}\right)\rho_r^5$$$$+ A_{10}\left(1 + A_{11}\rho_r^2\right)\frac{\rho_r^2}{T_r^3}\exp\left(-A_{11}\rho_r^2\right)$$

Where the reduced density is calculated iteratively from:

$$\rho_r = \frac{0.27 p_r}{Z T_r}$$

Coefficients:

Calculation procedure:

1. Calculate $p_r = p/p_{pc}$ and $T_r = T/T_{pc}$
2. Initialize $Z = 1.0$ (first guess)
3. Calculate $\rho_r = 0.27 p_r / (Z T_r)$
4. Evaluate $Z$ from equation
5. Repeat steps 3-4 until convergence (typically 3-5 iterations)

Accuracy:

• Within 1% of Standing-Katz chart for 0.2 < $p_r$ < 15, 0.7 < $T_r$ < 3.0
• Within 3% for 15 < $p_r$ < 30 (very high pressure)

Advantages:

• Direct algebraic evaluation (no chart reading)
• Highly accurate across wide range
• Extrapolates well outside original data range
• Industry-standard implementation

Brill-Beggs Z-Factor (1973)

Simplified correlation for quick hand calculations (less accurate than DAK):

$$A = 1.39(T_r - 0.92)^{0.5} - 0.36 T_r - 0.101$$$$B = (0.62 - 0.23 T_r) p_r + \left(\frac{0.066}{T_r - 0.86} - 0.037\right) p_r^2 + \frac{0.32}{10^{9(T_r-1)}} p_r^6$$$$C = 0.132 - 0.32 \log T_r$$$$D = 10^{(0.3106 - 0.49 T_r + 0.1824 T_r^2)}$$$$Z = A + (1 - A) e^{-B} + C p_r^D$$

When to use:

• Quick estimates without iteration
• Spreadsheet without circular reference capability
• Accuracy ±5% (adequate for many engineering calculations)

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Gas Formation Volume Factor (Bg)

The gas FVF relates reservoir volume to standard volume:

$$B_g = \frac{V_R}{V_{sc}} = \frac{Z T}{P} \times \frac{P_{sc}}{T_{sc}}$$

Using standard conditions (14.65 psia, 60°F = 520°R):

$$B_g = 0.00502 \frac{Z T}{p}$$

Or in field units (res bbl/scf):

$$B_g = \frac{0.00502 \times Z \times T}{p}$$

Where:

• $B_g$ = gas formation volume factor, res bbl/scf
• $Z$ = compressibility factor at $(p, T)$
• $T$ = temperature, °R
• $p$ = pressure, psia

Physical interpretation:

• $B_g$ increases with temperature (expansion)
• $B_g$ decreases with pressure (compression)
• Typical values: 0.0005 to 0.01 bbl/scf (reservoir conditions)

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Gas Compressibility (Cg)

The isothermal gas compressibility measures volume change with pressure:

$$C_g = -\frac{1}{V}\left(\frac{\partial V}{\partial p}\right)_T = \frac{1}{p} - \frac{1}{Z}\left(\frac{\partial Z}{\partial p}\right)_T$$

On a pseudo-reduced basis:

$$c_{pr} = C_g p_{pc} = \frac{1}{p_r} - \frac{0.27}{Z^2 T_r}\left[\frac{(\partial Z/\partial \rho_r)_{T_r}}{1 + (\rho_r/Z)(\partial Z/\partial \rho_r)_{T_r}}\right]$$

The derivative $\partial Z/\partial \rho_r$ is obtained by differentiating the DAK equation.

Practical approximation:

For moderate pressures ($p_r$ < 5):

$$C_g \approx \frac{1}{p}$$

For all pressures, calculate from Z using numerical differentiation or use charts.

Typical values:

• Low pressure (100 psia): Cg ≈ 0.01 psi⁻¹
• Moderate pressure (1000 psia): Cg ≈ 0.001 psi⁻¹
• High pressure (5000 psia): Cg ≈ 0.0002 psi⁻¹

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Gas Density

Gas density at reservoir conditions:

$$\rho_g = \frac{p M_g}{Z R T}$$

Using molecular weight $M_g = 28.96 \gamma_g$ (where air MW = 28.96):

$$\rho_g = \frac{28.96 \gamma_g p}{10.73 Z T}$$

Simplifying:

$$\rho_g = \frac{2.70 \gamma_g p}{Z T}$$

Where:

• $\rho_g$ = gas density, lb/ft³
• $\gamma_g$ = gas specific gravity (air = 1.0)
• $p$ = pressure, psia
• $T$ = temperature, °R
• $Z$ = compressibility factor

At standard conditions (14.65 psia, 60°F, Z ≈ 1.0):

$$\rho_{g,sc} = 0.0764 \gamma_g \text{ lb/ft}^3$$

Or equivalently: 1 scf of gas weighs $(0.0764 \gamma_g / 5.615)$ lb/scf.

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Gas Viscosity — Lee-Gonzalez-Eakin (LGE) Correlation (1966)

Gas viscosity affects flow resistance in reservoirs, wells, and pipelines. The LGE correlation predicts μg from density and molecular weight:

$$\mu_g = K \exp\left(X \rho_g^Y\right) \times 10^{-4}$$

Where:

$$K = \frac{(7.77 + 0.0063 M_a) T^{1.5}}{122.4 + 12.9 M_a + T}$$$$X = 2.57 + \frac{1914.5}{T} + 0.0095 M_a$$$$Y = 1.11 + 0.04 X$$

And:

• $\mu_g$ = gas viscosity, cP
• $\rho_g$ = gas density, g/cm³ (divide lb/ft³ by 62.4)
• $M_a$ = apparent molecular weight = $28.96 \gamma_g$
• $T$ = temperature, °R

Accuracy:

• Standard deviation: ±1.9% for light hydrocarbons
• ±5% for natural gas mixtures
• Valid to 340°F and 8,000 psia

Physical trends:

• μg increases with pressure (increased density, molecular collisions)
• μg increases with temperature (faster molecular motion)
• Heavier gases have higher viscosity

Typical values:

• Light gas (γg = 0.6) at 1000 psia, 150°F: μg ≈ 0.015 cP
• Heavy gas (γg = 0.9) at 3000 psia, 200°F: μg ≈ 0.025 cP

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Related Documentation

• PVT Overview — Property correlation selection guide
• Water Properties — Formation water PVT
• Vertical Flow Correlations — Gas well hydraulics
• Gas Well Deliverability — Darcy and non-Darcy flow

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References

1. Dranchuk, P.M. and Abou-Kassem, J.H. (1975). "Calculation of Z Factors for Natural Gases Using Equations of State." Journal of Canadian Petroleum Technology, 14(3), pp. 34-36. PETSOC-75-03-03.

2. Lee, A.L., Gonzalez, M.H., and Eakin, B.E. (1966). "The Viscosity of Natural Gases." Journal of Petroleum Technology, 18(8), pp. 997-1000. SPE-1340-PA.

3. McCain, W.D. Jr. (1991). "Reservoir-Fluid Property Correlations—State of the Art." SPE Reservoir Engineering, 6(2), pp. 266-272. SPE-18571-PA.

4. Standing, M.B. (1977). "Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems." 9th Printing. Richardson, TX: Society of Petroleum Engineers.

5. Sutton, R.P. (1985). "Compressibility Factors for High-Molecular-Weight Reservoir Gases." SPE 14265, presented at SPE Annual Technical Conference, Las Vegas.

6. Wichert, E. and Aziz, K. (1972). "Calculate Z's for Sour Gases." Hydrocarbon Processing, 51(5), pp. 119-122.

7. Ahmed, T. (2019). Reservoir Engineering Handbook, 5th Edition. Cambridge, MA: Gulf Professional Publishing. Chapter 3: Fundamentals of Rock Properties.

8. Whitson, C.H. and Brule, M.R. (2000). Phase Behavior. Monograph Series Vol. 20. Richardson, TX: Society of Petroleum Engineers. Chapter 4: Natural Gas Properties.