Standing-Katz Z-Factor Chart

Overview

The gas compressibility factor (Z-factor) relates the actual volume of gas to the volume predicted by the ideal gas law: PV = ZnRT. The Standing-Katz (1942) chart is the industry-standard graphical correlation for Z-factor as a function of pseudo-reduced pressure (Ppr) and pseudo-reduced temperature (Tpr). Analytical methods — primarily Hall-Yarborough (1973) and Dranchuk-Abou-Kassem (DAK, 1975) — provide numerical solutions that replicate the chart.

Theory

Natural gas deviates from ideal gas behavior. The Z-factor quantifies this deviation:

Z = P*V / (n*R*T)

For mixtures, pseudo-critical properties are calculated from gas composition or gravity using Kay's mixing rule or correlations (Sutton, 1985):

Ppc = 756.8 - 131.0*γg - 3.6*γg^2
Tpc = 169.2 + 349.5*γg - 74.0*γg^2

Pseudo-reduced properties:

Ppr = P / Ppc
Tpr = T / Tpc

Formulas

Hall-Yarborough (1973)

Solve for reduced density Y using Newton-Raphson iteration:

F(Y) = -A*Ppr + (Y + Y^2 + Y^3 - Y^4) / (1 - Y)^3 - B*Y^2 + C*Y^D = 0

where:

t = 1 / Tpr
A = -0.06125 * Ppr * t * exp(-1.2*(1-t)^2)
B = 14.76*t - 9.76*t^2 + 4.58*t^3
C = 90.7*t - 242.2*t^2 + 42.4*t^3
D = 2.18 + 2.82*t

Then:

Z = 0.06125 * Ppr * t * exp(-1.2*(1-t)^2) / Y

Dranchuk-Abou-Kassem (DAK, 1975)

11-constant equation: solve for reduced density ρr iteratively:

F(ρr) = 0.27*Ppr/(ρr*Tpr) - 1 - (A1 + A2/Tpr + A3/Tpr^3 + A4/Tpr^4 + A5/Tpr^5)*ρr
        - (A6 + A7/Tpr + A8/Tpr^2)*ρr^2
        + A9*(A7/Tpr + A8/Tpr^2)*ρr^5
        - A10*(1 + A11*ρr^2)*ρr^2/Tpr^3 * exp(-A11*ρr^2)

Constants: A1=0.3265, A2=-1.0700, A3=-0.5339, A4=0.01569, A5=-0.05165, A6=0.5475, A7=-0.7361, A8=0.1844, A9=0.1056, A10=0.6134, A11=0.7210.

Then:

Z = 0.27 * Ppr / (ρr * Tpr)

Worked Example

Given: P = 2,000 psia, T = 200°F (660°R), γg = 0.70

Step 1: Pseudo-critical properties (Sutton):

Ppc = 756.8 - 131.0*0.70 - 3.6*0.49 = 756.8 - 91.7 - 1.76 = 663.3 psia
Tpc = 169.2 + 349.5*0.70 - 74.0*0.49 = 169.2 + 244.7 - 36.3 = 377.6°R

Step 2: Pseudo-reduced properties:

Ppr = 2000 / 663.3 = 3.015
Tpr = 660 / 377.6 = 1.748

Step 3: Hall-Yarborough (iterative):

t = 1/1.748 = 0.572
A = -0.06125 * 3.015 * 0.572 * exp(-1.2*(0.428)^2) = -0.1057 * exp(-0.220) = -0.0849

Newton-Raphson converges to Y ≈ 0.117

Z = 0.06125 * 3.015 * 0.572 * exp(-0.220) / 0.117 = 0.0849 / 0.117 = 0.726

Verification: From Standing-Katz chart at Ppr=3.0, Tpr=1.75 → Z ≈ 0.73. Matches.

Valid Ranges

Corrections for Sour Gas (Wichert-Aziz, 1972)

If gas contains H2S and CO2:

ε = 120*(A^0.9 - A^1.6) + 15*(B^0.5 - B^4)
A = yH2S + yCO2, B = yH2S
Tpc' = Tpc - ε
Ppc' = Ppc * Tpc' / (Tpc + B*(1-B)*ε)

References

1. Standing, M.B. & Katz, D.L. (1942). "Density of Natural Gases." Trans. AIME, 146, 140–149.
2. Hall, K.R. & Yarborough, L. (1973). "A New Equation of State for Z-factor Calculations." Oil & Gas Journal, 71, 82–92.
3. Dranchuk, P.M. & Abou-Kassem, J.H. (1975). "Calculation of Z Factors for Natural Gases Using Equations of State." JCPT, 14(3), 34–36.
4. PetroWiki — Real gases: https://petrowiki.spe.org/Real_gases