Natural Gas Compressibility Factor Z (Sutton, Wichert-Aziz, Dranchuk-Abou-Kassem)
The Z the gas pipeline flow and separator sizing calculators ask you to enter, from the gas gravity, pressure.
Example
You enter
- Gas specific gravity (air = 1) 0.887
- CO2 (mole %, 0 if sweet) 0
- H2S (mole %, 0 if sweet) 0
- Pseudo-critical temperature (°R, blank for Sutton) 396.6
- Pseudo-critical pressure (psia, blank for Sutton) 677.48
- Pressure (psig) 3485.3
- Temperature (°F) 282.44
You get
- Compressibility factor Z 0.9363
Checked against published worked examples from: IEOM Society (Mahmud, Elmabrouk, Sbiga).
Details, formula, and sources
ScopeThe Z the gas pipeline flow and separator sizing calculators ask you to enter, from the gas gravity, pressure, and temperature. Sutton gives the pseudo-critical point from gravity, Wichert-Aziz moves it for CO2 and H2S, and the Dranchuk-Abou-Kassem fit to the Standing-Katz chart gives Z, plus the gas density and formation volume factor. A 0.65 gravity sweet gas at 2,000 psig and 150 F is Z = 0.855, so the ideal-gas guess of 1.0 is 17% off. A lab report's own pseudo-criticals can be entered instead; with those, it matches a published table to 5 decimals. A screen; a lab PVT report governs.
Formula or tableTpc = 169.2 + 349.5 G - 74.0 G^2 degR; Ppc = 756.8 - 131.0 G - 3.6 G^2 psia (Sutton); epsilon = 120 (A^0.9 - A^1.6) + 15 (B^0.5 - B^4), T'pc = Tpc - epsilon, P'pc = Ppc T'pc / (Tpc + B (1 - B) epsilon) (Wichert-Aziz, A = CO2 + H2S, B = H2S mole fractions); Tpr = T/T'pc, Ppr = P/P'pc; Z from the Dranchuk-Abou-Kassem equation with rho_r = 0.27 Ppr / (Z Tpr), A1..A11 = 0.3265, -1.0700, -0.5339, 0.01569, -0.05165, 0.5475, -0.7361, 0.1844, 0.1056, 0.6134, 0.7210; density = P (28.964 G) / (Z 10.7316 T); Bg = Z T 14.696 / (P 519.67).
Source and editionSutton, R.P., Compressibility Factors for High-Molecular-Weight Reservoir Gases, SPE 14265 (1985); Wichert, E. and Aziz, K., Calculate Z's for Sour Gases, Hydrocarbon Processing (May 1972); Dranchuk, P.M. and Abou-Kassem, J.H., Calculation of Z Factors for Natural Gases Using Equations of State, J. Canadian Petroleum Technology (1975), by name.
Free accessThe DAK coefficients and a computed Z table using Sutton's pseudo-criticals are printed in Mahmud, Elmabrouk and Sbiga, Sensitivity Analysis of the Gas Compressibility Factor, IEOM 2018 Proceedings (free at ieomsociety.org/ieom2018/papers/363.pdf); this reproduces its Table 8 to 5 decimals at all nine pressures.
What governsEstimate. AHJ and licensed professional govern.
API field namesgas_gravity, co2_pct, h2s_pct, tpc_r, ppc_psia, pressure_psig, temperature_f, z
- Pseudo-criticals Sutton (1985) from gas gravity unless both are enteredSPE 14265
- Sour-gas correction Wichert-Aziz epsilon on the CO2 and H2S mole fractionsWichert and Aziz (1972)
- Z equation Dranchuk-Abou-Kassem eleven-constant fit to the Standing-Katz chart, 1.0 < Tpr <= 3.0, Ppr <= 30Dranchuk and Abou-Kassem (1975)
- Gauge to absolute pressure entered in psig plus 14.7 psithe sibling oil and gas calculators