Gas Compressibility Z-Factor Formula

Gas compressibility encompasses two related concepts: the Z-factor (gas deviation factor) and the isothermal gas compressibility coefficient (cg). Both are critical for gas reserves estimation, well testing, gas flow calculations, and material balance. This tool calculates Z-factor using multiple co...

Overview

Theory

Real Gas Equation of State

PV = ZnRT

Isothermal Gas Compressibility

cg = (1/P) - (1/Z) * (dZ/dP)|_T

At low pressures, cg ≈ 1/P (ideal gas behavior). At high pressures, the dZ/dP term becomes significant.

Pseudo-Reduced Compressibility

cpr = cg * Ppc

This is correlated to Ppr and Tpr by Mattar et al. (1975) and Trube (1957).

Formulas

Gas Density

ρg = P * Mg / (Z * R * T)

where Mg = 28.97 * γg (molecular weight of gas), R = 10.73 psi·ft³/(lbmol·°R).

Gas Formation Volume Factor

Bg = 0.02829 * Z * T / P (res ft³/scf)

or in RB/scf:

Bg = 0.00504 * Z * T / P

Isothermal Compressibility (Mattar et al., 1975)

Using DAK Z-factor correlation, cg can be computed analytically:

cpr = (1/Ppr) - (0.27/(Z^2 * Tpr)) * (dZ/dρr) / (1 + (ρr/Z)*(dZ/dρr))

Gas Viscosity (Lee-Gonzalez-Eakin, 1966)

μg = K * exp(X * ρg^Y) * 1e-4
K = (9.4 + 0.02*Mg) * T^1.5 / (209 + 19*Mg + T)
X = 3.5 + 986/T + 0.01*Mg
Y = 2.4 - 0.2*X

Worked Example

Given: P = 3,000 psia, T = 180°F (640°R), γg = 0.65, Z = 0.82 (from Standing-Katz)

Gas density:

Mg = 28.97 * 0.65 = 18.83 lb/lbmol
ρg = 3000 * 18.83 / (0.82 * 10.73 * 640)
   = 56,490 / 5,631
   = 10.03 lb/ft³

Gas FVF:

Bg = 0.02829 * 0.82 * 640 / 3000
   = 14.85 / 3000
   = 0.00495 res ft³/scf

Gas compressibility (approximate at moderate pressure):

If dZ/dP ≈ -0.0001 /psi (estimated from Z-P slope):
cg = 1/3000 - (1/0.82)*(-0.0001) = 3.33e-4 + 1.22e-4 = 4.55e-4 /psi

Valid Ranges

Parameter	Typical Range
Ppr	0.2 – 15
Tpr	1.05 – 3.0
γg	0.55 – 1.2
cg (at 1000 psi)	5e-4 – 1e-3 /psi
cg (at 5000 psi)	1e-4 – 3e-4 /psi

Common Pitfalls

Not correcting for H2S/CO2 (use Wichert-Aziz correction)
Using ideal gas cg = 1/P at high pressures (>2000 psi) — underestimates cg
Confusing Bg units (res ft³/scf vs RB/Mscf)

References

Standing, M.B. & Katz, D.L. (1942). "Density of Natural Gases." Trans. AIME, 146, 140–149.
Mattar, L., Brar, G.S. & Aziz, K. (1975). "Compressibility of Natural Gases." JCPT, 14(4), 77–80.
Lee, A.L., Gonzalez, M.H. & Eakin, B.E. (1966). "The Viscosity of Natural Gases." JPT, 18(8), 997–1000.
PetroWiki — Gas properties: https://petrowiki.spe.org/Gas_formation_volume_factor_and_density

Gas Compressibility Z-Factor