About

The compressibility factor Z = PVnRT quantifies deviation of a real gas from ideal behavior. An ideal gas has Z = 1. Real gases deviate due to intermolecular forces and finite molecular volume. At high pressures or low temperatures, Z can drop below 0.3 or exceed 1.5. Ignoring this in pipeline sizing, compressor design, or reactor engineering introduces errors of 30 - 70% in volumetric flow calculations. This tool computes Z via three methods: Van der Waals cubic equation, Pitzer’s two-parameter correlation, and the Lee-Kesler generalized correlation used in API and GPSA standards.

All methods rely on reduced properties: reduced temperature T_r = TT_c and reduced pressure P_r = PP_c. The Pitzer method adds the acentric factor ω as a third parameter to improve accuracy for polar and heavy molecules. Results are approximate: accuracy is typically ±2 - 5% for nonpolar gases at T_r > 1.0 and degrades near the critical point or for highly polar species like water and ammonia.

Formulas

The compressibility factor is defined as the ratio of real molar volume to ideal molar volume at the same temperature and pressure:

Z = P V_mR T

Reduced properties map any gas onto a universal curve via the principle of corresponding states:

T_r = TT_c P_r = PP_c

The Pitzer correlation extends the two-parameter corresponding states principle with the acentric factor ω:

Z = Z⁰ + ω ⋅ Z¹

Where Z⁰ and Z¹ are functions of T_r and P_r obtained from the Lee-Kesler modified Benedict-Webb-Rubin equation of state. The BWR equation in reduced form is:

Z = P_r V_rT_r = 1 + BV_r + CV_r² + DV_r⁵

The Van der Waals equation provides a simpler cubic approach:

(P + aV_m²)(V_m − b) = R T

Where the constants are derived from critical properties: a = 27 R² T_c²64 P_c and b = R T_c8 P_c.

Variable legend: P = absolute pressure, T = absolute temperature (K), V_m = molar volume, R = universal gas constant (8.314 J/(mol⋅K)), T_c = critical temperature, P_c = critical pressure, ω = Pitzer acentric factor, V_r = reduced volume (V_mP_c / RT_c).

Reference Data

Gas	Formula	T_c (K)	P_c (MPa)	ω	M (g/mol)
Methane	CH₄	190.56	4.599	0.0115	16.04
Ethane	C₂H₆	305.32	4.872	0.0995	30.07
Propane	C₃H₈	369.83	4.248	0.1523	44.10
n-Butane	C₄H₁₀	425.12	3.796	0.2002	58.12
n-Pentane	C₅H₁₂	469.70	3.370	0.2515	72.15
n-Hexane	C₆H₁₄	507.60	3.025	0.3013	86.18
n-Heptane	C₇H₁₆	540.20	2.740	0.3495	100.20
Nitrogen	N₂	126.19	3.396	0.0372	28.01
Oxygen	O₂	154.58	5.043	0.0222	32.00
Hydrogen	H₂	33.19	1.313	-0.2160	2.016
Carbon Dioxide	CO₂	304.13	7.375	0.2239	44.01
Carbon Monoxide	CO	132.86	3.494	0.0510	28.01
Hydrogen Sulfide	H₂S	373.53	8.963	0.0942	34.08
Ammonia	NH₃	405.40	11.353	0.2526	17.03
Water	H₂O	647.10	22.064	0.3449	18.02
Helium	He	5.19	0.227	-0.3900	4.003
Argon	Ar	150.69	4.898	0.0000	39.95
Neon	Ne	44.49	2.679	-0.0290	20.18
Krypton	Kr	209.41	5.510	0.0000	83.80
Xenon	Xe	289.73	5.841	0.0000	131.29
Ethylene	C₂H₄	282.34	5.041	0.0862	28.05
Acetylene	C₂H₂	308.30	6.139	0.1912	26.04
Sulfur Dioxide	SO₂	430.80	7.884	0.2451	64.07
Chlorine	Cl₂	416.90	7.977	0.0688	70.91
Isobutane	C₄H₁₀	407.80	3.640	0.1835	58.12
Air (pseudo)	N₂/O₂	132.52	3.786	0.0335	28.97

Frequently Asked Questions

Near the critical point (T_r ≈ 1.0, P_r ≈ 1.0), density fluctuations become large and the distinction between liquid and vapor phases vanishes. Generalized correlations lose accuracy here because the equation of state coefficients are fitted to data away from the critical region. Expect errors of 10 - 15% when 0.9 < T_r < 1.1 and P_r > 0.8.

Van der Waals is a two-constant cubic equation that predicts a universal critical compressibility of Z_c = 0.375, whereas real gases range from 0.23 to 0.29. The Lee-Kesler correlation uses the acentric factor ω as a third parameter and is calibrated against experimental PVT data. For engineering calculations (pipeline design, compressor sizing), Lee-Kesler provides ±2 - 3% accuracy for nonpolar gases. Use Van der Waals only for rough estimates or pedagogical purposes.

The acentric factor ω measures the non-sphericity and polarity of a molecule. Simple fluids like argon have ω ≈ 0. Heavier hydrocarbons reach ω > 0.3. Water has ω = 0.345. A higher ω increases the correction term ω⋅Z¹, typically lowering Z at moderate reduced pressures. For gases with ω > 0.4, even the Pitzer correlation loses reliability and specialized equations (e.g., GERG-2008) are recommended.

This tool computes Z for pure components only. For mixtures, you would need pseudo-critical properties via mixing rules such as Kay's rule: T_c,mix = n∑i y_iT_c,i. The pseudo-critical method introduces additional error of 5 - 10% for dissimilar components. For natural gas, the GPSA Engineering Data Book recommends the Standing-Katz chart or the Dranchuk-Abou-Kassem correlation.

The tool accepts pressure in MPa, bar, atm, or psi, and temperature in K, °C, °F, or °R. All inputs are internally converted to K and MPa before computation. Gauge pressures must be converted to absolute before entry. Forgetting to add atmospheric pressure (0.101325 MPa) to gauge readings is a common source of large errors.

No. At high reduced temperatures (T_r > 2) and high pressures, repulsive forces dominate and Z exceeds 1.0. Hydrogen exhibits Z > 1 at virtually all pressures above 10 MPa because its critical temperature (33.19 K) places ambient conditions at very high T_r. The Boyle temperature, where Z passes through a minimum and returns to 1, is approximately 2.75 T_c for Van der Waals gases.