๐งช Real Gas Compressibility Factor Z
Evaluate gas compressibility factor Z and molar volumes using Pitzer correlations, Van der Waals, and Peng-Robinson equations of state.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
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Released
Jun 2026
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< 1 ms
๐ Configuration
Key Equations:
Pitzer: Z=1+(Bโ+ฯBโ)Pr/Tr
VdW: Zยณ-(1+B')Zยฒ+A'Z-A'B'=0
PR: Zยณ-(1-B)Zยฒ+(A-3Bยฒ-2B)Z-(AB-Bยฒ-Bยณ)=0
Pitzer: Z=1+(Bโ+ฯBโ)Pr/Tr
VdW: Zยณ-(1+B')Zยฒ+A'Z-A'B'=0
PR: Zยณ-(1-B)Zยฒ+(A-3Bยฒ-2B)Z-(AB-Bยฒ-Bยณ)=0
๐ Results
Configure inputs and click Compute.
๐ Methodology
Pitzer Correlation
Z = 1 + (Bโ+ฯBโ)Pr/Tr where Bโ = 0.083โ0.422/Tr^1.6 and Bโ = 0.139โ0.172/Tr^4.2. Valid at low to moderate pressures.
Van der Waals
Cubic EOS with a = 27RยฒTcยฒ/(64Pc) and b = RTc/(8Pc). Simple but less accurate at high pressures.
Peng-Robinson
Most widely used cubic EOS. Uses ฮฑ(T) function with ฮบ = 0.37464+1.54226ฯโ0.26992ฯยฒ. Superior near critical point.
๐ Calculation Methodology: Nelson-Obert Generalized Compressibility Charts (Z-Factor)
Mathematical Model & Theory
The generalized compressibility factor $Z = P v / (R T)$ quantifies gas non-ideality as a universal function of reduced temperature $T_r = T/T_c$ and reduced pressure $P_r = P/P_c$:
$$Z = \frac{P v}{R T} = Z^{(0)}(T_r, P_r) + \omega Z^{(1)}(T_r, P_r)$$
$$T_r = \frac{T}{T_c}, \quad P_r = \frac{P}{P_c}, \quad v_{real} = Z \frac{R T}{P}$$
Assumptions
- Corresponding states theorem for non-polar or weakly polar gases.
- Nelson-Obert and Lee-Kesler correlation validities.
Academic References
- Nelson, L. C., & Obert, E. F. (1954): Generalized Compressibility Charts, Trans. ASME.
- Moran, M. J. et al.: Engineering Thermodynamics, Ch. 11.
Worked Engineering Example
Problem Statement:
Methane ($T_c = 190.6\text{ K}$, $P_c = 4.60\text{ MPa}$, $R = 518.3\text{ J/kg}\cdot\text{K}$) is stored at $T = 286\text{ K}$ and $P = 9.2\text{ MPa}$. Find $Z$ and real gas density.
Step-by-step Solution:
1. $T_r = 286 / 190.6 = 1.50$, $P_r = 9.2 / 4.60 = 2.00$.
2. Chart lookup: at $T_r = 1.50, P_r = 2.00 \implies Z \approx 0.86$.
3. Density: $\rho = P / (Z R T) = 9.2 \times 10^6 / (0.86 \times 518.3 \times 286) = 9.2 \times 10^6 / 127,480 \approx 72.17\text{ kg/m}^3$.
Final Result:
Compressibility factor is $Z = \mathbf{0.860}$ (density $\mathbf{72.17\text{ kg/m}^3}$, 16.3% denser than ideal gas).
Methane ($T_c = 190.6\text{ K}$, $P_c = 4.60\text{ MPa}$, $R = 518.3\text{ J/kg}\cdot\text{K}$) is stored at $T = 286\text{ K}$ and $P = 9.2\text{ MPa}$. Find $Z$ and real gas density.
Step-by-step Solution:
1. $T_r = 286 / 190.6 = 1.50$, $P_r = 9.2 / 4.60 = 2.00$.
2. Chart lookup: at $T_r = 1.50, P_r = 2.00 \implies Z \approx 0.86$.
3. Density: $\rho = P / (Z R T) = 9.2 \times 10^6 / (0.86 \times 518.3 \times 286) = 9.2 \times 10^6 / 127,480 \approx 72.17\text{ kg/m}^3$.
Final Result:
Compressibility factor is $Z = \mathbf{0.860}$ (density $\mathbf{72.17\text{ kg/m}^3}$, 16.3% denser than ideal gas).