fluid_properties · gas properties
Gas Compressibility (cg)
cpr = 1/Ppr − (0.27/(Z²Tpr))·(dZ/dρr)/(1+(ρr/Z)(dZ/dρr)); cg = cpr/Ppc [Mattar-Brar-Aziz 1975, on Dranchuk-Abou-Kassem 1975 Z]
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Inputs
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psia
Description
Computes isothermal gas compressibility (cg) analytically from the Dranchuk-Abou-Kassem (1975) Z-factor equation of state, using the closed-form derivative dZ/dPpr derived by Mattar, Brar, and Aziz (1975). This avoids the numerical-differentiation error of finite-differencing gas_zfactor at two nearby pressures, and closes the loop needed for total-compressibility and gas material-balance work.
Variables
| Symbol | Unit | Description |
|---|---|---|
| cg | μpsi⁻¹ | Gas Compressibility |
| Tpr | — | Pseudo-reduced temperature = reservoir absolute temperature ÷ pseudo-critical temperature. |
| Ppr | — | Pseudo-reduced pressure = reservoir absolute pressure ÷ pseudo-critical pressure. |
| Ppc | psia | Pseudo-critical pressure of the gas mixture (from gas gravity via Sutton or Standing correlations), used to convert dimensionless pseudo-reduced compressibility to an actual 1/pressure value. |
Assumptions
- Sweet natural gas, no sour-gas (Wichert-Aziz) correction applied to Tpr/Ppr or Ppc
- Single gas phase across the pressure range of interest (no retrograde condensation)
- Ppc supplied by the user is consistent with the same gas-gravity correlation used to compute Tpr and Ppr
Limitations
- Inherits the Dranchuk-Abou-Kassem Z-factor's stated range (0.2 ≤ Ppr ≤ 30, 1.0 ≤ Tpr ≤ 3.0) — outside this range both Z and its derivative lose accuracy
- Only the DAK derivative is implemented (not Hall-Yarborough's implicit form), per this session's Phase 1 finding that DAK gives a cleanly tractable closed-form derivative while Hall-Yarborough's does not
- As with gas_zfactor, this is a curve-fit to the Standing-Katz chart, not a substitute for lab-measured compressibility on a real gas sample
Use Cases
- → Total compressibility for gas well testing: Provide cg as the dominant term in total system compressibility ct for gas pressure-transient analysis and pseudo-pressure calculations.
- → Gas material balance: Use cg alongside gas_fvf and gas_zfactor to evaluate rock and fluid compressibility effects on the P/Z depletion trend at high pressure, where gas expansion no longer dominates rock/water compressibility.
- → Correlation cross-check: Compare an analytically-derived cg against a finite-difference estimate from two gas_zfactor evaluations at nearby pressures, to sanity-check either approach.
Related Calculations
Region Notes
Global
At low Ppr (< 1), cg approaches 1/P and gas is highly compressible; at high Ppr (> 10, dense-phase gas), cg falls sharply and approaches the same order of magnitude as liquid compressibility — a useful sanity check when validating Ppc/Tpr inputs.
Haynesville
High-pressure, high-temperature dry gas commonly sits at Ppr 10–15 where cg is far lower than at typical mid-range reservoir pressures — verify Ppc is calculated at the correct (very high) reservoir pressure before comparing to shallower-play type curves.
References
Primary source
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