DAK and Hall-Yarborough Gas Z-Factor Solver

Calculation sequence

1. Enter P_pr = absolute pressure / pseudo-critical pressure and T_pr = absolute temperature / pseudo-critical temperature. These are dimensionless ratios, not psi and degrees Fahrenheit. Select pseudo-critical properties using a method appropriate to the composition before forming the ratios. The tool does not estimate gas gravity, composition or sour-gas corrections, and it does not accept a gauge-pressure ratio.
2. The DAK branch uses all eleven published coefficients to evaluate its density-dependent Z expression. Bisection solves rho_r times Z minus 0.27 P_pr/T_pr on a positive-density bracket. Hall-Yarborough separately solves its rational density residual between zero and a point below the y = 1 pole. Their density variables have different definitions and must not be compared as if they were the same physical density.
3. Each result is checked against its original pressure-balance residual, normalized by the pressure-dependent term; a relative residual above 1e-9 is rejected. The output reports function evaluations, including bracket and final checks, rather than calling those counts Newton iterations. Twenty-five independently solved pressure points run from P_pr = 0.2 to the selected pressure at the same temperature; an unsupported point fails instead of being silently skipped.
4. Compare both Z values and their signed percentage difference relative to DAK. A small residual establishes that the numerical equation was solved, not that the correlation agrees with your gas sample. Both correlations approximate related reduced-property data, so agreement is not independent validation of the pseudo-critical properties or phase state. Use measured PVT or an appropriate compositional EOS for decisions outside this screening workflow.

Worked check

At P_pr = 3 and T_pr = 1.5, the two independently solved correlations give approximately Z_DAK = 0.776128 and Z_HY = 0.774828. The default inputs are synthetic reduced-property values, not a measured fluid. The source's DAK example A-4 uses rounded P_pr = 3.016 and T_pr = 1.849 and reports Z = 0.9076; the numerical regressions reproduce that rounded published check separately from the default comparison.

Synthetic examples for reproducibility, not measured field results.

Assumptions and limitations

• This comparison deliberately supports only 0.2 <= P_pr <= 15 and 1.2 <= T_pr <= 3. The software envelope is narrower than the cited DAK range; near-critical, subcritical and higher-pressure extensions are not implemented. Bounds are enforced, not treated as extrapolation warnings.
• Single gas-phase correlation evaluation only. No dew-point or phase-equilibrium test, composition adjustment, sour-gas correction, density in mass units, gas compressibility derivative or fluid flash is performed. Passing an envelope check does not establish that a supplied fluid is in one phase.
• Brackets, a bounded iteration count and final residual tests prevent an unverified number being returned. The chart shows correlation sensitivity within the selected interval, not measured error bars. Correlation difference and solver residual are different diagnostics and must not be presented as guaranteed accuracy.

Sources and maintenance

Published by PetroCalcHub Team. Implementation and source checks: 2026-10-13. This does not claim independent expert review.

• T.A. Blasingame: DAK coefficients, equations A-7 to A-12 and example A-4 (1989)
• zFactor: pinned DAK implementation for independent coefficient comparison
• zFactor: pinned Hall-Yarborough coefficients and residual

Related tools and references