Enhanced prediction of the compressibility factor for CO₂-rich natural gas: evaluation of mixing rules and correlations using a large databank

Accurate prediction of the compressibility factor (Z-factor) of CO₂-rich natural gas governs reserves estimates; facility and pipeline design; and density, hydraulics, storage, and compression calculations. This study evaluates and calibrates the well-known mixing rules and published Z-factor correlations used for these purposes while preserving physical consistency. An expanded databank of 3,140 measured points—45% larger than the earlier databank, extending the CO₂ content to 0.98 mole fraction and adding ethane-rich blends—was used to test the methods across reduced pressures from 0.014 to 30.8 and reduced temperatures from 0.748 to 2.42. Fifteen published Z-factor correlations were evaluated under seven mixing-rule pathways, yielding 15 × 7 = 105 correlation–mixing-rule combinations. The mixing rules were first ranked by data coverage, absolute percent error, and goodness of fit to establish a baseline; the correlations were then benchmarked under identical conditions and screened for physical admissibility. The correlations were subsequently recalibrated in two stages—within each method’s published pressure–temperature limits, and over the full databank—with both stages constrained to preserve physical-trend consistency. Under the Kay mixing-rule baseline, the untuned Londono set-2 correlation gave the best combination of accuracy and full coverage, spanning all 3,140 points with an absolute error of 3.63% and a coefficient of determination of 0.9765; the tuned Modified Dranchuk–Abou-Kassem correlation achieved full coverage with a lower error of 3.39% and a coefficient of determination of 0.9776 while remaining physically valid over the entire domain. Accordingly, the Kay mixing rule paired with the Londono set-2 correlation is recommended as a reliable non-iterative reference, and the tuned Modified Dranchuk–Abou-Kassem correlation as a computationally efficient, full-domain alternative for gas-reserve estimation, production-system design, transport, and storage calculations.