Universal wet-gas flow-rate correlation for Venturi differential-pressure meters: generalization beyond the two-phase mass flow coefficient's liquid-property, diameter-ratio, and size limits

He and Bai (2014) proposed correcting the over-reading of Venturi meters in wet gas flow through a two-phase mass flow coefficient $K=(m_g+m_l)/m_{g,\mathrm{app}}$, fitted to Colorado Engineering Experiment Station data (natural gas with water, kerosene, and Stoddard solvent) at a single diameter ratio $\beta=0.6$ on inlet diameters near 50 and 194 mm, achieving a 1.35% root-mean-square deviation (RMSD) on its development data while acknowledging that liquid surface tension and viscosity were unrepresented and that other diameter ratios, other meter sizes, and wider regimes remained untested - leaving a universal wet-gas correlation as an open challenge. The originating group extended the $K$ framework to other meter types but not along the named axes; independent assessments in 2020 and 2026 find no universally accepted correlation, with different correlations performing best in different installations; and the newest work turns to machine-learning and hybrid models that remain range-restricted and describe accurate wet-gas measurement as a longstanding challenge. The problem of a validated universal wet-gas correlation - explicit liquid-property dependence, multiple diameter ratios and meter sizes, cross-regime validity, and accuracy demonstrated on independent data - remains open.

Background

Wet gas - a gas flow carrying a small amount of liquid, in industrial usage a gas volume fraction (the share of the pipe cross-section occupied by gas) above roughly 95% - is common in petroleum production, wet-steam systems, and chemical plants, where the gas flow rate must be measured for custody transfer (the commercial handover of gas, where the measured quantity determines payment), allocation between fields, and process control. The standard instrument is the differential-pressure (DP) meter, most often the Venturi tube: a converging-diverging pipe section in which the pressure drop between inlet and throat determines the flow rate through a single-phase calibration. Liquid in the gas increases the measured pressure drop above that of the equivalent dry gas, so a naive reading over-states the gas rate - the over-reading, defined as the ratio of the apparent gas mass flow rate $m_{g,\mathrm{app}}$ (computed from the wet differential pressure with the dry-gas equation) to the true gas mass flow rate $m_g$.

Corrections have long taken the form of empirical correlations built on dimensionless groups: the Lockhart-Martinelli parameter $X=(m_l/m_g)\sqrt{\rho_g/\rho_l}$, which compares liquid and gas inertial forces for mass flows $m_g,m_l$ and densities $\rho_g,\rho_l$; the gas-to-liquid density ratio $\rho_g/\rho_l$; and the gas densiometric Froude number $Fr_g$, a dimensionless gas velocity $Fr_g=(U_{sg}/\sqrt{gD})\sqrt{\rho_g/(\rho_l-\rho_g)}$ with superficial gas velocity $U_{sg}$, inlet diameter $D$, and gravitational acceleration $g$. Early correlations were fitted to orifice-plate data; the first dedicated to Venturi tubes came from de Leeuw (1997) and Steven (2002), and the International Organization for Standardization technical report ISO/TR 11583:2012 standardized a wet-gas correction for Venturi meters and orifice plates. Every one of these is empirical, tied to the facility and fluids used to fit it, and valid only over a restricted range of $X$, pressure, and geometry.

He and Bai (2014) recast the correction through a two-phase mass flow coefficient $K=(m_g+m_l)/m_{g,\mathrm{app}}$, the ratio of the total (gas plus liquid) mass flow to the apparent gas mass flow. Using wet-gas data from the Colorado Engineering Experiment Station (CEESI, a commercial high-pressure test facility) with natural gas and three liquids (water, kerosene, and Stoddard solvent, a standard petroleum-spirit test solvent) at pressures of 1.5-7.2 MPa, they found that $K$ rises linearly with $X$ and fitted

$K=\left(\frac{0.5681}{\sqrt{\rho_g/\rho_l}}-0.1444\,Fr_g-0.1494\right)X+1,$

which reduces to the dry-gas equation at $X=0$ and, on its development data ($0\le X\le0.3$, $0.6\le Fr_g\le4.7$, $0.01<\rho_g/\rho_l\le0.081$), predicted the gas rate with 1.35% root-mean-square deviation - better on the same data than the de Leeuw, Steven, and ISO/TR 11583 correlations. The correlation was fitted at one diameter ratio $\beta=d/D=0.6$ (throat to inlet diameter), on inlet diameters of about 49 and 194 mm, for liquids resembling water and light hydrocarbons, and with no representation of surface tension or viscosity; the authors acknowledged these limits, noted that their computational fluid dynamics studies of liquid-property effects on DP meters were ongoing, and stated that a correlation valid across all relevant wet-gas regimes and fluid combinations - a universal wet-gas correlation - remained an open challenge.

Problem Statement

Construct, and validate on independent experimental data, a wet-gas correction for Venturi-type differential-pressure meters - expressed through the two-phase mass flow coefficient $K$, an over-reading correlation, or a model family defined by an explicitly stated physical (mass- or energy-) balance with documented free parameters - whose demonstrated validity extends across the axes on which the 2014 correlation and its predecessors were fitted and restricted:

(i) explicit dependence on liquid properties, in particular surface tension and viscosity, so that liquids substantially different from water and light hydrocarbons are covered rather than excluded; (ii) diameter ratios other than $\beta=0.6$ and inlet diameters outside the development range (reported as roughly 50-200 mm); (iii) the wet-gas flow regimes (stratified through annular-mist flow) encountered in industrial service; (iv) accuracy quantified on data from facilities and fluid pairs not used for fitting, within an explicitly stated applicability envelope.

The target is one correction whose stated applicability envelope spans these axes jointly, supported by independent validation rather than assertion. A correction valid over only a subset of axes (i)-(iv) remains range-restricted. Independent validation data may be drawn from the published wet-gas measurement literature or other openly accessible sources, provided the facilities and fluid pairs are distinct from those used for fitting. Installation orientation - horizontal versus vertical mounting - is a further open gap documented in the follow-up literature (for example Pan et al. 2019; Graham et al. 2020), not a required completion axis of this problem.

References

1. He, D., Bai, B. (2014). A new correlation for wet gas flow rate measurement with Venturi meter based on two-phase mass flow coefficient. Measurement 58: 61-67. doi:10.1016/j.measurement.2014.08.014. https://doi.org/10.1016/j.measurement.2014.08.014
2. He, D., Bai, B. (2012). Numerical investigation of wet gas flow in Venturi meter. Flow Measurement and Instrumentation 28: 1-6. doi:10.1016/j.flowmeasinst.2012.07.008. https://doi.org/10.1016/j.flowmeasinst.2012.07.008
3. He, D.-H., Bai, B.-F. (2014). Two-phase mass flow coefficient of V-Cone throttle device. Experimental Thermal and Fluid Science 57: 77-85. doi:10.1016/j.expthermflusci.2014.03.018. https://doi.org/10.1016/j.expthermflusci.2014.03.018
4. Zheng, X., He, D., Yu, Z., Bai, B. (2016). Error analysis of gas and liquid flow rates metering method based on differential pressure in wet gas. Experimental Thermal and Fluid Science 79: 245-253. doi:10.1016/j.expthermflusci.2016.07.017. https://doi.org/10.1016/j.expthermflusci.2016.07.017
5. Bai, B., Zheng, X. (2018). Comparison of the two-phase mass flow coefficient and the over-reading for wet gas flow metering with DP meters. Experimental Thermal and Fluid Science 90: 14-21. doi:10.1016/j.expthermflusci.2017.08.027. https://doi.org/10.1016/j.expthermflusci.2017.08.027
6. Xu, Y., Zhang, Q., Zhang, T., Ba, X. (2015). An overreading model for nonstandard Venturi meters based on H correction factor. Measurement 61: 100-106. doi:10.1016/j.measurement.2014.10.028. https://doi.org/10.1016/j.measurement.2014.10.028
7. Pan, Y., Hong, Y., Sun, Q., Zheng, Z., Wang, D., Niu, P. (2019). A new correlation of wet gas flow for low pressure with a vertically mounted Venturi meter. Flow Measurement and Instrumentation 70: 101636. doi:10.1016/j.flowmeasinst.2019.101636. https://doi.org/10.1016/j.flowmeasinst.2019.101636
8. Graham, E. M., Reader-Harris, M., Chinello, G., Harkins, K., Bowman, N., Wales, L. (2020). Vertically installed Venturi tubes for wet-gas flow measurement: Possible improvements to ISO/TR 11583 to extend its range of applicability. Flow Measurement and Instrumentation 74: 101757. doi:10.1016/j.flowmeasinst.2020.101757. https://doi.org/10.1016/j.flowmeasinst.2020.101757
9. Xu, Y., Cao, L., Yuan, C., Zhang, Y., Wang, J., Li, T., Zuo, R. (2023). Study of the factors influencing the over-reading characteristics of the precession Venturi. Flow Measurement and Instrumentation 89: 102272. doi:10.1016/j.flowmeasinst.2022.102272. https://doi.org/10.1016/j.flowmeasinst.2022.102272
10. Li, S., Zhao, F., Zheng, X., He, D., Bai, B. (2020). Wet gas metering by cone throttle device with machine learning. Measurement 164: 108080. doi:10.1016/j.measurement.2020.108080. https://doi.org/10.1016/j.measurement.2020.108080
11. Liu, X., Lao, L., Falcone, G. (2020). A comprehensive assessment of correlations for two-phase flow through Venturi tubes. Journal of Natural Gas Science and Engineering 78: 103323. doi:10.1016/j.jngse.2020.103323. https://doi.org/10.1016/j.jngse.2020.103323 (accepted manuscript: https://eprints.gla.ac.uk/214547/)
12. Salehi, S. M., Lao, L., Xing, L., Simms, N., Drahm, W. (2024). Devices and methods for wet gas flow metering: A comprehensive review. Flow Measurement and Instrumentation 96: 102518. doi:10.1016/j.flowmeasinst.2023.102518. https://doi.org/10.1016/j.flowmeasinst.2023.102518
13. Alkhurayef, A., Al-Sarkhi, A., AbdulMajeed, G., Gajbhiye, R. (2026). A comprehensive review of wet gas flow correlations for Venturi meter. Flow Measurement and Instrumentation 109: 103224. doi:10.1016/j.flowmeasinst.2026.103224. https://doi.org/10.1016/j.flowmeasinst.2026.103224
14. Alkhurayef, A., Alsarkhi, A. (2026). A new hybrid physics-ML model for predicting over-reading in differential pressure measurements under wet gas flow. Flow Measurement and Instrumentation 111: 103465. doi:10.1016/j.flowmeasinst.2026.103465. https://doi.org/10.1016/j.flowmeasinst.2026.103465
15. Steven, R. N. (2002). Wet gas metering with a horizontally mounted Venturi meter. Flow Measurement and Instrumentation 12(5-6): 361-372. doi:10.1016/S0955-5986(02)00003-1. https://doi.org/10.1016/S0955-5986(02)00003-1
16. ISO/TR 11583:2012. Measurement of wet gas flow by means of pressure differential devices inserted in circular cross-section conduits. International Organization for Standardization, Geneva. BSI implementation doi:10.3403/30197318. https://doi.org/10.3403/30197318
17. Sidaoui, Z., Alsunbul, Y., Abbad, M. (2022). Application of Machine Learning in Wet Gas Measurement Predictions. International Petroleum Technology Conference 2022, paper IPTC-22495-MS. doi:10.2523/IPTC-22495-EA. https://doi.org/10.2523/IPTC-22495-EA
18. de Leeuw, R. (1997). Liquid correction of Venturi meter readings in wet gas flow. North Sea Flow Measurement Workshop 1997 (workshop paper; no DOI). The open-access accepted manuscript of Liu, Lao and Falcone (2020), Journal of Natural Gas Science and Engineering 78: 103323, is available at https://eprints.gla.ac.uk/214547/1/214547.pdf