Wet gas - natural gas carrying a small liquid fraction, with gas volume fraction (GVF) above roughly 90% - is commonly metered with a differential-pressure device plus a gamma-ray attenuation phase-fraction measurement. Pan and co-workers proposed doing this with a horizontally mounted Venturi and a single gamma source/detector pair, converting the chordal void fraction seen by one beam into the cross-sectional void fraction through a two-eccentric-circle geometric model (the gas-liquid interface is idealized as an arc of a circle of the pipe radius, offset by an eccentricity computed from the chordal measurement), and closing the system with the Chisholm gas-liquid velocity-ratio correlation. Third-party tests at the UK National Engineering Laboratory yielded per-phase RMS mass-flow errors reported in the paper's abstract as 'well below 6%', but only on one Venturi geometry (inlet inner diameter approximately 172 mm), one fluid pair (nitrogen and a kerosene substitute), at a single fixed high pressure and temperature, over a high-GVF range (approximately 92-100%) at low liquid loading, in stratified flow. Whether the model remains valid for other diameters or beta ratios, real hydrocarbon fluids, other pressures and temperatures, and other flow regimes, and what role the Chisholm velocity-ratio closure plays within this architecture, remain open questions. The open problem is to determine the validity envelope - or the failure bounds and required corrections - of this horizontal single-gamma wet gas metering model across those axes.

Background

In oil and gas production, a gas stream that carries a small amount of liquid (water and/or hydrocarbon condensate) is called wet gas; it is usually characterized by its gas volume fraction (GVF), the fraction of the pipe volume occupied by gas, which in wet gas applications exceeds about 90%. Because the liquid makes a Venturi flowmeter (a converging-diverging tube whose pressure drop yields the flow rate) read high - the so-called over-reading - a wet gas meter needs both a differential-pressure element for the total mass flow and a separate measurement of the phase fractions. The standard phase-fraction technique is gamma-ray attenuation: a collimated beam from a radioactive source is attenuated according to the amount of liquid along its path (the Beer-Lambert law), giving the line-averaged, or chordal, void fraction along the beam. In a vertical pipe the phases are roughly symmetrically distributed, so a single chordal measurement represents the cross-sectional (area-averaged) void fraction; for this reason commercial wet gas meters usually force a vertical orientation at the measurement section. In horizontal and subsea installations, gravity stratifies the flow - liquid runs along the bottom of the pipe as a layer with a curved, concave-down interface under a gas core, a regime called stratified-wavy flow - so a single horizontal or angled beam is no longer representative, and the usual fixes (vertical spool pieces or multiple gamma beams and detectors) add cost, complexity, and installation burden that matter especially for subsea wellheads and marginal fields.

To remove that penalty, Pan et al. (2018) introduced a slip-ratio-based equal-diameter double-circle model for horizontal high-pressure wet gas: the stratified interface is idealized as the arc of a second circle having the same radius as the pipe but vertically offset by an eccentricity d. The model is a closed-form, parameter-free geometry: from the chordal void fraction measured by one gamma beam at a known angle to the horizontal, the eccentricity is computed, and the area-averaged void fraction follows from the area of overlap of two equal circles. Validated with nitrogen and kerosene in a 172.0 mm inner-diameter horizontal pipe at GVF 92-100%, it predicted the line-averaged void fraction within about 2% and identified the beam angle at which the chordal measurement equals the gas volume fraction. The equal-diameter double-circle interface is itself a standard idealization in the stratified two-fluid modeling literature, where it represents the curved interface for computing interfacial transfer terms and void fraction (recent refinements give explicit approximations for its central angle, e.g. Ahn et al. 2024 and Wu et al. 2025). Pan et al. (2020) turned the model into a complete horizontal wet gas meter: computational fluid dynamics (CFD) simulations were used to select the turbulence model best matching measured pressure drop and chordal void fraction, and the full system - horizontal Venturi, single gamma source/detector, two-eccentric-circle conversion, and the Chisholm correlation (a classical empirical gas-to-liquid velocity-ratio relation) for the remaining slip - was tested at the UK National Engineering Laboratory (NEL) against traceable reference meters, with per-phase RMS mass-flow errors reported in the paper's abstract as 'well below 6%'.

Everything in that validation, however, belongs to one envelope: a single Venturi geometry of approximately 172 mm inlet inner diameter with one beta ratio (the throat-to-inlet diameter ratio), one fluid pair (oxygen-free nitrogen and a kerosene substitute), one fixed high pressure and temperature, a high-GVF range of roughly 92-100% at low liquid loading as measured by the Lockhart-Martinelli parameter (the square root of the ratio of liquid to gas kinetic energies, the standard measure of liquid loading), and stratified flow with one gamma source. Related work in horizontal Venturi wet gas metering focuses mainly on over-reading correlations (Fang and Zhang 2008 at low pressure; Chen et al. 2022 derive the Lockhart-Martinelli parameter for horizontal Venturi correction; Alkhurayef et al. 2026 review the correlation literature), while the gamma mounting angle was studied by Pan et al. (2021) and the architecture was extended to three-phase flow with a homogenizing blind tee by Ma et al. (2021); recent reviews of the field are given by Salehi et al. (2024) and Shunashu et al. (2025).

Problem Statement

Determine, with quantified accuracy, whether and how far the two-eccentric-circle chordal-to-cross-sectional void-fraction conversion - used within the horizontal single-gamma Venturi wet gas metering architecture with the Chisholm gas-liquid velocity-ratio closure - remains valid outside the envelope in which it was validated: a single Venturi geometry of approximately 172 mm inlet inner diameter with one beta ratio, oxygen-free nitrogen and a kerosene substitute as the fluid pair, one fixed high pressure and temperature, GVF approximately 92-100% at low liquid loading, and stratified flow with a single fixed gamma source. Concretely, the question asks: (i) how the model and metering system perform for other pipe diameters and Venturi beta ratios; (ii) for real production fluids (natural gas with hydrocarbon condensate and/or water) in place of nitrogen and a kerosene substitute; (iii) at pressures and temperatures substantially different from the validated high-pressure laboratory conditions; and (iv) in flow regimes departing from stratified-wavy, such as annular flow at higher gas velocities or liquid loadings, where the equal-circle interface assumption may fail. Where the model degrades, the answer must establish the failure bounds and the corrections required, including isolating whether the residual error belongs to the geometric conversion or to the Chisholm velocity-ratio closure used within the architecture.

References

  1. Yanzhi Pan, Haujian Liu, Ziqiong Zheng, Pengrong Wen, Yueqian Zhao (2020). A New Method for Wet Gas Flow Measurement with Horizontal Venturi Meter Based on Numerical Simulation. International Petroleum Technology Conference (IPTC-19894-MS). DOI 10.2523/IPTC-19894-MS. https://doi.org/10.2523/iptc-19894-ms
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