Wet gas (gas carrying a small liquid fraction) can in principle be metered with a single-modality vortex cross-correlation meter: two axially separated fluctuating-pressure probes behind a bluff body are cross-correlated to obtain the vortex convection velocity, from which the superficial gas velocity follows through a convection coefficient modeled as a piecewise function of a modified Weber number, with dry/wet discrimination by a correlation-coefficient threshold and an iterative solution. The method was proposed and validated only for a 15 mm pipe at 160-400 kPa, superficial gas velocities up to about 37 m/s, Weber numbers up to about 5x10^3, and droplet mass loadings up to 5.7% in annular mist flow. The open problem is whether this concept - which needs no auxiliary liquid-content sensor - extends to larger pipe diameters, higher pressures, higher Weber numbers, and other two-phase flow regimes, and whether its dry/wet discrimination threshold remains reliable under varying liquid properties, flow disturbances, and sensor aging; the micro pressure sensors used also have an upper frequency limit, and robust piezoelectric probes have been suggested for high-pressure, medium-diameter service but are untested in the transit-time scheme. Later work by the same group and others has instead added a second sensing modality (conductance or capacitive) mostly at the same small scale, or developed void-fraction-based over-reading corrections, leaving the stated extension of the convection-coefficient cross-correlation model itself untested.

Background

Wet gas - a natural-gas-like flow carrying a small fraction of liquid (water and/or hydrocarbon condensate) - occurs throughout hydrocarbon production, and its flow rates must be measured for reservoir management, allocation, and fiscal purposes. A standard measure of how much liquid a wet gas carries is the Lockhart-Martinelli parameter, the ratio of the frictional pressure drops the gas and the liquid would each exert if flowing alone through the pipe; wet gas corresponds roughly to values below 0.3. At high gas velocity and small liquid fraction in a vertical pipe, the flow takes the annular-mist form: most liquid travels as a film on the pipe wall, and part of it is sheared off and entrained as droplets in the gas core (the entrainment fraction quantifies this part).

A vortex flowmeter inserts a bluff body across the pipe; alternating vortices are shed at a frequency proportional to the flow velocity (through the Strouhal number, a dimensionless shedding frequency), which yields the gas velocity in dry gas from a single frequency measurement. In wet gas the liquid biases the shedding, so the meter 'over-reads', and classical corrections relate the over-reading to the Lockhart-Martinelli parameter. A different principle is cross-correlation flowmetering: two sensors spaced an axial distance LL apart observe the same convected flow structures with a delay equal to the transit time τ\tau, obtained as the lag of the peak of the cross-correlation function of the two signals; the convection velocity is then L/τL/\tau.

Li, Wang, Ding, Sun and Li (2020) combined these ideas into a wet-gas meter that requires no separate liquid-content measurement. Two micro pressure probes (probe-transducer systems) downstream of a bluff body measure the fluctuating pressure of the passing vortices; the normalized cross-correlation of the two signals gives both a transit time and a peak correlation coefficient ρpeak\rho_{peak}. The vortex convection velocity UcU_c divided by the superficial gas velocity UsgU_{sg} (the gas flowrate divided by the full pipe cross-section) defines the convection coefficient KcK_c. In dry gas, KcK_c is a constant calibrated on a positive-pressure sonic-nozzle gas-flow standard facility; in wet gas it was fitted as a piecewise function of a modified Weber number, We=ρgUsg2D/σ⋅((ρl−ρg)/ρg)1/4We = \rho_g U_{sg}^2 D / \sigma \cdot ((\rho_l - \rho_g)/\rho_g)^{1/4}, which contrasts gas inertial stress with surface tension σ\sigma and is corrected for the gas-liquid density ratio. The segmentation of the fit - and the discrimination between dry gas and wet annular mist - is decided by the correlation-coefficient threshold ρpeak=0.5\rho_{peak} = 0.5: in the experiments, dry-gas cases showed ρpeak>0.5\rho_{peak} > 0.5 and wet cases fell below. The physical rationale runs through entrainment: over the tested range the entrainment fraction follows the Weber-number-dependent branch of the Sawant-Ishii-Mori correlation for vertical annular flow, so KcK_c inherits Weber-number scaling and is nearly independent of liquid fraction. Because WeWe itself contains the unknown UsgU_{sg}, the gas flowrate is obtained by iterating Usg=Uc/Kc(We)U_{sg} = U_c / K_c(We) to convergence. On an air-water annular-mist loop (pipe diameter D=15D = 15 mm, pressure 160-400 kPa, gas flowrate 15-24 m^3/h, i.e. superficial gas velocity up to about 37 m/s, droplet mass loading up to 5.7%), 91% of the gas-flowrate predictions fell within ±5% error bands, with a mean absolute percentage error of 2.54% and a measurement uncertainty of 2.85%. The attraction of the scheme is economic: one vortex element plus two pressure probes, with no conductance, capacitance, or other liquid-content sensing, in contrast to the dual-modality wet-gas meters that dominate the field.

That validated envelope is, however, far from industrial wet-gas service (typical field conditions involve larger pipe diameters and much higher pressures), and the source paper itself states the unresolved questions: the model's applicability to larger diameters, higher pressures, higher Weber numbers, and different two-phase flow regimes - where the entrainment behavior may leave the Weber-number-dependent region and additional parameters such as the liquid-phase Reynolds number may become important - remains unknown; the robustness of the ρpeak=0.5\rho_{peak} = 0.5 threshold under varying liquid properties, flow disturbances, and sensor aging needs investigation; and the present micro pressure sensors have an upper frequency limit that constrains the smallest pipe sizes and highest velocities, with robust piezoelectric sensors suggested for high-pressure, medium-diameter applications but untested in the transit-time correlation scheme.

Problem Statement

Establish the applicability envelope and robustness of the single-modality vortex cross-correlation wet-gas metering concept of Li et al. (2020) beyond its validated conditions. The overarching objective is to determine whether the pressure-fluctuation cross-correlation scheme - one vortex element plus two pressure probes, with no auxiliary liquid-content measurement - can meter wet gas accurately at industrial conditions, and where its limits of validity lie. Two aspects of this objective are:

  1. Convection-coefficient model extension. Determine whether the piecewise relation Kc(We)K_c(We) between the convection coefficient and the modified Weber number - validated only at D=15D = 15 mm, 160-400 kPa, We≤5×103We \le 5\times10^3, superficial gas velocity up to about 37 m/s, droplet mass loading up to 5.7%, in annular mist flow - remains valid, or must be revised, for larger pipe diameters, higher pressures, higher Weber numbers, and other two-phase flow regimes, where the entrainment fraction may leave the Weber-number-dependent branch of the Sawant-Ishii-Mori correlation and additional dimensionless groups (for example the liquid-phase Reynolds number) may become significant.

  2. Dry/wet discrimination robustness. Determine whether the correlation-coefficient threshold ρpeak=0.5\rho_{peak} = 0.5, which separated dry gas from wet annular mist in the original campaign, is robust under varying liquid properties (viscosity, surface tension), flow disturbances (upstream conditioning, pulsation, vibration), and sensor aging or drift - and if it is not, how the decision rule must be re-specified so that dry gas is not misclassified as wet or conversely.

The applicability of the concept beyond its validated envelope is either supported by an extended or revised model, valid over the specified enlarged conditions and accompanied by a reliable dry/wet decision rule, or bounded by the demonstrated limits of validity of the concept.

References

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