Comparison of throttle devices to measure two-phase flowrates of wet gas with extremely-low liquid loading

The online measurement of wet gas with extremely-low liquid loading (Lockhart-Martinelli parameter lower than 0.02) remains a challenge. In this study, three types of throttle devices, Venturi, orifice plate and cone, are compared experimentally with air-water two-phase flow in a horizontal pipe of inner diameter of 50 mm. High-precision correlations are established to measure the gas and liquid flowrates via a single throttle device. Results show that the two-phase mass flow coefficient (K) of the three throttle devices all increase linearly with the liquid densiometric Froude number and the K correlations are established respectively to correct the gas mass flowrate deviation. The pressure loss ratio (δ) for Venturi is sensitive and monotonous to the liquid loading, which contributes to the high accuracy of liquid flowrate measurement. By incorporating the K correlations, both the gas and liquid mass flowrates can be predicted precisely. The relative error of the gas mass flowrate predicted by the Venturi is within ±2.0% at 95% confidence level, and that of the liquid mass flowrate is within ±15% at 90% confidence level.     

Pressure drop of wet gas flow with ultra-low liquid loading through DP meters

The most common method to predict the gas and liquid flow rates in a wet gas flow simultaneously is to use dual pressure drops (dual-DPs) from two or even one single DP meter. In this paper, the metering mechanism of applying dual-DPs were overviewed. To fully understand the response of DP meters to wet gas flows, the pressure drops of wet gas flow with ultra-low liquid loading through three typical DP meters were experimentally investigated, including an orifice plate meter, a cone meter and a Venturi meter. The equivalent diameter ratio is 0.45. The experimental fluids are air and tap water. The pressure is in the range of 0.1–0.3 MPa and the Lockhart-Martinelli parameter (X_LM) is less than approximately 0.02. The results show that the upstream-throat pressure drop, the downstream-throat pressure drop and the permanent pressure loss of individual DP meters have unique response to liquid loading. The upstream-throat pressure drop of the orifice plate meter decreases at first and then increases as the liquid loading increases, while that of the cone meter and the Venturi meter increase monotonically. The non-monotonicity of the pressure drop for the orifice plate meter can be attributed to the flow modulation of trace liquid. The downstream-throat pressure drops of all the three test sections decrease at first and then increase. The reason is that the liquid presence in a gas flow increases the downstream friction and vortex dissipation. The permanent pressure loss of the orifice plate meter also shows non-monotonicity. To avoid non-monotonicity, the pressure loss ratio is introduced, which is defined as the ratio of the permanent pressure loss to the upstream-throat pressure drop. Results show that the pressure loss ratio of the Venturi meter has the highest sensitivity to the liquid loading.     

High GVF and low pressure gas–liquid two-phase flow measurement based on dual-cone flowmeter

Parameter measurement of gas–liquid two-phase flows with a high gas volume fraction (GVF) has received great attention in the research field of multiphase flow. The cone meter, as a new proposed differential pressure (DP) meter, is increasingly being applied in flowrate measurement of gas–liquid two-phase flow. A dual-parameter measurement method of gas–liquid two-phase flow based on a dual-cone meter is proposed. The two-phase flow is investigated in a horizontal pipeline with high GVF and low pressure, and exists in the form of annular flow. By adding a second cone meter, both gas mass fraction (GMF) and mass flowrate are measured. The pressure drop performances of five different sized cones have been discussed to make a cooperating cone selection and efficiently position the dual-cone in the pipe. Dual-cone flowmeter experiments of 0.45 and 0.65 equivalent diameter ratio combination, and 0.65 and 0.85 equivalent diameter ratio combination are respectively carried out to analyze the linearity of two-phase flow multiplier with Lockhart–Martinelli parameter and obtain the dual-parameter measurement results. The relative experiment error of GMF, gas mass flowrate and total mass flowrate are respectively within ±7%, ±5% and ±10%. The relative error of the liquid phase is within ±10% when the liquid mass fraction is beyond 40%. The experimental results show that it is efficient to utilize this dual-cone method for high GVF and low pressure gas–liquid two-phase flow measurement.     

Wet gas measurements of long-throat Venturi Tube based on forced annular flow

A wet gas dual-parameter measuring device composed of a cyclone and a long-throated Venturi tube is proposed to overcome the difficulty of measuring the liquid content of wet gases and reduce the error caused by the wet gas flow pattern. The flow pattern is transformed into an annular flow by a cyclone. In this study, the proposed device was compared with a traditional non-cyclone long-throat Venturi tube; furthermore, the pressure difference ratio W between the contraction and expansion sections of the long-throat Venturi tube was introduced as a parameter. Through numerical simulations, the relationship between W, the gas Froude number, over-reading, and liquid-gas mass flow ratio was analyzed, and a new wet gas flow measurement model was established. The reliability of the measurement model was verified through indoor experiments. The experimental results showed that the traditional wet gas measurement device had gas phase and liquid phase errors of ±4.5% and ±10%, respectively; on the other hand, the cyclone-based wet gas measurement device had gas phase and liquid phase errors of ±3% and ±8%, respectively. Thus, the performance of the wet gas measurement device with the cyclone was higher than that of the traditional wet gas measurement device.     

Gas–liquid two-phase flowrate measurement in pseudo-slug flow with Venturi

The importance of pseudo-slug flow research is becoming increasingly prominent in the petrochemical field. But the gas–liquid two-phase flowrate measurement in the pseudo-slug flow has not been properly understood and modeled. Based on the differential pressure of Venturi, this study proposes a new pseudo-slug flowrate prediction model. By means of Fast Fourier transform (FFT), the representative frequency range (3.125 Hz < f < 6.25 Hz) is determined. Then, the fourth detail component of the differential pressure after wavelet transform is selected as the flag to distinguish the liquid film region and the pseudo-slug body region. Based on the gas–liquid density ratio, a logarithmic model is established to predict the threshold value. In the liquid film region, the gas–liquid two-phase flow is regarded as wet gas and the flowrate is measured through the over-reading model. In the pseudo-slug body region, the volume gas holdup model is established based on the fluctuation information of the differential pressure. Then the gas–liquid two-phase flowrate can be obtained by solving the Bernoulli equation. Compared to the experiment, the confidence probability of ±10% relative deviation band is 97.78% for the gas, and the confidence probability of ±20% relative deviation band is 95% for the liquid.     

Coupled model of dual differential pressure (DDP) for two-phase flow measurement based on phase-isolation method

Phase-isolation is a novel ever-increasing multiphase separation technology, which can facilitate the multiphase fluid flowing concurrently with a substantially clear interface between two phases, and the phenomenon is promisingly employed for the separation and measurement of multiphase flows. Phase-isolation can be implemented by different kinds of lateral forces, of which the centrifugal force induced by the swirlers is the most convenient method. The radial pressure drop between pipe wall and pipe center, and the axial pressure drop along the pipe wall occurs at the downstream of the swirler. In the paper, the coupling model of dual differential pressure (DDP) including the radial-axial differential pressure and radial-radial differential pressure was built employing centrifugal phase-isolation for oil-water two-phase flow, and the theoretical measurement models were validated by our experimental data. At certain cross sections downstream of the swirler, the deviations between theoretical and experimental result of the volumetric oil fraction λ_o and mass flowrate Q_m were below ±7.16% and ±1.14% respectively when the radial-axial differential pressure was adopted, while the deviations between theoretical and experimental result of λ_o and Q_m were below ±6.91% and ±1.13% respectively using the radial-radial differential pressure. The acceptable deviation indicates that the DDP model can be the reference for the analysis and application of two-phase flow in the academic research and practical engineering.     

Compensation for Joule–Thomson effect in flowrate measurements by GMDH polynomial

The international standard for flowrate measurements ISO-5167 recommends the temperature sensor to be located downstream of the differential device what may cause a significant error in the measurement of the flowrate of natural gas, especially at high differential pressure, low temperature and low diameter ratio. The flowrate generally needs to be compensated for the temperature change due to the Joule–Thomson effect caused by the constriction of the metering device. The accurate compensation involves double calculation of both the natural gas properties and the flowrate. To decrease the computational load, an automatic correction of the flowrate by the GMDH polynomial surrogate is proposed. By using the compound measure of the approximation error and the execution time for model selection, the modified GMDH algorithm searches for the satisfactory model fulfilling the constraints of real-time application. The automatic correction of the flowrate measurements of a natural gas is simulated and the corresponding results are discussed. The derived model can be equally used for a natural gas specified by composition or by physical properties.     

Flow measurement based on the combination of swirler and differential pressure under slug flow

The alternating appearance of elongated bubbles and liquid slugs of slug flow in the pipe causes severe pressure fluctuation. As a result, measuring the flow rate of the slug flow with the throttling unit based differential pressure method is difficult. This paper investigates a new swirler-based flow measurement method in slug flow. The swirler converts the slug flow into a swirling annular flow, and the differential pressure method is used to measure the flow rate. The influences of gas and liquid flow rates on the differential pressure ΔP_X across the swirler as well as its downstream axial differential pressure ΔP_Z are investigated. ΔP_X^0.5 increases linearly as the liquid mass flow rate increases, and the slope of the curve increases as the gas mass flow rate increases. The influence of gas mass flow rate on ΔP_X^0.5 is comparable to that of liquid mass flow rate on ΔP_X^0.5. ΔP_Z^0.5 increases linearly with increasing gas/liquid mass flow rate, and the slope of the curve of ΔP_Z^0.5 with m_l differs slightly from the slope of the curve in single-phase water conditions. Based on the research presented above, new empirical correlations of mass flow rate based on ΔP_X and ΔP_Z are established respectively. The superficial liquid velocity ranges from 0.6 to 2 m per second, while the superficial gas velocity ranges from 2 to 6 m per second. If the gas mass flow rate and ΔP_X are known, the relative error of liquid mass flow is less than 3%. The relative error of the gas mass flow rate is less than 10% if the liquid mass flow rate and ΔP_X are given. The calculation accuracy of the flow measurement model using ΔP_X is better than the calculation accuracy of the flow measurement model using ΔP_Z.     

Study of the factors influencing the over-reading characteristics of the precession Venturi

In the energy industry, such as the gas field, precise measurement of wet gas is becoming increasingly crucial. Many studies have focused on the over-reading (OR) of throttle flowmeter in wet gas measurement. By using the dimensional analysis method, we proposed a precession Venturi and established a new OR correlation based on the gas Froude number, liquid-gas density ratio, and the Lockhart–Martinelli parameter. Experimental tests of air-water flow were conducted, and the relationships between differential pressure and OR with liquid volume fraction were investigated at various pressures and superficial gas velocities. The experimental results show that the uncertainty of gas flow rate measurement is in the range of 0.35%–0.56%, and 90.8% of the points are in the range of 0.35%–0.45%, with a relative error band of ±2.94% calculated by the OR correlation at a confidence probability of 95.5%.     

Study on the parallel pressure differential type gas laminar flow sensing technique

Parallel pressure differential (PPD) type laminar flow sensing technique was invented several years ago to reduce nonlinear effect in a traditional laminar flow element (LFE). In this paper, the internal flow of each branch in a PPD LFE is numerically simulated for gas flow. The results show that the relative deviation of the pressure drops of the two branches in a PPD LFE is within ±0.05% as inlet mass flow being the same, indicating that the flow resistance characteristics of the two branches are consistent, which means that the hypothesis of a same flow rate for the two branches in a real PPD LFE is tenable. There is little difference, ±0.01%, in the local pressure losses of the two upstream capillaries outlet flows, which can be ignored in a real measurement, further verifying that the theoretical analysis of the PPD principle is reliable. Capillary length effect in a PPD LFE is also examined. The bigger capillary length, the higher measurement precision can be achieved for a certain length range. For instance, it is suggested that the length of the short components should not be shorter than the laminar flow dimensionless entrance length defined by X_e (L_e/d/Re, where L_e is the entrance length) = 0.035, for flow measurement uncertainty within ±1.0%. The simulation and experiment results of gas flow show that the suitable value of K_exp is 1, and in the flow range of (0.0256–5.2985) m³/h measurement error of a PPD LFE is within ±0.8% only with expansion correction, indicating that the PPD laminar flow measurement technique is suitable for the gas flow.     

Wet gas metering technique based on slotted orifice and swirlmeter in series

Wet gas flow is a subset of gas–liquid two-phase flow, and wet gas metering is gaining considerable attention due to its importance in the nuclear, oil and gas industry. Wet gas meter based on slotted orifice and swirlmeter combination in series was designed and investigated. A wet gas measurement model with the simultaneous equations from the two flowmeters' correlations has been established, and then an iterative solution algorithm is given. The novel proposed approach predicts the gas mass flow rate relative errors within ±6% from 89.2% tested samples, and the gas mass flow rate relative errors within ±20% from all tested samples, which is accepted for many wet gas applications. Therefore, it implies that the proposed wet gas metering technique may be used to meter both gas and liquid flow rates for wet gas flow at the Lockhart Martinelli parameter X≤0.12.     

Investigation on the swirlmeter performance in low pressure wet gas flow

Wet gas flow is a subset of gas-liquid two-phase flow, and the swirlmeter has been used in wet gas flow metering more and more recently. The swirlmeter performance in low pressure wet gas flow was investigated. It is found that the entrained liquid present in a gas stream tends to induce a negative bias in the gas flow rate reading of swirlmeter comparing with equal gas flow rate. When the Lockhart-Martinelli parameter X, which is closely related to the liquid fraction, is bigger than a threshold value, the swirlmeter will not properly work due to the disappearing of vortex precession. It is also found that the liquid-induced gas flow rate reading errors of swirlmeter are dependent on X and the gas densiometric Froude number Fr_g. A correlation for swirlmeter in low pressure wet gas flow is proposed, and it corrects the liquid-induced gas flow rate errors to an accepted accuracy under the tested conditions. It implies that the swirlmeter with the proposed correlation and the known liquid fraction may be used to meter the gas flow rate in wet gas applications with a relatively low liquid fraction.     

Study on the similarity of wet gas pressure drop in long-throat Venturi

This study investigates the effect of pipe diameter on pressure drop with the same diameter ratio, similar pressure-sampling position and throat length of long-throat Venturi. Considering the factors including the void fraction, the friction between the two phases and the entrainment in the gas core, the one-dimensional momentum equation for gas has been solved in the axial direction of long-throat Venturi. A novel void fraction model is established, by considering the effects of dryness and gas-liquid density ratio, then predicting the distribution of wet gas static pressure between the two pressure tapings of the long-throat Venturi. The comparison between the values predicted by the model and those measured experimentally reveals that all the relative deviations of the predicted points by the modified model were within ±15%. In the same entrance conditions, the effect of pipe diameter on pressure drop in long-throat Venturi is similar.     

On fluctuation of the dynamic differential pressure signal of Venturi meter for wet gas metering

Venturi meters are playing an increasingly important role in wet gas metering in natural gas and oil industries. Convincible measurement of the flowrate of wet gas requires two parameters, namely, the whole mass flowrate and its quality. It is commonly believed that the two parameters can be obtained if the Venturi meter is combined with another device of a different principle. However, this is not always the case. Owing to the complexity of the model for wet gas metering, the problem of multiple solutions may occur. Proceeding from a static model on the differential pressure (DP) signal of the Venturi meter, a dynamic model is presented that can provide an extra functional relation to resolve this problem without the need of adding a third device. This functional relation monotonously maps the relative fluctuation of the DP signal to the quality of the wet gas and simplifies the selection of the true solution. Experiments have been carried out within static pressure range of 0.3–0.8 MPa, gas flowrate range of 50–100 m³/h and quality range of 0.06–0.412. Emphasis of the experiments has been on the demonstration of the validity of the static and dynamic models. Finally, appropriate discussions and conclusions are given.     

Study on double differential pressure measurement method of gas-liquid two-phase flow in high gas content wells

The production of natural-gas wells contains natural gas and a small amount of liquid, which is a wet gas composed of oil, gas and water. For dynamically monitor the liquid and gas production from a single well, there is an urgent need for a low-cost, small-volume online metering device for wet gas flows through a single well. Aiming at the problem, this paper designs a wet gas flow measurement device for a long-throated Venturi tube based on the double differential pressure method. By combining experiments and numerical simulations, a matching flow calculation model was developed. Based on the experimental data of NEL's 6-inch standard Venturi tube wet gas over-reading, the numerical simulation method is used to carry out the research of high-pressure wet gas measurement under the pressure condition of 2, 4 and 6 MPa. The simulation results of two multiphase flow models, DPM and Euler, are compared with the experimental values of NEL. The results show that the maximum relative error is less than 10%, and the Euler model is more suitable for the numerical simulation of high-pressure wet gas. According to the actual production from the gas well, a long-throated Venturi tube with a throttling ratio of 0.5 and a diameter of DN50 was designed, and a numerical simulation study of wet gas under a pressure of 2, 3 and 4 MPa was carried out. Numerical simulation results show that the change laws of over-reading and liquid-gas mass ratios of high-pressure wet gas are consistent with those of low-pressure wet gas. The numerical simulation results are used to correct the flow calculation model of low-pressure wet gas, and a flow calculation model suitable for high-pressure wet gas in gas wells is obtained. The gas flow prediction accuracy of the flow calculation model was lower than ±3%, and the liquid flow prediction value was lower than ±10%. Compared with other measurement methods without separation of wet gas, the long-throated Venturi tube based on the double differential pressure method has a simple structure and low measurement cost. By further optimizing and expanding the measurement model, after improving the accuracy, it can be installed in the wellhead pipeline to monitor the oil and gas production from a single well in real time. This can provide support for gas reservoir exploitation decisions.     

Horizontally installed cone differential pressure meter wet gas flow performance

Differential pressure (DP) meters which utilise a cone as the system’s primary element are increasingly being used to measure wet natural gas flows (i.e. mixtures of natural gas, light hydrocarbon liquids and water). It is therefore important to understand this meter’s response to wet natural gas flows. Research into the wet gas response of the horizontally installed cone DP meter is discussed in this paper. Consideration is given to the significant influence of the liquid properties on wet gas flow patterns and the corresponding influence of the flow pattern on the cone DP meter’s liquid phase induced gas flow rate prediction error. A wet natural gas flow correlation for 4 in. 0.75 beta ratio cone DP meters with natural gas, hydrocarbon liquid and water flow has been developed from multiple data sets from three different wet gas flow test facilities. This corrects the liquid induced gas flow rate prediction error of a wet gas flow up to a Lockhart–Martinelli parameter of 0.3, for a known liquid flow rate of any hydrocarbon liquid/water ratio, to ±4% at a 95% confidence level.     

Pressure measurement technique and installation effects on the performance of wafer cone design

The present study explores novel pressure averaging technique for wafer cone flowmeter design and its robustness in the presence of double 90° bend (out-of-plane) and gate valve as a source of upstream flow disturbance. The wafer cone flowmeter is tested in a circular pipe (inside diameter of 101 mm) with water as the working medium for the flow Reynolds number ranging from 1.19×10⁵ to 5.82×10⁵. Influence of the half cone angle (α) on the coefficient of discharge (C_d) of wafer cone flowmeter is studied with this new pressure averaging technique. Half cone angles considered in this study are 30° and 45° with a constant constriction ratio (β) of 0.75. The upstream static pressure tap is located at 1D upstream of the wafer cone. The downstream pressure averaging technique comprises eight circumferential holes of diameter 2 mm on the maximum diameter step of the wafer cone. The pressure taps are communicated through the support strut which serves as a downstream static pressure tap. The disturbance causing elements are individually placed at 1.5D, 5.5D, 9.5D and 13.5D upstream to the wafer cone flowmeter. The wafer cone flowmeter is also tested with gate valve opening of 25%, 50% and 75% for all the arrangements considered. The 30° cone is found to be better than 45° cone for the range of Reynolds number covered in the present study. The results show that the 30° wafer cone flowmeter with novel downstream pressure averaging technique is insensitive to the swirl flow created by a double 90° bend (out-of-plane) and requires an upstream length of 9.5D with a gate valve as a source of flow disturbance.     

A CFD study of low pressure wet gas metering using slotted orifice meters

Wet gas metering is becoming an increasingly important problem to many industries, in particular the oil and gas industry. Extensive studies have been done in the past on Venturi and standard orifice differential pressure (DP) flow meters to tackle wet gas flow problems. However in recent years, the slotted orifice flow meter has been developed in the attempt to improve the performance of the standard orifice meter. The novel flow meter is shown to be insensitive to the upstream flow profile with lower head loss and faster pressure recovery. This paper describes the numerical studies to establish the effect of different geometrical perforations on the performance of the slotted orifice. Three sets of slotted orifices with varying aspect ratios (1.5≤l/w≤3.0), of rectangular perforations and one slotted orifice with a circular perforation and a β ratio of 0.40 are simulated in a 1.6 m horizontal pipe using the k-ε turbulence model over a range of parameters, i.e. gas volume fraction (GVF) and gas mass flow rate. The commercial CFD code, FLUENT 6.3 was used to model the wet gas flow. Simulation results revealed that the shape of the perforation has no effect on the differential pressure, However, a marginally better pressure recovery was observed with rectangular perforations of l/w=3.0. The relatively higher over-reading values obtained in this work are consistent with the results of Geng et al. (2006) [1] that for a slotted orifice, a low β ratio is more sensitive to the liquid presence in the stream and hence is preferable for wet gas metering. Mass flow prediction by wet gas correlations showed that the homogeneous model, Steven’s and De Leeuw’s correlations had the best performance, with a calculated mean error of 4%-5%.     

A V-Cone meter measurement correlation in low pressure wet gas based on Chisholm model

To gain a deeper understanding of the performance of V-Cone meter in low pressure wet gas measurement, the over-reading of the V-Cone meter was experimentally investigated in the present study. The equivalent diameter ratio of the V-Cone meter is 0.55. The experimental fluids were air and tap water. The operating pressure and the gas volume fraction ranged from 0.1 MPa to 0.4 MPa and 97.52%–100%, respectively. The results showed that the existing V-Cone wet gas correlation, which was developed for the medium and high pressure wet gas cannot be well extended to the low pressure conditions. The Chisholm exponent monotonically decreased with the ratio of liquid-to-gas mass flow rate increasing, and was almost not affected by the gas to liquid density ratio and the gas densiometric Froude number in the present test ranges. A measurement correlation dedicated for the low pressure wet gas was developed. In the present cases, the relative deviation of the gas mass flow rate predicted by the new correlation was within ±4.0% and ±3.0% under the 95% and 90% confidence level, respectively; the average relative deviation was 0.046%. Our results provide insights into the measurement performance of V-Cone meter in low pressure wet gas and may help to develop a more comprehensive wet gas correlation.     

Wet gas meter based on the vortex precession frequency and differential pressure combination of swirlmeter

A wet gas meter, based on combination of two dissimilar output signals from swirlmeter, i.e. the vortex precession frequency and the differential pressure of swirlmeter, was designed and investigated in low pressure wet gas flow. A wet gas measurement model with the simultaneous equations from the two correlations of swirlmeter has been established, and then the iterative solution algorithm is given. The proposed wet gas meter predicts the gas mass flow rate errors within ±8% from 91.3% tested samples, and the liquid mass flow rate errors within ±20% from 89.2% tested samples, which may be used to meter both gas and liquid flow rates for wet gas flow with X?0.12$X?0.12$. In view of installation, maintenance and cost, the proposed approach is cost-effective due to using only a flow sensor.