Lockhart-Martinelli Parameter Research Articles

Experimental study on the influence of the riser on the gas-liquid flow in the horizontal pipeline of the offshore pipeline-riser system

The study of gas-liquid interface evolution and pressure fluctuation mechanism in the pipeline-riser system is the key to ensuring the safety of oil and gas transportation. This paper investigates the influence of the riser on the gas-liquid interface in the system with a 1657 m pipeline and risers of 16 m, 22 m, and 29 m. In severe slugging, the differential pressure in the horizontal pipeline exhibits a low-frequency large-amplitude fluctuation consistent with those in the riser. During the gas blowdown of the riser, the pressure fluctuation breaks the force equilibrium of the gas-liquid interface and induces numerous liquid slugs in the horizontal pipeline. A strong correlation is found between the differential pressure in the riser and the slug velocity in the horizontal pipeline by the Spearman Rank coefficient. The correlations between the slug velocity and the gas volume fraction and the void fraction under different riser heights are established, and the errors are 15% and 10%, respectively. The linear relationship between the Strouhal number of liquid slugs and the Lockhart-Martinelli parameter is constructed during the gas blowdown.

Flow boiling pressure drop correlation in small to micro passages

An accurate and acceptable correlation for the prediction of two-phase pressure drop is considered a crucial step in heat exchanger design. Although many existing models and correlations were developed and proposed in the past, their ability to predict within acceptable error bands when applied in general to flow boiling flows is limited, even within their originally recorded ranges. The discrepancies are worse when predicting two-phase pressure drop in small to micro-scale passages. Therefore, the aim of the work described in this paper is to assess the most well-known models and correlations using a large experimental data-bank. The data-bank includes four refrigerants, namely R134a, R245fa, HFE-7100 and HFE-7200, small to micro heat exchangers made of different metals and different channel configurations. In addition, the data cover a large range of operating conditions, which can allow generally applicability of new correlations developed. This range covers channel hydraulic diameter of 0.46−4.26 mm, heated length of 20−500 mm, system pressure of 1 − 14 bar, mass flux of 50−700 kg/m2 s, wall heat flux ranging from 2 to 234 kW/m2 and exit vapour quality up to one. Twenty six existing models and correlations that were developed and proposed for vertical/horizontal flow, single/multi-channels and circular/non-circular channels were evaluated. Moreover, the effect of using different equations for calculating the two-phase mixture viscosity, void fraction, Fanning friction factor and Lockhart–Martinelli parameter was assessed and discussed. The mean absolute error of the existing correlations when compared with our data-bank was more than 30 %. Therefore, a new correlation for calculating the two-phase multiplier, which was strongly dependent on the Boiling number and the Lockhart–Martinelli parameter, was developed and then the frictional component and total two-phase pressure drop relationships were completed.

Experimental and numerical study on wet steam flow metering overreading characteristics in venturi tube

The precise measurement of wet-steam flow is of great importance in various industrial systems, including nuclear reactors, oil and gas transportation, and cogeneration systems. However, the measurement accuracy of wet-steam flow can be affected by overreading (OR) when using venturi meters. This paper presents a systematic numerical simulation using the DPM model and an experimental study on the characteristics of overreading in wet-steam flow metering. The experiments are carried out on a two-phase flow liquid and steam platform. Firstly, the OR characteristics of a venturi structure with fixed dimensions (a throttling ratio of 0.6, a divergence angle of 15°, and a venturi diameter of 20 mm) are quantitatively analyzed at different flow rates (0.14-0.32 kg/s) and qualities (ranging from 0.14 to 0.90). It is found that the Lockhart-Martinelli parameter (XLM) plays a more significant role than the gas Froude number (Frg) in determining the overreading (OR) characteristics of a venturi under a given temperature, pressure, and venturi structure. Secondly, a venturi overreading prediction model based on XLM is proposed, and its ability to predict overreading for larger mass flow rates and venturi diameters is verified by numerical simulation data. As evaluated through numerical simulation data, the proposed model’s maximum relative error and average deviation are below 15% and 10%, respectively. This study provides valuable insights into developing an overreading model for industrial applications under large flow and venturi diameter conditions.

Devices and methods for wet gas flow metering: A comprehensive review

Wet gas is commonly encountered in various industries, including energy, chemical, and electric power sectors. For example, natural gas extracted from production often contains small amounts of liquid, such as water and hydrocarbon condensates, which classifies it as wet gas. The presence of liquid within the gas poses challenges for accurate flow measurement. To improve the performances of wet gas flow metering methods, significant research and development efforts have been invested into the wet gas flow metering technologies due to their vital importance in the production, transfer, and trade benefits.This paper presents a comprehensive overview of the recent development of wet gas flow metering. Firstly, a comprehensive discussion of the Lockhart-Martinelli parameter (Xlm) and its relation to the gas void fraction (αg) is presented, which was mostly overlooked in previous wet gas research work. The occurrence of various flow patterns in wet gas conditions at different orientations (horizontal and vertical) was explored. Following an investigation of pressure impact on the wet gas flow patterns and development of the wet gas regions, a different test matrix for further research work was suggested. After a novel classification of wet gas measurement methods, the paper offers a detailed comparison of differential pressure (DP) meters including Venturi, Cone meter, and orifice meters, by considering both liquid and gas flow rate measurements. Secondly, the paper discusses and compares vortex flow meters, Coriolis and ultrasonic meters in comparison to DP meters. Notable phase fraction meters are also examined and compared to one another. Thirdly, the paper reviewed the concept of existing and potential hybrid wet gas meters, conducting a detailed discussion and comparison with commercial solutions by evaluating their ranges and accuracies. This assessment provides valuable insights into the capabilities of these hybrid meters, highlighting their potential to enhance the measurement of wet gas flow rates.

Development of the concept of a multiphase flowmeter

In a number of industries: oil and gas, chemical and nuclear industries, the task of controlling multiphase flow regimes arises. In the nuclear and chemical industries, the flow regime directly affects the nature of technological processes and their safety. In the oil and gas industry, the products extracted from wells are usually a mixture of oil, water and gas, and the task of monitoring the flow regime is related to compliance with the permissible parameters of pumping and control equipment. When using multiphase flowmeters of the flow type, the algorithms for calculating phase flow rates in a multiphase flow are very sensitive to a violation of the uniformity and homogeneity of the measured flow. Excessive noise of the signal of pressure sensors, volume content and flow caused by projectile, cork or stratified modes can negatively affect the accuracy of measurements. As a rule, flow mode maps are used when determining the current mode. This approach is based on the calculation of a number of dimensionless flow parameters (Froude number, Lockhart–Martinelli parameter, etc.). In the case of a dynamically changing flow, this approach may not be suitable. For a more accurate and reliable determination of flow modes, it is proposed to use a direct method of analyzing the spatial distribution of phases in the flow and recognizing the type of flow using artificial convolutional neural networks. This approach allows you to get rid of classification errors and get more accurate information about the flow. The aim of the study is to develop a technique for neural network analysis of images of a multiphase flow with subsequent determination of its type. In the course of the work, approaches to the formation of a training sample are considered, the search for the optimal structure of the neural network is carried out and an accuracy assessment is given for the classification of multiphase flow modes by a convolutional neural network. The study was carried out on two types of data: 1) synthetic images obtained using numerical simulation of multiphase flows, and 2) experimentally obtained flow images on a multiphase flow stand.

Air Bubble Size and Its Transition in a Horizontal Tube Produced by Venturi-Nozzle Bubble Generator

This paper investigates the air bubble size and its transition in a horizontal tube of 700 mm. The tube was assembled with a venturi-nozzle bubble generator. Air and water flow-rates vary in the present study. The data collection mainly used high-speed camera to capture the bubbles at different distances along the horizontal tube at water flow-rates (Qw) of 120-170 litre per min (LPM) and air flow-rates (Qa) of 2-10 LPM. MATLAB was used in image processing for evaluating the bubble size. The data interpretation used YW dimensionless parameter in representing the height of the bubbles’ vertical rise in the horizontal tube. The bubble size along the horizontal tube was characterized by the Weber number as well. The type of two-phase (water-air bubbles) flow along the horizontal tube from the venturi-nozzle bubble generator was determined using flow pattern map and Lockhart-Martinelli parameter. The bubble generator produced bubbles in the range of 0.8-3.1 mm at the inlet of horizontal tube. The bubble diameters increased as the bubbles moved horizontally from inlet to outlet of the horizontal tube and this finding was statistically significant. The vertical rise height of bubbles along the horizontal tube at different water and air flow-rates had been quantified and compared. The vertical rise height of bubbles increased axially from 41 % to 89 % from inlet to outlet of the horizontal tube. The bubbles’ vertical rise height increased when either the air flow-rate or water flow-rate is reduced. The mean Weber number increased along the horizontal tube due to an increase in bubble size. The decrease in water flow-rate caused a decrease in the mean Weber number. The Lockhart-Martinelli parameter of the water-air bubbles flow in the horizontal tube was within 0.58-2.94, indicating that it was a multiphase flow. The findings from this study give fundamental insight into bubble dynamics behaviour in its horizontal transition. This study focuses on the size and transition of air bubbles produced by venturi-nozzle bubble generator along a horizontal tube at different water and air flow-rates, unlike previous studies which only investigate the air bubbles inside or near bubble generator. These findings are very useful for practical industrial applications because the exact air bubble size before being used is known.

Flow pattern criteria for vapor condensation inside a downward inclined tube

Vapor condensation in inclined tubes is a widely used process in various industries, but currently there is no verified map available for predicting flow patterns during condensation. This study aimed to develop a method to predict flow patterns during condensation in downward inclined tubes. The literature on condensation flow patterns in downward inclined tubes was thoroughly investigated, and this paper presented a summary of experimental data on condensation in downward inclined tubes, covering inclination angles from 7° to 75° (downward flow), tube diameters from 5.79 to 25.0 mm, pressures from 0.1 to 1.0166 MPa, mass fluxes from 8.1 to 705 kg/m2s, and three fluids including water and refrigerants. By comparing the existing flow pattern maps with the data, it was found that the existing flow pattern maps were deficient and did not predict the condensation flow pattern well. Based on extensive condensation flow pattern data, a set of criteria for predicting the flow pattern during condensation, using the modified Froude number F and the Lockhart-Martinelli parameter X as map coordinates, was proposed. The results showed good prediction accuracy for inclined in-tube condensation flow patterns.

Characterization of liquid film distribution and sub-flow regimes of annular flow in helically coiled tubes using ring island array sensor

The distribution of liquid film thickness in helically coiled tubes (HCTs) directly affects the heat transfer performance of the annular flow region. However, due to the limitation of measurement technology, accurate measurement data of liquid film thickness in HCTs is very rare. In this paper, a non-invasive contact liquid film thickness sensor (ring island array sensor) is successfully developed to obtain the refined three-dimensional spatial-temporal distribution data of liquid film thickness in HCTs. According to the results, four typical liquid film flow regimes are defined based on the circumferential position of the thicker liquid film appearing in the tube wall, i.e., the bottom distribution (BD) dominated by liquid phase gravity force, the outside distribution (OD) dominated by liquid phase centrifugal force, the inside distribution (ID) dominated by gas centrifugal force and the inside-outside distribution (IOD) dominated by the secondary flow. These circumferential distributions of liquid film thickness are mainly affected by the HCT structure (e.g., coil diameter and coil pitch) and superficial gas-liquid velocities. Based on the modified Dean number De* and the modified Lockhart-Martinelli parameter X*, which consider the influence of HCT structures, fluid properties and operating parameters, a general sub-flow regime map of annular flow is proposed. The prediction models of transition boundaries of different liquid film flow regimes are also established and verified with present and available data in the literature.

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%.

A new correlation to determine the Lockhart-Martinelli parameter from vertical differential pressure for horizontal venturi tube over-reading correction

Venturi tubes are widely used to measure the gas flow rate in a wet-gas stream. To calculate the gas flow rate, wet-gas Venturi tubes require the liquid loading (i.e. Lockhart-Martinelli parameter) to be known as an input to a so-called over-reading correction correlation. It is challenging to derive the Lockhart-Martinelli parameter without installing additional devices in series to the Venturi tube thus adding significant cost and complexity. A relatively low cost and easy to implement method is to derive the Lockhart-Martinelli parameter by measuring the pressure drop across the Venturi tube or along a pipe section. A correlation that predicts the Lockhart-Martinelli parameter by measuring the pressure drop along a vertical pipe section downstream of the Venturi tube is presented. The correlation was obtained by fitting experimental results from TUV-SUD National Engineering Laboratory's wet-gas test facility with nitrogen-water in a 4″ vertical pipe, Lockhart-Martinelli from 0.04 to 0.29, and gas Froude number from 1 to 2.7. Further experiments were conducted at Spirax Sarco Engineering plc to evaluate the performance of the proposed correlation under steam-water conditions. Tests were conducted with steam-water in a vertical 2″ pipe, Lockhart-Martinelli from 0.005 to 0.064, and gas Froude number from 0.55 to 1.35. The Lockhart-Martinelli parameter is predicted within ±0.035 absolute value with the proposed new correlation for both the National Engineering Laboratory and Spirax Sarco datasets. Gas flow rate values within approximately ±5% error are obtained with the proposed correlation together with ISO/TR 11583 over-reading correlation for the NEL dataset. Although further improvements to the proposed method are required, this work demonstrates the efficacy of an agile, simple, and low-cost differential pressure method to aid the Venturi meter to determine the gas mass flow rate in wet-gas flow.

New flow boiling frictional pressure drop multipliers for smooth and microfin tubes

Abstract The accurate calculation of pressure drop of evaporators/condensers are crucial and related with the pumping power, performance coefficient and energy consumption in a refrigeration equipment. This work aligns frictional pressure drop models/correlations with the experimental outcomes of boiling pressure drop of R134a in horizontal smooth and microfin copper tubes with equivalent outer diameter of 9.52 mm. The pressure drop through the test tube is obtained with a differential pressure transducer directly. Effective parameters are specified for smooth and microfin tubes and the most compatible models/correlations, 12 for smooth tubes and 9 for microfin ones, are determined accurately in relation to the consequences of investigation during intermittent and annular flow regime. Moreover, new two-phase multipliers have been developed by using regression analyses of 182 data points based on Lockhart-Martinelli parameter for each test tubes separately, and their predictability are found to be better than others in the literature as novel ones. Average errors of the developed empirical correlations are 11% for smooth and for 7% for microfin tubes. Finally, the measured data is given for the validation issues of researchers who can benefit from most of the investigated pressure drop models with tolerable accuracy regarding with their HEX design analyses.

Optimization and application of the concentric conductance probes in liquid film thickness measurement in a helically coiled tube

The liquid film distribution in the helically coiled tube (HCT) is affected by curvature-induced centrifugal force and gravity force, showing more complex characteristics than straight tubes. However, due to the limitation of the measurement technology, the relevant data on liquid film in HCT are still rare. In this paper, based on the time-multiplexed excitation-probing scheme, a type of non-intrusive concentric conductance probes (CCPs) is developed at first. After reporting the operation principle of CCPs, the numerical simulation of potential field distribution in CCPs is conducted, and the effects of electrode structure parameters and liquid film thickness on the performance of CCPs are then analyzed in detail. It is found that in a certain range, the larger the inner electrode and outer electrode diameter, the greater the signal penetration depth (i.e. the larger the measurement range of liquid film thickness). Finally, the spatio-temporal distribution of liquid film on the wall of the HCT is experimentally studied using the optimized CCPs. The results indicate that this probe can realize the high-frequency accurate capture of liquid film flow details such as the occurrence and evolution process of liquid film inversion and the fluctuation characteristics of liquid film in HCT. The wave frequency of the liquid film is demonstrated to be not consistent along the circumferential direction. Using Strouhal number and Lockhart–Martinelli parameter, the wave frequency correlation at the maximum film thickness in the state of film inversion in HCT is obtained.

Void Fraction Measurement Using the Coaxial Line Phase Sensor in the Vertical Gas-Liquid Slug Flow

Void fraction is one of the most important parameters in gas-liquid two-phase flow, which plays a crucial role in the pressure gradient calculation and the flow pattern analysis. In this paper, a new coaxial line phase sensor based on the electromagnetic wave propagation is designed and phase shift principle is proposed for the void fraction measurement, and the function relationship between the void fraction and phase difference is derived. By the theoretical analysis and 56 static calibration experiments, the measurement model is proposed in this paper. Air-water two-phase flow experiments have been conducted in a vertical tube at 48 flow conditions in a stainless-steel tubular test section which has an inside diameter of 50.0mm. The dimensionless quantities related to the void fraction, e.g. dynamic viscosity ratio, gas-liquid density ratio, gas-phase Froud number (Frg) and Lockhart-Martinelli parameter ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {X}}_{{\mathrm {LM}}}$ </tex-math></inline-formula> ), are dimensional analyzed. According to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi $ </tex-math></inline-formula> theorem, a new void fraction correlation which could acceptably handle all the available data of different flow conditions (authors’ and literature) is proposed. Laboratory results indicate that the mean absolute error (MAE) of the correlation is 6.46% within an error band of ±10% and 8.03% (183 literature data points) within an error band of ±15%. The void fraction correlation has good prediction accuracy and a certain extrapolation for different flow regimes and fluid characteristic parameters.

A New Correlation to Determine the Lockhart-Martinelli Parameter from Differential Pressure Measurement in a Vertical Pipe

A New Correlation to Determine the Lockhart-Martinelli Parameter from Differential Pressure Measurement in a Vertical Pipe

Heat transfer and pressure drop characteristics of two phase flow in helical coils

This paper presents a review on heat transfer coefficient and pressure drop during condensation and boiling in helically coiled tubes. The geometric parameters such as coil diameter, coil pitch and operating parameters containing saturation temperature, system pressure, mass flux, heat flux and vapor quality have significant effects on the heat transfer characteristics. The frictional pressure drop during flow boiling increases with increasing vapor quality and mass flux, and decreases with increasing system pressure. Also, the effect of the curvature on the two-phase frictional multiplier is negligible. The frictional pressure drop in condensation increased with increasing average vapor quality and mass flux, and decreased with increasing saturation temperature. According to the results reported, heat flux had little effect on the pressure drop during condensation. Flow boiling heat transfer coefficient in helical coils of large diameter showed the similar characteristics and trend with the straight tube as the system pressure decreased. Lockhart-Martinelli parameter was generally preferred to be used by the authors as a function in the correlations to predict flow boiling heat transfer coefficient. There was a decrease in the average Nusselt number with increasing heat flux for the constant Dean number during condensation. This reduction in the average Nusselt number indicated that the turbulence effect created by the secondary flow in the helically coiled tubes eliminated the effects caused by the difference in density. The correlations used for determination of Nusselt number and pressure drop in helical coils with their major findings are presented in details.

Experimental investigation of the thermal performance in a single-component two-phase flow in multistream multi-fluid plate-fin heat exchangers

This paper focuses on evaluating the effects of flow rate and temperature changes of hot and cold fluid flows in multistream multi-fluid plate-fin heat exchangers with a single-component two-phase flow in the middle heat exchanger. This three-fluid heat exchanger included three layers with offset strip and wavy fin configurations. In the adjacent heat exchanger with offset strip fins, hot and cold fluids were flowing, while the middle heat exchanger with wavy fins contained a single-component two-phase flow (condensed vapor). The Nusselt number, friction factor, the thermal performance factor, and the heat transfer surface contribution of the middle heat exchanger with each of the adjacent heat exchangers, were obtained using the measured experimental data. The results indicate that the two-phase Reynolds number was between 500 and 1800, and the vapor quality varied in the range of 0.17–0.56. Also, the heat transfer surface contribution of the adjacent cold and hot fluids was between 0.18 and 0.5. The two-phase flow in the wavy channel has a wavy and stratified pattern. The examinations showed that raising the Reynolds number of hot and cold fluids, respectively, led to maximum 13.8 % and 9.5 % of reduction in the vapor quality, 8.8 % and 9 % of increase in the two-phase Nusselt number, and 18 % and 12 % of reduction in the average value of friction factor. The domain change in the two-phase vapor quality, the two-phase fluid heat transfer surface contribution, and the flow pattern determination parameters including the dimensionless mass parameter and the Lockhart-Martinelli parameter was 33.67 %, 80.81 %, 32.72 %, and 19.09 %, respectively. As the Reynolds number of the cold fluid was changed, the variation domain of these parameters was higher compared to when the Reynolds number of the hot fluid was altered. Increasing the dimensionless temperature of the hot and cold raised the vapor quality by 12–16 %. The experimental results revealed that by decreasing the temperature of adjacent fluids and increasing their Reynolds number, the thermal performance factor of the two-phase flow was increased.

Gas–liquid intermittent flow rates measurement based on two-phase mass flow multiplier and neural network

Online flow rates measurement is encountered in many areas, and efforts are being committed to improving the accuracy of measurement, especially in intermittent flow. This paper concerns gas and liquid flow rates predictions in intermittent flow by fusing the information of the cone meter and conductance ring sensors. A novel correlation of two-phase mass flow multiplier (K) is derived from the separated flow model and modified by experiment data. The feed-forward neural network (FFNN) is used to established the predicted model of Lockhart–Martinelli parameter (X LM). Five FFNNs with different input parameters are compared and results show that FFNNs with dual conductance ring sensor signals have better performance than those with differential pressures of cone meter. Then, the FFNN with conductance ring sensor signals as inputs is used to establish the X LM predicted model. The effect of temperature on the conductance of liquid is also innovatively considered in the neural network. Therefore, no extra reference conductance ring sensor is needed. Finally, combining the X LM model and K correlation, gas and liquid mass flow rates are measured. The relative error of the predicted liquid mass flow rate is less than ±5.0% at the confidence level of 99%. For the gas phase, the relative error is within ±15.0% at the confidence level of 98%. The newly developed metering method provides a high-accuracy as well as a cost-effective measurement method for the intermittent flow.

The dominant frequency analysis of interfacial wave in wet-gas pipeline transportation based on NIR absorption

During the long-distance transportation of wet-gas, the dominant frequency is of great significance for the study of pipeline fatigue and damage, and the safety production. Therefore, the theoretical and experimental researches for dominant frequency are carried out increasingly. However, most of the current prediction correlation of dominant frequency are mainly applicable to atmospheric pressure conditions (0.1 MPa), and the prediction accuracy is not accurate enough. The paper obtains the time series signal of liquid film thickness by near-infrared (NIR) sensor, and then calculates the wave frequency by the power spectrum density (PSD). The performance of typical predictive correlation is evaluated and analyzed by utilizing the experimental data at different flow and pressure conditions (0.1–0.8) MPa. The structure of Strouhal number and Lockhart-Martinelli (L-M) parameter are optimized reasonably, the mean velocity of the liquid film surface, the density increment of gas core, the gas core mass flow and average liquid film velocity are considered in the L-M parameter, a modified interfacial wave frequency correlation is proposed. The results indicate that the mean absolute error of the predictive correlation is 9.06% (current data) and 25.64% (literature data). The new correlation has a better predictive accuracy.

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.

Wet gas metering by cone throttle device with machine learning

Abstract The online measurement of gas and liquid flow rates in wet gas is of great significance. This paper presents a new method to measure gas and liquid flow rates of wet gas by combining the cone throttle device and machine learning techniques. The equivalent diameter ratio of the cone device is 0.45. Experiments are carried out in a horizontal pipe of diameter 50 mm and the operating pressure ranges from 100 kPa to 250 kPa. The working fluids are the mixture of air and water with the Lockhart-Martinelli parameter (XLM) less than 0.3. The multilayer feedforward neural network is used for developing the measurement model. The model requires representative features as inputs and uses the gas and liquid flow rates as outputs. In addition to the mean values of the permanent pressure loss and the upstream-throat differential pressure, the probability density function (PDF) and power spectral density (PSD) of the upstream-throat differential pressure fluctuation are also extracted as representative features. With the principal component analysis method, the independent PDF and PSD features are obtained. The untrained dataset is used to evaluate the performance of the neural network model. Predictions of the flow rates are in good agreement with the experiments. The mean relative errors of the gas and liquid flow rates are 0.05% and −3.66%, respectively. The results show that the proposed method is capable of establishing the implicit correlations between the characteristic parameters of wet gas and the corresponding flow rates.