Void fraction measurement of gas–liquid two-phase flow from differential pressure

Void fraction is an important process variable for the volume and mass computation required for transportation of gas–liquid mixture in pipelines, storage in tanks, metering and custody transfer. Inaccurate measurement would introduce errors in product measurement with potentials for loss of revenue. Accurate measurement is often constrained by invasive and expensive online measurement techniques. This work focuses on the use of cost effective and non-invasive pressure sensors to calculate the gas void fraction of gas–liquid flow. The differential pressure readings from the vertical upward bubbly and slug air–water flow are substituted into classical mathematical models based on energy conservation to derive the void fraction. Electrical Resistance Tomography (ERT) and Wire-mesh Sensor (WMS) are used as benchmark to validate the void fraction obtained from the differential pressure. Consequently the model is able to produce reasonable agreement with ERT and WMS on the void fraction measurement. The effect of the friction loss on the mathematical models is also investigated and discussed. It is concluded the friction loss cannot be neglected, particularly when gas void fraction is less than 0.2.     

Void fraction measurement in steam–water two-phase flow using the gamma ray attenuation under high pressure and high temperature evaporating conditions

The void fraction is one of the most important parameters used to characterize gas–liquid two-phase flow, and a myriad of researchers have investigated it under the adiabatic flow conditions. The gamma ray attenuation is a frequently used non-intrusive method for measuring component volume fraction in gas–liquid two-phase flow system. In this paper, firstly, the influence of the various parameters and test conditions on the gamma ray attenuation have been completely examined, such as the calibration of Count Rate for pure gas and liquid phases, the influences of fluid temperature, phase changing point and fluid mass velocity, distance between gamma ray attenuation measuring instrument and experimental section etc. Secondly, the measurement of void fraction was taken in the vertically upward pipes under high pressure and high temperature evaporating conditions. The experimental results of void fraction were compared with the data in reference literature for measurement, the results from the gamma ray attenuation show good agreement with the literature for air–water two-phase flows, but for the evaporating conditions, a small number of compared data beyond the statistical approach for 90% of confidence interval due to some reasons, such as heat flux, the diameter of Taylor-bubbles, longitude of slugs etc. Finally, six predicted correlations from four groups were selected for comparing with the experimental data. The most of compared data were within the statistical approach for 85% of confidence interval. In general, the void fraction was rarely investigated and the available data was limited under high temperature and high pressure evaporating conditions. The investigations of present study are helpful to resolve the difficulties of measuring for gas–liquid two-phase flows concerning to the heated evaporating condition.     

Investigation of using 60Co source and one detector for determining the flow regime and void fraction in gas–liquid two-phase flows

In this study, a simple detection system comprised of one ⁶⁰Co source and just one NaI detector was investigated in order to identify flow regime and measure void fraction in gas–liquid two phase flows. For this purpose, 3 main flow regimes of two-phase flows including stratified, homogenous and annular with void fractions in the range of 5–95% were simulated by Monte-Carlo N Particle (MCNP) code. At first step, 3 features (count under full energy peaks of 1.173 and 1.333 MeV, and count under Compton continuum) were extracted from registered gamma spectrum. These 3 extracted features were used as inputs of artificial neural network (ANNs). A primary network was trained for identifying the flow regimes, but after testing many different structures, it was found that just two regimes of stratified and annular could be completely identified from each other. After identifying the mentioned two flow regimes by the first ANN, two specific ANNs were also implemented for predicting the void fraction. Using the proposed method in this work, void fraction percentages were predicted with a mean relative error (MRE) of less than only 0.42%. Using fewer detectors is of advantage in industrial nuclear gauges, because of reducing economical expenses and also simplicity of working with these systems.     

A new method of entrainment fraction measurement in annular gas–liquid flow in a small diameter vertical tube

A new method was introduced to measure liquid entrainment fraction in gas–liquid two-phase upward annular flow in a vertical tube (i.d.=9.525 mm). In this method, a new liquid–gas separator was designed and the chemically-based titration method was used to effectively measure the entrainment fraction in real time. Experiments were conducted at low system pressure (∼1 atm), and relatively low gas and liquid superficial velocities ($V_{\mathrm{sg}}=25.8$–45.5 m/s, and $V_{\mathrm{sl}}=0.15$–0.30 m/s). Data analysis shows that the results are repeatable and occupy the range commonly seen in annular flow. The entrainment fraction was found to be under 7% for all the experimental set points. The repeatability of the test results and comparisons with previous entrainment data indicate that the new technique can perform as well as the film removal technique.     

The parameters measurement of air–water two phase flow using the electrical resistance tomography (ERT) technique in a bubble column

The air–water two-phase flow is investigated in a bubble column with a height of 2 m and a diameter of 0.282 m by using the Electrical Resistance Tomography (ERT) technique. The flow characterization are measured by applying ERT sensors of three vertical sections with superficial gas velocities in the range 0.027–0.156 m/s. Based on the cross-correlation technique and dynamic gas disengagement (DGD) theory, the bubble Saunter diameters are obtained and the local axial velocity about two phases flow can be calculated. The results show that with increased gas superficial velocity the distribution of bubble size is gradually widespread. Moreover, the local velocity of gas bubble swarm has a center peak distribution with increased gas superficial velocity.     

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.     

Generation,validation and application of dynamic load profiles in flow measurement using cavitating Herschel–Venturi nozzles

Today, utility meters for water are tested for measurement behavior at stable operating conditions at specified flow rates as part of the approval process. The measurement error that occurs during start and stop or when changing between flow rates may not be taken into account. In addition, there are new technologies whose measuring behavior under real-world conditions is only known to a limited extend. To take these facts into account, a new method has been developed and tested to determine the measurement behavior of water meters under dynamic load profiles as they occur in the real application. For this purpose, a test rig for flow rate measurement was extended by a cavitation nozzle apparatus and the generation of dynamic load profiles was validated. For the cavitation nozzles used, possible factors influencing the flow rate, such as temperature and purity of the water as well as the upstream pressure were investigated. Using different types of domestic water meters, the applicability of the dynamic test procedure was demonstrated and the measurement behavior of the meters was characterised.     

Velocity measurement of the liquid–solid flow in a vertical pipeline using gamma-ray absorption and weighted cross-correlation

Developing technology for the deep-sea mining of polymetallic nodules requires, theoretical analyses, simulation and numerous experimental studies. In this paper authors focused on nuclear methods adoption to velocity of solid phase measurement in an extremely hard and varying environment. Selected results of the experimental studies of two-phase liquid–solid particles flow in a vertical pipeline obtained by probing with photon beams are presented. With the use of the sealed ²⁴¹Am isotopes emitting gamma radiation of 59.5 keV, and the scintillation probes with NaI(TI) detectors, the average transport velocity for ceramic models representing natural polymetallic nodules were determined. In the paper for analysis of the signals coming from the probes, the cross correlation function (CCF) and its modifications consisting in the combination of the CCF with such procedures as the average square difference function (ASDF) and the average magnitude difference function (AMDF) were used. An example of measurement is presented and its resulting uncertainties determined. In described experiment the relative values of the combined uncertainty of solid particles average velocity estimation are equal to: 3.2% for the CCF, 3.0% for the CCF/AMDF and 2.8% for the CCF/ASDF.     

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.     

Ultrasonic detection of moving interfaces in gas–liquid two-phase flow

Ultrasound reflects strongly off the gas–liquid interface when there is a large change in acoustic impedance. We exploit this phenomenon to detect the instantaneous position of the interface from the time of flight of pulsed ultrasound. Because the characteristics of the reflected wave depend on the shape and size of the interface relative to the ultrasound wavelength, the single-sensing principle is insufficient to capture the interface for generalized gas–liquid two-phase flows. In the present study, we design and examine three types of ultrasound interface detection techniques: the echo intensity technique, the local Doppler technique, and the velocity-variance technique, and investigate and compare the merits and limitations of each. The results indicate that the echo intensity technique is appropriate for turbulent interfaces that cause ultrasound scattering over wide angles. In contrast, the local Doppler technique is required to capture information from waves reflected from smooth interfaces and bubbles. Finally, we find that the velocity-variance technique works for quasi-steady and periodical two-phase flow, and we apply this technique to horizontal slug flow in a tube.     

Voidage measurement of gas–liquid two-phase flow based on Capacitively Coupled Contactless Conductivity Detection

Based on Capacitively Coupled Contactless Conductivity Detection (C⁴D) technique, a new method for the voidage measurement of conductive gas–liquid two-phase flow is proposed. 15 Conductance signals, which reflect voidage distribution of gas–liquid two-phase flow, are obtained by a six-electrode C⁴D sensor. With the conductance signals, the flow pattern of gas–liquid two-phase flow is identified by flow pattern classifiers and then the voidage measurement is implemented by a corresponding voidage measurement model (for each typical flow pattern, a corresponding voidage measurement model is developed). The conductance measurement of the six-electrode C⁴D sensor is implemented by phase sensitivity demodulation (PSD) method. The flow pattern classifiers and the voidage measurement models are developed by partial least squares (PLS) technique and least squares support vector machine (LS-SVM) technique. Static voidage measurement experiments and dynamic voidage measurement experiments show that the proposed voidage measurement method is effective, the developed six-electrode C⁴D sensor is successful and the measurement accuracy is satisfactory.     

Refined reconstruction of liquid–gas interface structures for stratified two-phase flow using wire-mesh sensor

Wire-mesh sensors (WMS), developed at HZDR [4], [13], are widely used to visualize two-phase flows and measure flow parameters, such as phase fraction distributions or gas phase velocities quantitatively and with a very high temporal resolution. They have been extensively applied to a wide range of two-phase gas–liquid flow problems with conducting and non-conducting liquids. However, for very low liquid loadings, the state of the art data analysis algorithms for WMS data suffer from the comparably low spatial resolution of measurements and from boundary effects, caused by e.g. flange rings – especially in the case of capacitance type WMS. In the recent past, diverse studies have been performed on two-phase liquid–gas stratified flow with low liquid loading conditions in horizontal pipes at the University of Tulsa. These tests cover oil–air flow in a 6-inch ID pipe and water–air flow in a 3-inch ID pipe employing dual WMS with 32×32 and 16×16 wires, respectively. For oil–air flow experiments, the superficial liquid and gas velocities vary between 9.2 m/s≤ν_SG≤15 m/s and 0.01 m/s≤ν_SL≤0.02 m/s, respectively [2]. In water–air experiments, the superficial liquid and gas velocities vary between 9.1 m/s≤ν_SG≤33.5 m/s and 0.03 m/s≤ν_SL≤0.2 m/s, respectively [17], [18]. In order to understand the stratified wavy structure of the flow, the reconstruction of the liquid–gas interface is essential. Due to the relatively low spatial resolution in the WMS measurements of approximately 5 mm, the liquid–gas interface recognition has always an unknown uncertainty level. In this work, a novel algorithm for refined liquid–gas interface reconstruction is introduced for flow conditions where entrainment is negligible.     

Electrical resistance tomography coupled with differential pressure measurement to determine phase hold-ups in gas–liquid–solid outer loop bubble column

Radial variation of the gas hold-ups and mean hold-ups are investigated in a 90 mm outer loop bubble column using electrical resistance tomography (ERT) with two axial locations (Plane 1 and Plane 2). In all the experiments, air is used as the gas phase, tap water as liquid phase, and polypropylene particles as solid phase where the superficial gas velocity is varied from 0.02 to 0.25 m/s. The effect of operating conditions, solid concentration on mean hold-ups and radial gas hold-ups distribution is discussed. Gas hold-ups and solid hold-ups results using ERT are in very good agreement with conventional estimation and correlations obtained using pressure transmitter methods. Meanwhile, the results show that the gas hold-ups in the centre region increase constantly with an increase in the superficial gas velocity, namely there is a maximum hold-up at the centre of cross-section. But, solid hold-ups distribution is very homogeneous for high gas velocity. According to the visible image, the gas–liquid flow behaviours are obtained for gas–liquid–solid outer loop bubble column. Furthermore, the results also indicate that ERT is a very powerful tool for diagnosing the ‘inside’ flow behaviour of gas–liquid–solid three phase bubble column.     

Studying local liquid velocity in liquid–solid packed bed using the newly developed X-ray DIR technique

Combination of X-ray Digital Industrial Radiography (DIR) and Particle Tracking Velocimetry (PTV) techniques for local liquid velocity measurement (V_LL) has been newly developed and successfully applied for trickle bed reactor (TBR). The technique was validated against newly developed fiber optical probe technique. This work attempts to highlight the applicability of this newly developed technique on a liquid–solid packed bed reactor. In this work, liquid was represented by water and solids were represented by EPS beads. The EPS beads were chosen because of its low density property. Three superficial liquid velocities (V_SL) were applied to the system. The experiment was replicated four times. The digital industrial radiography (DIR) consists of a complementary metal oxide semiconductor (CMOS) digital detector and X-ray source. Results of this work suggest that the technique has been successfully applied and comparable with previous work that has been done in the literature. It also suggests that there will be a maximum measurable interstitial liquid velocity when it travel inside the packed bed. The measured V_LL can have a maximum range that is between 4 and 4.7 times that of its V_SL. For V_SL=0.42±±2%, the V_LL-Max is in between 1.7 cm/s and 1.9 cm/s, V_SL=0.84±±2%, the V_LL-Max is in between 3.6 cm/s and 4.0 cm/s, and for V_SL=1.11±±2%, the V_LL-Max is in between 4.3 cm/s and 4.8 cm/s.     

Research on signal amplitude of the Kármán vortex street in gas–liquid two-phase flow with high void fraction

Based on Biot–Savart law and single-phase flow Kármán vortex characteristics, flow field has been analyzed when gas–liquid flow past a fixed bluff body with high void fraction. Vortex signal characteristics have been studied for stratified two-phase flow on atmospheric conditions in a horizontal pipe. To discuss the relation between void fraction and vortex signal amplitude spectrum, this paper sets up the vortex-induced pressure field model for gas–liquid two-phase flow and gives the relationship between void fraction and relative amplitude spectrum of two-phase flow to single-phase flow. An algorithm is proposed for predicting the two-phase flow parameters. Experiments were performed using air–water as working fluid along with a test tube diameter of 50 mm, at gas volume flow rate of 20–68 m³/h, and void fraction of 0.9–1. The results indicate that calculations by the vortex-induced pressure field model on the amplitude spectrum of vortex signal are in good agreement with the experimental data, and relative errors of the algorithm predictions on gas volume flow rate and liquid volume flow rate are 0.08 and 0.56, respectively.     

Identification of oil–gas two-phase flow pattern based on SVM and electrical capacitance tomography technique

The correct identification of two-phase flow patterns is the basis for the accurate measurement of other flow parameters in two-phase flow measurement. Electrical capacitance tomography (ECT) is a new visualization measurement technique for two-phase/multi-phase flows. The capacitance measurements obtained from the ECT system contain flow pattern information, and then six feature parameters are extracted. The support vector machine (SVM) has a desirable classification ability with fewer training samples. The inputs of the SVM are extracted feature parameters of different flow patterns. Simulation and static experiments were carried out for typical flow patterns. Results showed that this method is fast in speed and can identify these flow patterns correctly.     

Liquid holdup measurement in horizontal oil–water two-phase flow by using concave capacitance sensor

Due to the complex flow structures of horizontal oil–water flows, the liquid holdup measurement is still a challenging problem. In this paper, we using the finite element analysis build a two-dimensional model of the concave capacitance sensor and investigate the effect of sensor geometry on the distribution of the sensitivity field. Through calculating the sensor static response for different horizontal oil–water flow patterns, we figure out the optimum geometry of the concave capacitance sensor. In addition, we conduct experiment to obtain the measured response of the concave capacitance sensor and achieve the oil-holdup by using quick closing valve. The results indicate that the optimized concave capacitance sensor shows good performance for liquid holdup measurement of horizontal oil–water two-phase flow.     

Air–water two-phase flow measurement using a Venturi meter and an electrical resistance tomography sensor

A method for air–water two-phase flow measurement is proposed using a Venturi meter combined with an Electrical Resistance Tomography (ERT) sensor. Firstly, the real-time flow pattern of the two-phase flow is identified using the ERT sensor. Secondly, the void fraction of the two-phase flow is calculated from the conductance values through a void fraction measurement model, developed using the LS-SVM regression method. Thirdly, the mass quality is determined from the void fraction through void fraction-quality correlation. And finally, the mass flowrate of the two-phase flow is calculated from the mass quality and the differential pressure across the Venturi meter. Experimental results demonstrate that the proposed method is effective for the measurement of the mass flowrate of air–water flow. The proposed method introduces the flow pattern information in the measurement process, which minimizes the influence of flow pattern on the conventional differential pressure based methods. In addition, the mass quality is calculated from the void fraction, so the difficulty to obtain the mass quality in conventional methods is also overcome. Meanwhile, the new method is capable for providing concurrent measurements of multiple parameters of the two-phase flow including void fraction, mass quality and mass flowrate as well as an indication of the flow pattern.     

Precise volume fraction prediction in oil–water–gas multiphase flows by means of gamma-ray attenuation and artificial neural networks using one detector

Artificial neural network (ANN) is an appropriate method used to handle the modeling, prediction and classification problems. In this study, based on nuclear technique in annular multiphase regime using only one detector and a dual energy gamma-ray source, a proposed ANN architecture is used to predict the oil, water and air percentage, precisely. A multi-layer perceptron (MLP) neural network is used to develop the ANN model in MATLAB 7.0.4 software. In this work, number of detectors and ANN input features were reduced to one and two, respectively. The input parameters of ANN are first and second full energy peaks of the detector output signal, and the outputs are oil and water percentage. The obtained results show that the proposed ANN model has achieved good agreement with the simulation data with a negligible error between the estimated and simulated values. Defined MAE% error was obtained less than 1%.     

Note: Non-destructive measurement of thermal effusivity of a solid and liquid using a freestanding serpentine sensor-based 3ω technique

A non-destructive thermal effusivity characterization method described as a freestanding serpentine sensor-based 3ω technique was reported. This freestanding serpentine sensor was fabricated by the mature flexible printed circuit production technique. Expression for the temperature response of the freestanding serpentine sensor with respect to the thermal effusivity of the test sample was presented. The technique was further verified by measuring four kinds of standard samples at room temperature. Experimental results which well agree with reference values demonstrate the new technique is of great application value to thermal effusivity characterization of solids, liquids, and structures to which the conventional 3ω technique is not applicable, e.g., solids with porous surfaces.