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.     

Volume fraction measurement and flow regime recognition in dynamic gas–liquid two phase flow using gamma ray radiation technique

Gas–liquid two phase f low is probably the most important form of multiphase f lows and is found widely in industrial applications, particularly in the oil and petrochemical industry. In this study, in the first instance a gas–liquid two phase f low test loop with both vertical and horizontal test tube was designed and constructed. Different volume fractions and f low regimes were generated using this test loop. The measuring system consists of a ¹³⁷Cs single energy source which emits photons with 662 keV energy and two 1-inch NaI (Tl) scintillation detectors for recording the scattered and transmitted counts. The registered counts in the scattering detector were applied to the Multi-Layer Perceptron neural network as inputs. The output of the network was gas volume fraction which was predicted with the Mean Relative Error percentage of less than 0.9660%. Finally, the predicted volume fraction via neural network and the total count in transmission detector were chosen as inputs for another neural network with f low regime type as output. The f low regimes were identified with mean relative error percentage of less than 7.5%.     

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.     

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.     

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.     

Electric conductance method for the assessment of liquid–gas injection into a large gas–solid fluidized bed

Liquid injections are applied widely in fluidized bed reactors such as Fluid Cokers, fluid catalytic crackers and polymerization reactors. In such industrial processes, it is necessary to optimize the contact between the injected liquid and the bed solids as it has a significant effect on product yields and quality, and reactor operability.     

Numerical simulation of bubble separation length in a gas–liquid separator based on the Euler–Lagrange method

In this study, the bubble separation behavior in a gas–liquid separator is numerically investigated on the basis of the Euler–Lagrange approach, in which the forces acting on bubbles in a swirling flow field are modeled to calculate the trajectories of the bubbles. By adopting this approach, the effects of five parameters, namely, back pressure, Reynolds number, bubble diameter, void fraction, and swirl number, on separation performance in terms of pressure loss, separation efficiency, separation length, and split ratio are computed and analyzed. On the basis of the analysis, correlations of separation length with the two main parameters are established, which can serve as a basis for the optimal design of separator.     

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.     

Imaging of gas–liquid annular flows for underbalanced drilling using electrical resistance tomography

The underbalanced drilling technique, which is also known as managed-pressure drilling, is playing an important role in oil and gas sector, as it reduces common conventional drilling problems such as minimal drilling rates and formation damage, differential sticking and lost circulation. Flow regime monitoring is one of the key topics in annular multiphase flow research, particularly for underbalanced drilling technique. Prediction of the prevailing flow regime in an annulus is of particular importance in the design and installation of underbalanced drilling facilities. Especially, for establishing a suitable pressure-drop model based on the characteristics of the active flow regime. The methods of flow regime prediction (or visualisation) in an annulus that are currently in use are very limited, this is evidently due to poor accuracy or they are simply not applicable to underbalanced drilling operation in practice. Therefore, this paper presents a monitoring method, in which Electrical Resistance Tomography (ERT) is used to rapidly image the prevailing flow regime in an annulus with a metallic inner pipe. Experiments were carried out using an air–water flow loop with a test section 50 mm diameter flow pipe. The two-phase air–water flow regimes are visualised in the upward vertical annulus with a radius ratio (r/R) 0.4. This paper highlights the visualisation results of only three flow regimes, namely bubble flow, transitional bubble-slug flow and slug flow. The flow regimes are visualised through axial images stacked from 50 mm diameter-pixels of 2D tomograms reconstructed with the Conjugate Gradient Method (SCG). Gas volume fraction profiles within the annular flow channel are also illustrated. The profiles are extracted using the Modified Sensitivity coefficient Back-Projection (MSBP) method with a sensitivity matrix generated from a realstic phantom in the finite element method software. The results are compared with visual observations (e.g. photographs) of the active flow regime at the time of ERT measurements.     

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.     

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.     

Evaluation of hot-film,dual optical and Pitot tube probes for liquid–liquid two-phase flow measurements

An experimental study of kerosene–water upward two-phase flow in a vertical pipe was carried out using hot-film, dual optical and Pitot tube probes to measure the water, kerosene drops and mixture velocities. Experiments were conducted in a vertical pipe of 77.8 mm inner diameter at 4.2 m from the inlet (L/D=54). The tests were carried out for constant superficial water velocities of 0.29, 0.59 and 0.77 m/s (flow rates = 83, 167 and 220 l/min) and volume fractions of 4.2%, 9.2%, 18.6% and 28.2%. The Fluent 6.3.26 was used to model the single and two-phase flow and to reproduce the results for the experimental study. Two methods were used to evaluate the accuracy of the probes for the measurement of the velocities of water, drops and mixture for two-phase flow: (i) comparison of measured local velocities with predictions from the CFD simulation; (ii) comparison between the area-averaged velocities calculated from the integration of the local measurements of water, drops and mixture velocities and velocities calculated from flow meters’ measurements.The results for single phase flow measured using Pitot tube and hot-film probe agree well with CFD predictions. In the case of two-phase flow, the water and drops velocities were measured by hot-film and dual optical probes respectively. The latter was also used to measure the volume fraction. These three measured parameters were used to calculate the mixture velocity. The Pitot tube was also used to measure the mixture velocity by applying the same principle used for single phase flow velocity. Overall the mixture local velocity measured by Pitot tube and that calculated from hot-film and dual optical probe measurements agreed well with Fluent predictions. The discrepancy between the mixture area-averaged velocity and velocity calculated from flow meters was less than 10% except for one test case. It is concluded that the combined hot-film and optical approach can be used for water and drop velocity measurements with good accuracy for the flow conditions considered in this study. The Pitot tube can also be used for the measurement of mixture velocities for conditions of mixture velocities greater than 0.4 m/s. The small discrepancy between the predictions and experimental data from the present study and literature demonstrated that both instrumentation and CFD simulations have the potential for two-phase flow investigation and industrial applications.     

On-line measurement of the size distribution of particles in a gas–solid two-phase flow through acoustic sensing and advanced signal analysis

Acoustic emission (AE) technology is a promising approach to non-intrusively measure the size distribution of particles in a pneumatic suspension. This paper presents an experimental study of the AE sensing technology coupled with signal processing algorithms for on-line particle sizing. The frequency characteristics of the AE signals under different experimental conditions are studied and compared. Initially, the characteristics of the background noise and AE signals are compared in the frequency domain for different air velocities and particle feeding rates. Through short-term energy analysis the working features of the suction unit and the vibration feeder are revealed. To find the effective characteristic frequency band of the AE signals, a multiple scanning and accumulation method assisted with a Savitzky–Golay smoothing filter is used to denoise the power spectra of the signals. Wavelet analysis is also deployed to denoise the signals. The denoising performance of different wavelet parameters (wavelet function, decomposition level and thresholding) is compared in terms of signal-to-noise ratio and signal smoothness. Finally, particle size is predicted through a neural network with energy fraction extracted through wavelet analysis. Experimental results demonstrate that the relative error of the particle sizing system is no greater than 23%.     

Flow noise characterization of gas–liquid two-phase flow based on acoustic emission

Flow noise of gas–liquid two-phase flow in horizontal pipeline was detected by using the acoustic emission technique (AE); signals were processed by wavelet transform and chaotic analysis. Conclusions were drawn that stratified flow, annular flow and their transition can be divided clearly through multi-scale energy distribution of flow noise, and that dynamic characteristic of flow pattern transition from stratified flow to annular flow, which is described via correlation dimension, acts in accordance with that of annular flow. The dynamic characteristic of the transition condition has already been consistent with that of the annular flow, but due to the low gas flow rate, the energy of the hydrodynamic noise was not enough to reach the complete annular flow pattern. Results were in accordance with experimental facts. Flow noise reflects the complexity of gas–liquid two-phase flow by means of multi-scale energy distribution and chaotic features. Consequently, flow noise based on acoustic emission is a novel and promising point for researching gas–liquid two-phase flow.     

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.     

Design of a Conductance and Capacitance Combination Sensor for water holdup measurement in oil–water two-phase flow

Oil–water two-phase flow widely exists in the process of petroleum industry. The liquid holdup measurement in horizontal pipeline is very important and difficult. In this work, a Conductance and Capacitance Combination Sensor (CCCS) system with four conductance rings and two concave capacitance plates is designed and validated for its measurement performance of in situ water holdup through dynamic experiments. A set of fast electronic switches controls the conductance rings and the capacitance plates alternatively set up each own sensing field in the same sensing volume. This configuration ensures the water holdup estimation in the range from 0% to 100% regardless of flow direction. A set of quick closing valves was used to acquire the in situ holdup for the on-line calibration of the CCCS system. The theoretical correlations of conductance sensor and capacitance sensor were established to make the real-time measurement convenient. A real-time measurement method by CCCS system is provided based on the fusion of the conductance and the capacitance measurement without flow pattern recognition. This method delivers an average error of 1.06% for the CCCS system measuring the water holdup of oil–water two-phase flow, with a standard deviation of 0.038 and a relative error less than ±5%.     

A new mathematical model for predicting the diameter expansion of flat ring in radial–axial ring rolling

An accurate prediction for the diameter expansion is quite essential for the ring rolling with large diameter since it determines the compatibility between the work rolls and the deformed ring in kinematics, so that the rolling stability and the final forming quality of the ring are influenced. A new mathematical model for predicting the diameter expansion of the flat ring in the radial–axial rolling process has been proposed, in which the variation of cross section, the particularity of initial rolling phase, and the effect of slip are all taken into consideration. Based on the proposed mathematical model, a 3D-FEM model for the radial–axial ring rolling process has been developed, and the corresponding experimentation has also been carried out. The diameter expansion in the simulation shows a good agreement with that in the experimentation. The forming quality comparison concerning the circularity, coaxiality, and tilting of the rolled ring has been executed between the former and new proposed method. The result indicates that the new mathematical method is very helpful to control the forming stability and hence improve the ring rolling quality significantly.     

A signal interpolation method for Fabry–Perot interferometer utilized in mechanical vibration measurement

In this investigation, a self-developed signal processing method for Fabry–Perot interferometer is proposed which can be utilized for high-speed dynamic displacement measurements, e.g. mechanical vibration measurements. The lookup table (LUT) integrated with the interference intensity equation has been employed for the interpolation processing of interference signals. With the aid of this method, the interpolation error has been reduced by 40% in comparison with that resulting from the commercial sinusoidal signal processing module. By operations of Fast Fourier Transform (FFT), the displacement measurement distribution can be converted into the frequency spectrum diagram. The interpolation resolution of the proposed interferometric displacement measurement system is about 0.1 nm. Experimental results demonstrate that this interferometer system is available for measuring frequencies till 2 kHz where its corresponding amplitude is 0.15 μm.     

Experimental validation of the calculation of phase holdup for an oil–water two-phase vertical flow based on the measurement of pressure drops

The performance of metering the phase holdup of an oil–water two-phase vertical flow has been investigated based on the measurement of the gravity and frictional pressure drops. A U-tube, in which the same flow patterns can be obtained in downward and upward vertical flows, is designed to measure both gravity and fractional pressure drops. During the experiments, the mixture velocities of the oil and water are in the range of 0.28–4.65 m/s and the oil volume fraction from 0 to 1.0. The results show that the oil holdups calculated are satisfactory with the absolute error of ±10%. The method presented in this work can be used to verify the results of tomography due to its simplicity and therefore is sufficient enough to be applied in industry.