Cross-correlation Flowmeter Research Articles

Validation of a mathematical model of ultrasonic cross-correlation flow meters based on industrial experience

In 2020, Ton [1] published an article named “A mathematical model of Ultrasonic Cross-Correlation Flow Meters Based on Industrial Experience” from here on it will be referred as “the model”. The model provided detailed mathematical derivation for the entire process involved in ultrasonic cross-correlation flow measurement (USCCFM). As such, the inputs and output parameters involved in USCCFM are defined, so their relationships are also described. Based on these relationships, the output parameters behavior of the model can be predicted by the input parameters variations. These relationships are exploited to validate the model. The results of this article show the USCCFM output parameters behave exactly as the model predicted in lab and field measurement conditions. Simulated data produced by an emulator further validate the model. Furthermore, the measured time delay error (using emulator) is within 0.1 ms of the set points. This result assures that USCCFM can measure the time it takes the flow to carry the signature from upstream to downstream very accurately.

Comparison of Transverse With Axial Excitation Modes Cross Correlation Flowmeters in High Water-Cut Oil–Water Flow Measurement

Due to long-term exploitation of oil wells, high water-cut oil–water two-phase flow has become one of the most common flow types in offshore oil fields. In this work, two cross correlation flowmeters for this type of flow, i.e., the newly proposed transverse excitation mode flowmeter and the conventional axial excitation mode flowmeter, are theoretically analyzed, numerically solved, and experimentally compared. By building theoretical models, the resolutions and sensitivities of the sensors are systematically compared to demonstrate their abilities to detect oil bubbles in water. From the numerical solutions by the finite-element method (FEM) models, the resolutions of the sensors are analyzed in the spatial frequency domain, and more accurate analysis of sensitivities can be made. Results show that the resolution of the transverse excitation mode flowmeter is approximately three times higher, and the sensitivity is at most 3.47 times higher than the axial excitation mode one. Experiments with 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{{3}}$ </tex-math></inline-formula> /d, 90%-water-cut oil–water two-phase flow are carried out to demonstrate the dynamic performances of the two flowmeters. It can be concluded that the transverse excitation mode flowmeter has higher accuracy and reliability in flow rate measurement.

Numerical study on the effect of circumferential position of ultrasonic transducers on ultrasonic cross-correlation flowmeter performance under asymmetric air flow profile

There are several ultrasonic flowmeter technologies such as transient time, cross-correlation, Doppler and etc. The performance of different types of ultrasonic flowmeters under disturbed flow profile due to elbow at upstream has been well studied recently except the cross-correlation type. The ultrasonic cross-correlation flowmeter (UCCF) has different mechanism of flow measurement in comparison with other types of ultrasonic flowmeters that strongly requires its own studies. In case of disturbed flow profile in pipe, due to asymmetrical velocity profile, the UCCF accuracy and required calibration factor are strongly dependent on the circumferential position of ultrasonic transducers on the pipe. Study on UCCF transducers circumferential position and specifying transducers proper position could incredibly improve the UCCF accuracy. The effect of transducers circumferential position on the accuracy in both single path and multipath has not been investigated for a UCCF so far. In this work, Computational Fluid Dynamics (CFD) simulations were conducted using turbulence model of RSM (Reynolds Stress Model) Stress-ω to simulate the asymmetrical air flow profile inside the elbow and the connected straight pipe in order to study the effect of circumferential position of transducers on calibration factor for special type of ultrasonic flowmeters ,UCCF, at different Reynolds numbers and various locations of flowmeter, for the first time. Moreover, the effects of Reynolds numbers and the flowmeter distances from the elbow on the calibration factor were analyzed. Finally, based on calculated calibration factors at different transducer circumferential positions, the best transducers arrangement at different flowmeter locations were proposed for single and multipath cross-correlation flowmeter. Also, in multipath ultrasonic cross correlation flowmeter, the optimum number of transducers were investigated.

A mathematical model of ultrasonic cross correlation flow meters based on industrial experience

A new model for Ultrasonic Cross Correlation Flow Meters (USCCFM) has been developed as result of industrial experience at Ontario Power Generation (OPG). Industrial applications of USCCFM have encountered cases where the frozen pattern model failed. The new model is based on the mathematical properties of turbulent velocity fields and correlation functions. It contains a proof that USCCFM measurement in a particular situation is successful, if and only if certain mathematical conditions are satisfied. In this document, the term “successful” means that the USCCFM is able to obtain a consistent cross correlation peak, and a stable time delay from the flow condition; otherwise the measurement is considered unsuccessful. This model applies to all measurement conditions encountered so far.

УЛЬТРАЗВУКОВЫЕ МЕТОДЫ И ПРИБОРЫ ДЛЯ ИЗМЕРЕНИЯ РАСХОДА ВОДЫ НА ГИДРОМЕ-ЛИОРАТИВНЫХ СИСТЕМАХ

Purpose: analysis of existing ultrasonic methods and devices for metering water flow in irrigation and drainage systems. The problem of rational use of water resources exists in all areas, including agriculture. It cannot be resolved without considering the issue of water metering and water distribution. The main task of the water accounting system in irrigation and drainage systems is measuring the volume of water taken from the water intake and delovered to the irrigation network. For these purposes, flow meters – devices that measure the flow of water, are used. Ultrasonic (acoustic) flow meters are flow meters capable of solving complex problems in flow measurement. Currently, there are several measurement methods to determine the water flow rate at reclamation facilities: ultrasonic, radar, Doppler method, cross-correlation method and Transit-Time method. Based on these methods, a large number of modifications of devices for determining water flow rates have been created: level gauges, radar flow meters, Doppler flow meters, submersible cross-correlation flow meters, pulse-time flow meters. Conclusions. Flow meters based on level gauges and radar flow meters are impractical to use in commercial water metering units. They have high flow measurement errors, since level gauges measure only the level, and the speed is taken as a constant value, while radar flow meters measure the flow rate, but this is not the speed of the entire flow, but only of the surface layer. The flow rate measured by Doppler and cross-correlation meters depends on the amount of solids in the flow. But since the water in canals and closed pipelines on irrigation and drainage systems has a large number of solids, these flow meters have a high accuracy of flow measurement. Pulse time meters, as well as Doppler and cross-correlation meters, have high measurement accuracy, but do not depend on the amount of solids in the flow.

Methodology for production logging in oil-in-water flows under low flow rate and high water-cut conditions

This study aimed to obtain the production profiles of oil-in-water flow under low flow rate and high water-cut conditions in oil wells. A combination production profile logging composed of an arc-type conductance sensor (ATCS) and a cross-correlation flow meter (CFM) with a center body is proposed and experimentally evaluated. The ATCS is designed for water holdup measurement, whereas the CFM with a center body is proposed to obtain the mixture velocity. Then, a drift-flux model based on flow patterns is established to predict the individual-phase superficial velocity of oil-in-water flows. Results show that the ATCS possesses high resolution in water holdup measurement and that flow pattern information can be deduced from its signal through nonlinear time series analysis. The CFM can enhance the correlation of upstream and downstream signals and simplify the relationship between the cross-correlation velocity and mixture velocity. On the basis of the drift-flux model, individual-phase superficial velocities can be predicted with high accuracy for different flow patterns.

Measurement of Oil-Gas-Water Mixture Velocity Using a Conductance Cross-Correlation Flowmeter With Center Body in Small Pipe

To be able to acquire the mixture velocity of water continuous oil-gas-water three-phase flow in 20-mm inner diameter small pipe based on the cross-correlation method (CCM), accurate measurement of the cross-correlation velocity, and establishing valid relationship between cross-correlation velocity and mixture velocity is of importance. Due to the severe slippage effect and the non-uniform distribution of phases in three-phase flow, the correlation between the upstream and downstream signals is seriously affected, and the relationship between the cross-correlation velocity and the mixture velocity is extremely complicated. Moreover, the low-sampling frequency and noise also reduce the accuracy of cross-correlation velocity measurement. In this paper, a cross-correlation flowmeter (CCFM) with two ring-shape conductance sensors embedded on the center body is proposed. Based on the finite element method (FEM), the geometry of the CCFM is designed and optimized. A novel fast Fourier transform (FFT) interpolation algorithm is investigated to increase the sampling frequency while eliminating the noise. Afterward, the performances of the CCFM and the FFT interpolation algorithm combined with the CCM are experimentally evaluated. The results show that the CCFM can enhance the correlation of upstream and downstream signals while FFT interpolation algorithm can effectively increase the sampling frequency and eliminate the noise, which can improve the accuracy of cross-correlation velocity measurement. The CCFM also can simplify the relationship between the cross-correlation velocity and mixture velocity, and thus the mixture velocity can be satisfactorily predicted.

Flow measurement of oil-in-water flows in vertical low flow rate and high water-cut flow conditions

This paper reports on the flow measurement of oil-in-water flows with low flow rare and high water-cut in vertical 20mm inner diameter pipe. By using arc type conductivity sensor (ATCS) and cross-correlation flow meter (CCFM) based on conductance method, water holdup and mixture velocity are obtained. Afterward, oil-in-water flows drift-flux model is established to predict individual phase superficial velocity. The research results show that ATCS has high resolution on water holdup and CCFM performs well in mixture velocity measurement. Based on drift-flux model, individual phase superficial velocity can be predicted with high accuracy.

Note: A vortex cross-correlation flowmeter with enhanced turndown ratio.

In the present study, a novel dual sensor vortex cross correlation technique is suggested and implemented to extend the lower operating range of the flowmeter. The first sensor located at an optimum streamwise location of 0.85 times the width of the bluff body is employed to compute the vortex shedding frequency under high Reynolds number conditions. Under low Reynolds number conditions, when the strength of the vortex signal is poor, the outputs from the two piezoelectric sensors are correlated to compute the vortex convection velocity. This vortex convection velocity is used to compute the volume flow rate. This novel dual flow rate estimation technique has demonstrated its robustness under low Reynolds number flow conditions with a remarkable turndown ratio of 1:66 as compared to 1:20 for conventional vortex flowmeters.

Flow rate estimation using acoustic field distortions caused by turbulent flows: time-reversal approach

A new acoustic technique for flow rate estimation is proposed here. This technique is based on the traditional ultrasonic cross-correlation flow meter, but instead of using a continuous wave or pulse trains in each transmitter-receiver pair, the acoustic time-reversal technique is applied. The system relies on the principle that a turbulent flow with multiple vortices will cause random distortions in a given acoustic field; hence, analyzing this noise caused in the ultrasound signal by the turbulence over time allows a "signature" or "tag" of the flow to be defined. In other words, the vortices modify the frequency response function of the flowing system uniquely, since the distortion is assumed to be random. The use of the time-reversal procedure in the cross-correlation flow meter provides improvements in several aspects: it simplifies the signal processing needed after the reception of the signals, avoiding the use of a demodulator to obtain the signature of the vortex; the signal is focused at the position of the reception transducer and; the sensitivity is also increased because the wave travels twice in the acoustic channel. The method is theoretically discussed showing its limitations and improvements. Experimental results in a laboratory water tank are also presented.

Analytical model of an ultrasonic cross-correlation flow meter, part 2: Application

An analytical model of an ultrasonic cross-correlation flow meter has been developed to relate the time delay measured by the meter to the mean velocity profile and statistical properties of turbulent pipe flow. In Part 2 of this two-part paper, the cross-correlation and cross-spectrum of the demodulated ultrasonic signal are obtained using the stochastic model of the turbulent velocity fluctuations from Part 1. Calculations of the bulk velocity calibration factor using computational fluid dynamics simulations of fully-developed pipe indicate that the calibration factor has a logarithmic dependence on Reynolds number. In addition, the model was used to investigate the sensitivity of the device to transducer spacing and wall roughness. It was found that increased transducer spacing and increased pipe roughness both decrease the bulk velocity calibration factor.

Analytical model of an ultrasonic cross-correlation flow meter, part 1: Stochastic modeling of turbulence

An analytical model of an ultrasonic cross-correlation flow meter has been developed to relate the time delay measured by the meter to the mean velocity profile and statistical properties of turbulent pipe flow. The model expresses the cross-correlation and cross-spectrum of the demodulated ultrasonic signal in terms of the space–time correlations of the turbulence. In Part 1 of this two-part paper, a stochastic model of the turbulent velocity fluctuations is developed. The model provides closed-form analytical formulas for the turbulence correlation and spectrum functions in terms of parameters which can be obtained from empirical data or computational fluid dynamics.

A water flowmeter using dual fiber Bragg grating sensors and cross-correlation technique

In this paper, a principle and experimental results of a cross-correlation flowmeter using fiber Bragg grating (FBG) sensors are presented. The flowmeter has no electronics and no mechanical parts in its sensing part and the structure is thus simple and immune to electromagnetic interference (EMI). For water flow measurement, the flowmeter uses the time delay of the vortex signal generated by a bluff body. Karman vortex shedding frequency is also detected and utilized for the flow velocity estimation in the system. In order to realize a low noise and wide bandwidth system, we employed interferometric detection as a FBG wavelength-shift detection method. The noise spectral density of the FBG sensor with the interferometric detection was 4×10 −4 pm/(Hz) 1/2 corresponding to 0.33 nε/(Hz) 1/2. A water flow experiment showed that the flowmeter had a linear characteristic at velocity range from 0 to 1.0 m/s and the minimum detectable velocity of 0.05 m/s.

FLOW-RATE MEASUREMENT IN TWO-PHASE FLOW

▪ Abstract Online, continuous, two-phase flow measurement is often necessary, particularly in the oil and gas industry. In this article, we describe some of the commercially most important techniques for gas-liquid, gas-solid, liquid-solid, and liquid-liquid flows, and provide associated illustrative sketches and regime maps. These techniques involve Venturi pressure drop, Coriolis, electromagnetic, and cross-correlation flow meters, gamma-ray absorption and gradio-manometer densitometers, and local electrical and fiber-optic sensors, for which we describe the principles of operation and interpretation. References are given to more comprehensive texts and papers; these are representative rather than exhaustive. It is emphasized that empirical calibration is the norm and that detailed fluid-mechanical analysis has so far played little part in instrument design and operation.

Quantitative analysis of the cross-correlation ultrasonic flow meter by means ofsystem theory

The physical principles of the ultrasound cross-correlation flow meter aredescribed quantitatively by means of an approach based on system analysis. Weextend an earlier theoretical model of Shu (1987 PhD Thesis UniversitätKarlsruhe) by accounting for additional characteristics of the turbulent pipe flowand making use of characteristic turbulence parameters. The velocity obtained bycross-correlation of the phase-modulated ultrasound signals can be predicted withthe theoretical model as a function of the Reynolds number. These theoreticalpredictions agree favourably with experimental results. It is shown that thevelocity determined by cross-correlation is nearly the ‘modal value’ of theturbulent velocity profile and, thereby, higher than the bulk velocity in the pipe.The investigations include studies of the influence of a number of parameters thatcan be varied in a practical set-up. It is shown that a calibration of thesystem, as it is done in practice, is only valid for a specific set of valuesof these parameters and restricted to fully developed flow in the pipe.

Integrating cross-correlation techniques and neural networks for feedwater flow measurement

This paper reports an early progress of a feasibility study of a computational intelligence approach to the enhancement of the accuracy of flow measurements in the framework of an ongoing cooperation between Tecnatom s.a. in Madrid and the OECD Halden Reactor Project (HRP) in Halden. The aim of this research project is to contribute to the development and validation of a flow sensor in a nuclear power plant (NPP). The basic idea is to combine the use of applied computational intelligence approaches (noise analysis, neural networks, fuzzy systems, wavelets etc.) with existing traditional flow measurements, and in particular with cross-correlation flowmeter concepts.

Measurement of the homogeneous velocity of inclined oil-in-waterflows using a resistance cross correlation flow meter

This paper describes an investigation into a cross correlationflow meter, using `global' resistance sensors, for measuring thehomogeneous velocity of inclined oil-in-water flows. The cross correlationflow meter measures the axial propagation speed Ucc of intermittentKelvin-Helmholtz structures in the flow. It is shown that, for inclinationangles in the range 15° to 45° from the vertical, themeasured velocity Ucc is dependent only upon the homogeneous velocityand is independent both of the inclination angle θ of theflow and of the oil volume fraction α. For an angle of inclinationto the vertical of 60°, Ucc is dependent both upon thehomogeneous velocity and upon the oil volume fraction α.For inclination angles in the range 15°⩽θ⩽45°predictions of the homogeneous velocity were obtained using only themeasured cross correlation velocity Ucc. For 15°⩽θ⩽45°, the mean percentage error Ē in the predicted homogeneousvelocity was 0.1% whilst the standard deviation S̄ of thepercentage error in the predicted values of the homogeneous velocity wasfound to be 4.0%. For the angle of inclination to the vertical of60° predictions of the homogeneous velocity were obtained using themeasured cross correlation velocity Ucc and the measured oil volumefraction α. For θ = 60° the mean percentage errorĒ in the predicted homogeneous velocity was -0.39% whilst thestandard deviation S̄ of the percentage error in the predictedvalues of the homogeneous velocity was 5.2%.

A new kinematic wave model for interpreting cross correlation velocitymeasurements in vertically upward, bubbly oil-in-water flows

A new model for the speed of propagation of kinematic waves invertical upward, bubbly oil-in-water flows has been proposed. The newkinematic wave model has been used in conjunction with (i) appropriate valuesfor the `distribution parameter' C0, the single-droplet terminal risevelocity vt0 and an exponent n, obtained from a drift velocity model;(ii) a statistical relationship for the quantity αUh(dC0/dα); and (iii) measurements of a cross correlation velocityUcc and the volume fraction of oil α to make predictions of thesuperficial velocities of the mixture, the oil and the water in verticalupward, bubbly oil-in-water flows. The systematic errors in these predictedvalues of the superficial velocities of the mixture, the oil and the waterwere 0.16, -0.04 and 0.04%, respectively. The kinematic wave model can thusbe used in conjunction with a cross correlation flow meter for accuratemeasurement of flow rates in vertical oil wells. It was inferred from thekinematic wave model and the experimental data that, for low values of thevolume fraction of oil α, the distribution parameter C0 decreasesrapidly with increasing α. At higher values of α the decrease inthe value of C0 with increasing α is less marked. This result isconsistent with the physical explanation that, at low values of α, theoil droplets tend to preferentially accumulate in the relatively fast movingregions of the flow. As α increases the oil droplets become moreuniformly distributed amongst the faster and slower moving regions of theflow.

A clamp-on ultrasonic cross correlation flow meter for one-phase flow

The correlation technique presented offers a good possibility for measuring the average rate of flow of fluids through pipes. The only physical parameter required for the measurement principle is the well known distance between the sensors. The new system presented consists of ultrasonic sensors, transforming the natural, stochastic fluctuations of velocity, pressure and density into two signals with a delay time T, and a real-time correlator, extracting the delay time from the signals and calculating the average rate of flow of the fluid. In contrast to established flow measuring methods, no bluff bodies are necessary and electrical conductivity of the fluid is not required. In contrast to time-of-flight flow meters, a small amount of air bubbles or particles causes no signal losses and does not interrupt the measurement process. In this paper a detailed theoretical signal model describing the interaction of sound waves in random continuum and turbulent media will be presented. With this model the phase modulation of the ultrasonic waves and systematic errors can be described and some design parameters can be optimized. Measurements have been carried out with 40 and 50 mm pipe diameters for direct fluid contact and clamp-on transducers. The measurement error of the new flow meter has been found to be less than 2% from the reference value for a Reynolds number range 25 000-250 000 and, even down to a Reynolds number of 4000, it has been found to be less than 3%.

Flow rate measurement by kinematic wave detection in vertically upward, bubbly two-phase flows

This paper describes a technique for measuring the flow rates of both phases in one-dimensional, vertically upward, bubbly oil–water flows. Measurements of the speed of naturally occurring kinematic waves, obtained using an impedance cross-correlation flow meter, were combined with measurements of the disperse phase volume fraction and an appropriate kinematic wave model to yield predictions of the flux density of both the oil and the water. A systematic error of −3.16%, and an additional random error with a standard deviation of 2.58%, was observed in the predicted oil flux density (and the predicted oil volumetric flow rate). A systematic error of +4.41%, and an additional random error with a standard deviation of 4.83%, was observed in the predicted water flux density (and the predicted water volumetric flow rate). The impedance cross-correlation flow meter has no moving parts and is of robust construction, making the technique described here suitable for implementation in vertical oil wells.