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In view of the fact that Coriolis mass flowmeter is sensitive to noise and has poor anti-jamming ability, this paper applies an improved wavelet threshold signal processing method to overcome this problem. This method can be changed with the number of decomposed layers, as it is shown flexibility in practice situation. In this paper, Signal Noise Ratio and Mean Square Error are used as the parameters to evaluate the denoising performance. The simulation results show that the improved wavelet threshold signal processing algorithm can better reduce the influence of noise and improve the quality of output signal compared with the traditional wavelet threshold processing algorithm. It lays a foundation for the accurate measurement of Coriolis mass flowmeter.

The estimation accuracy of phase difference of Coriolis mass flowmeter signal directly impacts the measurement accuracy. In order to improve the measurement accuracy of Coriolis mass flowmeter, a real-to-complex conversion phase difference estimation method is proposed. The precise phase difference is obtained by means of frequency estimation, initial phase estimation and an iterative interpolation procedure. The results of numerical testing indicate that the proposed method can suppress the influence of negative frequency component, and can improve overall estimation accuracy of phase difference. Especially, when the signal frequency is low, and the SNR is medium or high, the estimation advantage of the proposed method is more obvious. In addition, the experimental results indicate that the proposed method can improve the measurement accuracy of Coriolis mass flowmeter, which verified the effectiveness of the proposed method.

В связи с разработкой методики измерения параметров потоков «жидкость-газ» кориолисовыми массовыми расходомерами (КМР) предпринята попытка оценить влияние присутствия пузырьков газа на параметры колебаний измерительной трубки КМР. Разработана балочная конечноэлементная модель прямой трубки, реализованная средствами пакета MATLAB. Поток флюида описывается в ID-приближении, присутствие газового пузырька моделируется локальным (с точностью до размера конечного элемента) изменением плотности потока в месте расположения пузырька в данный момент времени. Возбуждение поперечных колебаний трубки осуществляется с помощью внешней гармонической силы, приложенной в центре трубки. Частота возбуждения задается равной частоте собственных колебаний заполненной трубки с пузырьком. Выполнена серия численных экспериментов, в которых варьировались объемная доля газовой фазы и скорость флюида. Выявлена зависимость от этих факторов обусловленного эффектом Кориолиса фазового сдвига между колебаниями плеч расходомера. Оценена погрешность определения массового расхода, обусловленная присутствием пузырьков. Проведена серия экспериментов по наблюдению пузырьковых эффектов с промышленным расходомером ДУ15. Найдено качественное согласие результатов расчетов и экспериментов. In developing a methodology for measuring the mass flow rates of liquid-gas flows by Coriolis mass flowmeters (CMF), an attempt is made to estimate the effect of the presence of gas bubbles on the observed parameters of the vibrations of the CMF measuring tube. The finite-element model CMF with a straight tube, created in MATLAB package, is presented. The fluid flow is described in the 1D- approximation, the presence of a gas bubble is modeled by a local change in the flux density at the bubble location at a given time (the size of the bubble depends on the size of the finite element). Bending vibrations of the tube are carried out by means of an external harmonic force applied at the center of the tube. The drive frequency is set equal to the modal frequency of the filled tube. A series of numerical experiments has been performed, in which the gas volume fraction (GVF) and the fluid velocity varied. Испытания проведены с использованием оборудования ЦКП «Экспериментальная механика» ЮУрГУ. Работа выполнена при финансовой поддержке Минобрнауки России (грант № 9.9676.2017/8.9). И.А. Лех, П.А. Тараненко, В.П. Бескачко Южно-Уральский государственный университет, г. Челябинск, Российская Федерация E-mail: taranenkopa@susu.ru I.A. Lekh, P.A. Taranenko, V.P. Beskachko South Ural State University, Chelyabinsk, Russian Federation E-mail: taranenkopa@susu.ru

In this paper, the normalized least mean square (NLMS) algorithm, a time-varying signal processing method, is employed in a Coriolis mass flowmeter (CFM) to improve its weak anti-jamming capability. Initially, the fundamental principles of the NLMS algorithm adopted in the adaptive filter are analysed. Then, the NLMS algorithm is applied to analyse the signal processing of the CFM at different flow rates in experiments. By comparing several performance indicators and spectrum diagrams from being filtered by the NLMS algorithm and the least mean square (LMS) algorithm, the results indicate that the NLMS algorithm can lead to a better anti-jamming capability and reduce the influence of noise efficiently for the CFM. In addition, the NLMS method has a faster convergence speed and fewer stable errors than the LMS method. Therefore, the NLMS can improve the quality of the output signal of the CFM.

Coriolis mass flowmeters are used for many applications, including as transfer standards for proficiency testing and liquified natural gas (LNG) custody transfer. We developed a model to explain the temperature dependence of a Coriolis meter down to cryogenic temperatures. As a first step, we tested our model over the narrow temperature range of 285 K to 318 K in this work. The temperature dependence predicted by the model agrees with experimental data within ± 0.08 %; the model uncertainty is 0.16 % (95 % confidence level) over the temperature range of this work. Here, basic concepts of Coriolis flowmeters will be presented, and correction coefficients will be proposed that are valid down to 5 K based on literature values of material properties.

Certain nonlinear influences are found in dual-tube Coriolis mass flowmeters (CMFs). According to experimentation, a nonlinearity dominated by frequency-doubling signals can be observed in the measuring signal. In general, such nonlinear effects are simplified as linear systems or neglected through processing. In this paper, a simplified model has been constructed for dual-beam CMFs based on the theory of nonlinear dynamics, with the spring–damper system as the medium for the dual-beam coupled vibrations. Next, the dynamics differential equation of the coupled vibrations is set up on the basis of the Lagrangian equation. Furthermore, numerical solutions are obtained using the Runge–Kutta fourth-order method. The study then fits discrete points of the numerical solutions, which are converted into the frequency domain to observe the existence of frequency-doubling signal components. Our findings show that frequency-doubling components exist in the spectrogram, proving that these nonlinear influences are a result of the motions of coupled vibrations. In this study, non-linear frequency-doubling signal sources are qualitatively analyzed to formulate a theoretical basis for CMFs design.

Coriolis mass flowmeter (CMF) is widely used in the industrial field. In mass flow measurement, there are many impurities in measured fluids that will adhere to the inner wall of the vibrating tube of CMF. The vibration characteristics of CMF would change due to the structural change, i.e., wall clung state, which will generate the wall clung state fault. In this paper, aiming at the wall clung state fault of CMF, the finite element model of CMF is established based on ANSYS. The velocity distribution of fluid in the vibrating tube of CMF is analyzed, considering the fluid–structure interaction. The location of the wall clung state in a vibrating tube is determined. Then, the fault model is established. The mechanism of the vibration transmission characteristics outwards of CMF caused by the wall clung state is analyzed by harmonic response analysis. Finally, the failure mode of CMF is investigated.

Trials have taken place to determine the response of a prototype Coriolis mass flowmeter to step changes in flow rate. The meter typically exhibits a delay of 16 ms, and tracks step changes well. Comparison with previously published results suggests that this performance represents an improvement over several types of current commercial flowmeters. The effect of a correction technique to reduce noise is demonstrated. This is considered valuable, even though it is responsible for 6 ms of the overall delay. A good dynamic response is important in process industry applications with short batch times. © 2003 Elsevier Science Ltd. All rights reserved.

This paper investigates spectrum leakage influence on the performance of discrete Fourier transform (DFT) based phase difference measurement and proposes a novel method with spectrum leakage considered. In the proposed method, spectrum is firstly corrected by interpolation algorithm to remove the influence of short range leakage. To avoid negative frequency interference caused by the long range leakage, real-time phase difference is calculated in succession by a recursive DFT based algorithm with negative frequency contribution. And then, precision of the proposed method is theoretically demonstrated in detail. Furthermore, the method is applied to Coriolis mass flowmeter (CMF). Simulation and experimental results show that the accuracy of phase difference measurement has largely improved, as compared with the existing method based on the sliding Goertzel algorithm.

In this paper, an online measurement method of oil discharge ratio (ODR) is experimentally investigated based on a compressor calorimeter with the Coriolis mass flowmeter (CMF). In this method, the oil concentration is determined by a linear mixing law of the specific volume model using the density of the refrigerant, oil and refrigerant-oil mixture obtained by CMF. During the testing, the light absorption method is also conducted simultaneously for the comparison. The results indicate that the presented CMF based density method has an average relative deviation of 4.28%. The accuracy of the CMF based density method is superior to the light absorption method, which has the relative deviation of −8∼23% compared with the standard sampling method. The presented CMF-based method can be expected to be used for future ODR measurement due to its non-sampling, online, and accurate features.

Coriolis mass flowmeter instrumental and dynamic errors are studied. They can be decreased by the thermocouple usage of R or S types instead of Pt100 sensors. The dynamic error analysis shows that it is able to improve the operation accuracy in the dynamic regime and eliminate the initial period of the flowmeter exploitation in the error compensation absence regime. In consequence of the instrumental error consideration the expediency of the differential thermocouples installation with the reduced performance dispersion, lowered by taking into account of local and extensive inhomogeneities as result of technological deviations of wire production.

As a resonate sensor, Coriolis Mass Flowmeter (CMF) provides a direct measurement of mass flow and is widely used in flow measurement field. However, defect of dynamic characteristics has become the main factor which restricts its further application in batch filling processes. Based on theoretical analysis, a dynamic compensation system, BP (Back-Propagation) neural network dynamic compensation method is designed in order to solve this problem. Adding a neural network dynamic compensation segment after the sensor’s output, the method uses the gradient descent method with an additional momentum factor for neural network training. Studies have shown that this method greatly improves the dynamic characteristics of the Coriolis mass flowmeter.

Accurate detection of zero point is significant for improving working performance and measurement accuracy of Coriolis Mass Flowmeter. In this paper, wavelet transform technology is adopted to form the pre-filter to suppress noise jamming, to get sensor’s zero point precisely in working condition. Implementation scheme of software and hardware is given, correlative simulation and field experiment are carried out to verify the feasibility of the method.

A simple analytical method is introduced to calculate the sensitivity of Coriolis mass flowmeter (CMF). The definition of the sensitivity is further developed based on the reciprocity principle, through employing two approaches: selecting the moment when the displacement of drive point is zero as the calculation moment; reducing the degree of high-order static indeterminacy by taking a half of the structure due to symmetry in structure and anti-symmetry in load. With these approaches, the method can be used to calculate sensitivities for the flowmeters with any shaped tubes and anywhere detected positions; thus, provides theory basis for tube shape design and detected positions determination. Detail analytical calculations for typical Straight-Circle-joint-shaped CMFs are illustrated. The method is validated on a published U-CMF and then, is further illustrated and experimentally validated through predicting the most sensitive detected point for a narrowed-U-CMF.

Bulk metallic glasses (BMGs) have potential applications for both structural and functional components owing to their good mechanical properties. With the aim of demonstrating great engineering value of BMGs, we have developed a direct melt-forming technique based on suction casting for the production of glassy alloy tubes. We have examined the fabrication, structure, geometry, properties and sensor performance of the tubes. We have observed that the Coriolis mass flowmeters using the Ti-based glassy alloy sensor tube exhibit excellent measurement sensitivity compared to the conventional flowmeter manufactured using stainless steel (SUS316) tube.

Massedurchfluss-Messgeräte nach dem Coriolisprinzip haben sich schon seit langem als präzise und robuste Feldgeräte bewährt. Diese Geräte lieferten schon bisher Prozessinformationen über Durchfluss, Dichte und Temperatur. Nun ist es gelungen, auch noch den wichtigen Prozessparameter Viskosität gleichzeitig und unabhängig zu erfassen. Damit steht ein wirklich „multivariables“ Prozessmessgerät zur Verfügung.

In this thesis a design of a Coriolis mass flow-meter is chosen by considering all advantages and disadvantages and the project requirements. The chosen geometry is imported into COMSOL, because modelling is implemented by FEM and two different physics should be coupled. To consider both applications of the device include measuring density and flow rate, modeling is divided into two parts: Coriolis density meter and Coriolis mass flow-meter. Both applications are based on Fluid Structure Interaction. The results are compared to existing setup’s experimental data. Keywords: Coriolis mass flowmeter, Fluid Structure Interaction, Modal order, FEM, Acoustic Shell Interaction, Phase-shift, Disposable and Polymer. +46-737260449

Modeling and simulation of coriolis mass flowmeter (CMF) is necessary to explore the dynamic characteristics. The knowledge of dynamic characteristics of CMF is useful for insvestigating the CMF performance on pulsation of fluctuation flow phenomena. Some researchers have studied the dynamic characteristic of CMF in very diverse level of complexity. In this work, a model of CMF for arcuate type was developed by some simple mechanical laws and some assumptions. We simulated and analyzed the CMF response for some typical fluctuation flow, based on the CMF parameters. We found that the steady state gain and dynamic response of CMF were depends on the CMF parameter such as radius of arcuate and diameter of tube.

This paper presents some tests which have been carried out on a commercial model of Coriolis mass flowmeter under medium-pressure conditions ( p > 15 bar), utilizing a primary standard flow calibration facility. The experimental results show that the fluid pressure affects the accuracy of the tested meter, which provides underestimated readings (i.e. negative errors). Finally, some diagrams which allow to correct the output signal (or the reading) provided by the tested meter (according to the operating fluid pressure) are also presented.

Inter-laboratory comparison testing is fundamental to assuring the accuracy of a laboratory’s stated measurement uncertainty, and a requirement for accreditation to ISO/IEC 17025:2005. Inter-laboratory comparisons using Emerson’s Micro Motion® ELITE® Coriolis mass flowmeters support the claimed mass flow uncertainties of 0.014% (k=2k=2) for the high-accuracy liquid mass flow calibration facilities, and 0.03% (k=2k=2) for the production and service mass flow calibration facilities. This paper describes multiple calibration methodologies, international traceability to National Metrology Institutes, test results and future design requirements of an inter-laboratory test program required to support multiple, accredited flow calibration centers around the globe.

CMFs are gaining a good reputation in the metering of liquid. However, because of some undesirable influences of the process parameters and fluid properties of the meter characteristics, it is recommended that the instrument be calibrated in situ when high accuracy must be achieved and/or the metering conditions (process parameters and fluid properties) differ noticeably from the calibration conditions. Field calibration is not always technically feasible and/or economically desirable. Therefore it is important to be able to predict the behaviour of the instrument. Taking the example of gas measurement, it is shown that straight pipe CMFs fulfil this requirement.

This paper reviews the generally accepted guidelines covering the application and use of vortex shedding, magnetic and Coriolis mass flowmeters. General rules governing installation of each device is included as well as tips in trouble shooting installations where optimum meter performance has not been achieved. The information contained in this paper is generic to each technology and not based upon a particular design, but on the experience of the authors.

Builds a cantilever beam model with concentrated added mass on its end, analyses the relation between concentrated mass and vibration frequency of the cantilever beam. Assuming the mass flowmeter with mixed fluid in its flow tube, obtains the relation of measured density value and concentrated mass distribution. The simulation and experiment has proved the validity of the analysis. The paper lays the foundation of improving the non-uniform mixed liquid density measurement accuracy.

Coriolis Mass Flowmeter(CMF) provides direct measurement of mass flow and is widely used in steady flow measurement. With the development of dynamic flow measurement technology and the increasing of application requirement, the question about dynamic response of CMF has become a hotspot. Recently a lot of research work has been done on this issue and a few papers have been yielded. This paper provides a summary and analyses of the dynamic research method of CMF in latest research work. Furthermore, we proposes a new concise way of specifying and improving the dynamic performance of CMF, discusses the feasibility of this method on the basis of existing investigation and describes the emphases of the future development work.

Established wet gas metering techniques are typically based on differential pressure devices, and their measurement accuracy is still unsatisfactory to natural gas industry. Coriolis mass flowmeter (CMF) is the most superior flow measurement technology at now, it can provide mass flowrate and density output simultaneously. Putting CMF into wet gas metering may be a reasonable and high accuracy solution to natural gas industry demands. The problems and advantages of CMF in gas-liquid two-phase flow metering has been analyzed, a serious experiments has been carried out to test the possibility and feasibility of CMF as wet gas meter. Experimental conclusions are promising，CMF can work properly in wet gas metering condition, and the repeatability test of CMF is perfect, and the relationship between the true mass flowrate and CMF readings are almost linear. When gas flowrate is kept to a constant, CMF can follow the variations of liquid flowrate accurately. At last, some open problems deserving further investigation are propose

Resonant Coriolis mass flowmeter (CMF) measures liquid mass flux via the Coriolis theory of the measurement tubes resonant vibration. So vibration disturbance impacts CMFs, especially the vibration at the meter drive frequency. This paper deduces the spatial finite element model of CMFs, then models double U-tube CMFs using ANSYS MATRIX27 elements; analyzes CMFs’ response subjected to the vibration at the drive frequency. The result shows there are some laws between the error of CMFs and the vibration. This paper is instructive to eliminate the impact of vibration on the CMFs and improve the accuracy of CMFs.

Normall, it is very difficult to measurement oil volume fraction under low oil volume fraction in multi phase flow measurement, in this study, Slip property of oil-water two phase flow in horizontal pipe under low oil volume fraction was investigated though a Coriolis Mass Flowmeter, the difference of water cut and water hold up was analyzed with experiment under the same liquid flow rate, and the same water cut with different oil water speed, the results will offer valuable reference to oil content measurement.

The single straight-tube Coriolis mass flowmeter is modelled using the theory of vibrating beams, taking into account the effects of the added masses of the electromagnetic drive and detectors. Many experiments are conducted to assess the performance of an experimental flowmeter. Additionally, the influences of fluid temperature and external vibrations on the sensitivity of the flowmeter are identified.

Motivated by the high industrial and metrological interest of Coriolis Mass Flowmeters (CMFs), and by the limitations of the existing CMFs, the authors have started a study of prototypes of new-concept CMFs, not subject to elastic deformation. The prototype described here belongs to a second type of sensor realised at the University of Naples, and it is called DIME-2 in order to distinguish it from the first type DIME-1 sensor. After the mathematical model, reported in a previous work, in this paper the experimental characterisation of the DIME-2 is presented and discussed.

In this paper a second prototype of a Coriolis mass flowmeter (DIME-2) is described. Its sensor is a straight rigid pipe, provided with elastic suspension, and connected with the line by means of suitable metal bellows. The new prototype (DIME-2) optimises the structural and fluid-dynamic criteria adopted in the first prototype (DIME-1). The present work gives an account of the mathematical model on which the DIME-2 prototype is based.

The precision of frequency tracking method and phase difference calculation method affects the measurement precision of Coriolis Mass Flowmeter directly. To improve the accuracy of the mass flowrate, a novel signal processing method for Coriolis Mass Flowmeter is proposed for this time varying signal, which is comprised of a modified adaptive lattice notch filter and a revised sliding recursive discrete-time Fourier transform algorithm. The method cannot only track the change of frequency continuously, but also ensure the calculation accuracy when measuring phase difference. The computational load of the proposed method is small with higher accuracy. Simulation and experiment results show that the proposed method is effective.

Field test results of a Coriolis mass flowmeter are presented for a crude oil gathering facility located in a mature part of the Ghawar field in Saudi Arabia. Due to the maturity of the field, conventional well test measurements under low flow rate and high water cut conditions suffered from inaccuracies and gave erroneous and sometimes incorrect readings; consequently there was a need to find a replacement mode of measurement. This paper highlights advantages mass flowmeter technology has to offer under such difficult conditions. The Coriolis technology has been around for several years but its performance has not been adequately documented in oilfield applications and only recently has become economically viable and user-friendly as a result of the manufacturer's efforts to expand their application base. In the past, 3-phase testing was necessary due to inability of conventional sensors to accurately measure flow at low and high water cut ranges. The instrumentation was expensive to maintain and large quantity of chemicals were required to achieve proper separation. Moreover, error was introduced due to an additional water rate measurement that was necessary to quantify the total water production. This field test covered a very wide range of flow rates and water cuts and gave an insight into the improvements this technology has to offer. The test results established the accuracy and repeatability of this measurement. This technology has therefore been adopted as the primary measurement for all well testing in Central Ghawar where the water cut ranges are extreme. The field test also concluded that 3-phase testing was no longer necessary, which resulted in significant saving in maintenance and chemical costs.

The effects of flow disturbances on the performance of the Coriolis mass flowmeter(CMF) with two straight parallel tubes were invetigated numerically. Two types of flow disturbances were studied numerically using the bond-graph presentation. The first one represents a local restriction in one of the pipes that causes asymmeric flow in pipes. In the second case of operating conditions, uniformly obliterated tubes were considered. The effect of the obliterated layer thickness with different densities was analysed. It was found that the local restriction at the tube entrance does not effect the sensitivity coefficient, while the flowrate in the tube changes from zero to a rate equal to that in the parallel tube. The obliteration does not effect the sensitivity coefficient either, but changes the first natural mode of tube vibration. If the CMF is used for density measurement, the obliteration may cause significant error.

The sensor of the Coriolis mass flowmeter, consisting of the two elastic, straight and parallel tubes, is presented by a system of partial differential equations. The tubes are divided into the final elements and presented in the form of bond graphs. The equations of motion are discretized and solved numerically. The effects of different densities (500, 1000 and 3000 kg/m3) have been studied in the velocity range from 0 to 15 m/s. It was found that above some mass flow rate the sensor linearity increases. The positions of the motion sensors effect more the sensitivity coefficient then the linearity. The length of the vibrating tubes effects the natural frequency and the sensitivity coefficient. If the natural frequency is used to determine the fluid density accurately it is necessary to introduce the correction for fluid velocity. The fluid velocity effects the natural frequency too. The modelling results were compared with the experimental data for the commercially available meter.

This paper describes the principle of operation of the Coriolis mass flowmeter (CMF). The principle of operation is explained by means of the rotating tube after which the vibrating tube is introduced. The advantages of mass measurement over volume measurement are discussed. The most important characteristics of the CMF from different manufactures are presented. The application of the CMF in the petroleum and natural gas industry is considered and how to cope with the eventual problems is shown. Local and international recommendations and standards relevant to the CMF are cited.

The Coriolis mass flowmeter (CMF) has been increasingly used over the last two decades for liquid and gas mass flow measurements. However, performances under real installation conditions have not yet been completely investigated. This paper briefly describes the effect of flow pulsations on the sensitivity coefficient. The CMF with two parallel elastic tubes was studied based on the distributed physical model. The model is presented in the form of bond graphs. It was found that the flow pulsations with specific frequencies equal to the sum and the difference of the frequencies of the first two natural modes cause significant errors in meter reading.

In this paper the CMF with elastic parallel tubes was modelled. The tube is divided into final elements (FE), presented in the form of bond graphs and simulated by BondSim (Bondgraph Simulation System). The direct numerical integration method was applied for prediction of a time difference and other effects for the commercially available CMF. The phase or time difference was found to be proportional to the mass flow rate. The agreement between the experimental data for the given CMF with theoretical results using the equivalent length is good.

In this paper a unified approach to the analysis of Coriolis mass flowmeter and a fluid angular rate sensor has been presented. A new type of the fluid angular rate sensor is proposed. The operation of both sensors has been mathematically modelled. The system of equations was solved by the bond graph method using BondSim. The method of solution permits simulation of the complex metering systems. The results of simulation for the Coriolis mass flowmeter showed the linear relationship between the mass flow rate and the time difference of reference signals. In the simplest case of the angular rate sensor with the circulating flow the tube deformation was proportional to the angular rate.