The Coriolis mass flow meter as a volume meter for the custody transfer in liquid hydrocarbons logistics

In recent years, the Coriolis mass flow meters (CMF), devices based on the Coriolis effect over a vibrating pipe, have developed better metrological performance and they are now a reasonable alternative for the custody transfer measurements. Nowadays, many custody transfer operations require measurement of the net volume (volume measured at a certain reference temperature) and, therefore, it is not feasible to use the CMF as a mass flow meter. However, the actual CMF can be used as net volume meters because they have special equipment to measure density and temperature, and a flow computer. In this work, firstly a mathematical simplification of the physical model is proposed for the CMF. We part from the dimensional analysis of the flow-phase relationship produced by the Coriolis force, the main physical principle behind these devices. A simplified formula is obtained and it permits identifying the magnitudes of influence of the CMF as a mass meter. Secondly, its metrological properties are characterized. For such purpose, a 4” straight tube commercial meter has been calibrated in volume, in the 50 to 165 m³/h range against a standard container and a bidirectional prover, employing gas oil and kerosene (JET-A1). These calibrations have turned out to be compatible with the ones performed by the manufacturer in mass and using water. Then it is verified that the CMF fulfills the requisites of the legal metrology: maximum error allowed, linearity and repeatability. Skewness is observed in the relative error (expressed in %) of the CMF and it has been researched to be due to systematic effects related to constructive parameters of the meter. Lineal correlation is verified between relative error and temperature, and between relative error and flow rate, with negative slopes of −0.03% °C⁻¹ and −0.001% h/m³ respectively.     

The performance characteristics of a micro-machined Coriolis flow meter: An evaluation by simulation

Micro-machined Coriolis meters will enable measurement of very low flow rates (0.1–500 g/h) and, potentially, ultra-low flows (0.1–100 mg/h). Application areas include the delivery of medical drug infusions to patients, and a wide variety of micro-fluidic devices. An evaluation of the performance of two prototype micro-machined flow-tubes of differing shapes is reported, based upon results obtained from a virtual Coriolis meter. This tool comprises a finite element modelling capability which simulates the meter flow-tube in motion, with the flow represented simply as a continuous string, i.e. 1-dimensional and frictionless, and the model allows the generation of pseudo-data at points on the tube corresponding to sensor locations. Application of signal processing algorithms then enables the representation of an indicated flow time history output by a Coriolis meter in response to a prescribed input flow. Results indicate that the devices investigated were all highly linear and that meter sensitivity is independent of fluid density. One flow-tube shape confers higher stiffness than the other and, for both tube shapes, increasing wall thickness increases tube stiffness at a greater rate than the tube mass. Higher stiffness results in reduced meter sensitivity, but increased drive frequency (hence, faster dynamic response). The spatial averaging resulting from the use of ‘distributed’ internal sensors inevitably yields meter sensitivity values that are lower than the potential maximum value that might be achieved by use of ‘point’ sensors; however there are practical reasons why this latter approach would not work. The dynamic response to a flow step is essentially the same as found for macro-Coriolis meters.     

Performance evaluation of Coriolis mass flow meter in laminar flow regime

In many fluid flow applications, mass flow rate is preferred over volume flow rate, as it is more beneficial in terms of cost and material balance calculations. Coriolis mass flow meter (CMFM) is accepted widely for mass flow measurement owing to its accuracy and reliability. However, it has been found to under-read the mass flow rate in laminar flow region [1], thus limiting its application in this region. The secondary flow in the curved tube section influences the generated Coriolis force and leads to a deviation in meter readings. Commercial CMFMs are available with various curved tube configurations and need to be analyzed for their application in laminar region. This paper presents comprehensive experimental and numerical investigations performed to evaluate the influence of tube configuration and other meter parameters, such as drive frequency, amplitude of vibration, and sensor position, on the performance of the CMFM in laminar region. The findings of this study have put forth a suitable combination of tube configuration, drive frequency, and sensor position while using the CMFM in laminar flow regime.     

Understanding the experimental response of Coriolis massflow meters to flow pulsations

Recently published theoretical work on the response of a simple Coriolis massflow meter does not agree with the data in the only published report of experiments on this topic. In order to try and explain this discrepancy a new set of experiments has been performed on a meter closely similar to that used in the original experiments. The present paper reports the results of the new experiments which both confirm and extend the original findings. With the aid of additional experiments on the response of the Coriolis meter to mechanical vibrations, an explanation is given of the mechanism by which the meter can give erroneous readings. The paper concludes with a discussion of methods by which the occurrence of errors can be mitigated, and one of the methods suggested in the current ISO standard for these meters is shown to be ineffective.     

Quantification of the influence of external vibrations on the measurement error of a Coriolis mass-flow meter

In this paper the influence of external vibrations on the measurement value of a Coriolis mass-flow meter (CMFM) for low flows is investigated and quantified. Model results are compared with experimental results to improve the knowledge on how external vibrations affect the mass-flow measurement value. A flexible multi-body model is built and the working principle of a CMFM is explained. Some special properties of the model are evaluated to get insight into the dynamic behaviour of the CMFM. Using the model, the transfer functions between external vibrations (e.g. floor vibrations) and the flow error are derived. The external vibrations are characterised with a PSD. Integrating the squared transfer function times the PSD over the whole frequency range results in an RMS flow error estimate. In an experiment predefined vibrations are applied on the casing of the CMFM and the error is determined. The experimental results show that the transfer functions and the estimated measurement error correspond with the model results.The agreement between model and measurements implies that the influence of external vibrations on the measurement is fully understood. This result can be applied in two ways; firstly that the influence of any external vibration spectrum on the flow error can be estimated and secondly that the performance of different CMFM designs can be compared and optimised by shaping their respective transfer functions.     

Two-phase flow metering of heavy oil using a Coriolis mass flow meter: A case study

The use of Coriolis mass flow metering for two-phase (gas/liquid) flow is an emerging theme of both academic research and industrial application. The key issues are maintaining flow-tube operation, and modelling and correcting for the errors induced in the mass flow and density measurements. Experimentally-derived data is used to illustrate that these errors vary most notably with gas void fraction (GVF) and liquid flow rate, but other factors such as flow-tube geometry and orientation, and fluid properties such as viscosity are also influential. While undoubtedly a universal two-phase flow correction model is the ultimate research goal, there is currently no obvious candidate to explain the range of behaviours observed. This paper describes and demonstrates an empirical methodology that has proven effective in developing good correction models for a given choice of Coriolis flow-tube and flow mixture.

A growing proportion of the world’s oil reserves may be described as “heavy”, implying high density and high viscosity. Of the various metering challenges heavy oil poses, one of the most significant is its ready entrainment of gas, and the difficulties entailed in separating gas from the oil. Accurate two-phase measurement of heavy oil is therefore an especially desirable technical goal.

Trials were carried out at the National Engineering Laboratory (NEL), Scotland on a 75 mm flowmeter using a high viscosity oil. Flowrates from 1 kg/s to 10 kg/s were examined, with gas void fraction (GVF) up to 80%. The resulting models were tested online in a commercial Coriolis mass flow meter and demonstrated good performance for both steady and slugging two-phase flows, with the corrected measurements typically within 1%–5% of the nominal mass flow and density.

Field trials in Venezuela have confirmed the performance of this two-phase solution.

While research continues into the development of a generic two-phase correction, this case study demonstrates that the current state of the art can provide, for economically important fluids, tailored models with good two-phase flow performance.     

Prism Signal Processing of Coriolis meter data for gasoline fuel injection monitoring

Prism Signal Processing is a new recursive FIR technique offering rapid filter design and calculation. It has previously been applied to Coriolis mass flow metering to generate fast (48 kHz) flow measurement updates, facilitating for the first time the direct mass flow measurement of individual fuel pulses injected into a laboratory diesel fuel injection test bench. In this paper we describe an augmented sensor signal filtering scheme which enables rapid tracking of the desired mode of flow tube vibration while notching out undesired modes. The new scheme is applied to a gasoline injection test bench where the vibrational interference is greater than for the previously described diesel system due to increased hydraulic shock. The paper presents experimental findings which illustrate the further challenges to be overcome in order to achieve the goal of traceable direct mass flow measurement of individual fuel injection pulses. For example, when a fuel pulse is shorter than the resonant period of the flow tube, the observed phase difference appears to show dependence on the instantaneous phase of the flow tube vibration.     

Fast Coriolis mass flow metering for monitoring diesel fuel injection

Prism signal processing is a new recursive FIR technique that facilitates the rapid tracking of sinusoidal signals, such as those used in a Coriolis Mass Flow Meter (CMFM). A Prism-based CMFM prototype has been developed using a commercial flowtube and a dual ARM processor-based transmitter, which is capable of generating flow measurement updates at 48 kHz. This has been applied in a feasibility study to the tracking of fast (e.g. 1.5 ms) injections of diesel fuel on a laboratory rig at engine speeds of up to 4000 rpm equivalent and at fuel pressures of up to 100 MPa. Due to the high level of vibration in the system, Prism-based notch filtering is used to suppress undesired modes of flowtube vibration in the sensor signal. Individual flow pulses can be detected by the system, but the relatively long period of oscillation of the flowtube compared to the fuel injection duration results in a spreading out over time of each flow pulse measurement. More precise measurement results may be obtained using a higher frequency resonant flowtube.     

Dynamic analysis of Coriolis flow meter using Timoshenko beam element

Coriolis mass flow meter (CFM) is used to measure the rate of mass flow through a pipe conveying fluid. In the present work, the Coriolis effect produced in the pipe due to a lateral excitation is modeled using the finite element (FE) method in MATLAB©. The coupled equation of motion for the fluid and pipe is converted to FE equations by applying Galerkin technique. The pipe conveying fluid is excited at its fundamental natural frequency. The time lag observed between symmetrically located measurement points which are equidistant from the point of excitation, is utilized to predict the mass flow rate. The results predicted by the present code is validated using the experimental, and numerical results published in the literature. The main contribution is the development of a FE model, using three node Timoshenko beam element to analyse the dynamics of fluid conveying pipes subjected to external excitation. The direction of the Coriolis force is perpendicular to the plane containing the velocity of flow vector and angular velocity vector of the pipe. Hence a three dimensional FE model is essential. This model can include curved geometry, damping, velocity and gyroscopic effects for three dimensional flexible tubes. The reduced integration used for overcoming shear locking in two node elements, will result in the formation of spurious modes leading to an incorrect prediction of natural frequencies and velocity. These modes will not occur while using three node elements. Influence of spatial as well as temporal discretisation on the time lag and frequency are also discussed. The sensitivity analysis shows that the time lag varies linearly with the mass flow rate.     

Calibration of hydrogen Coriolis flow meters using nitrogen and air and investigation of the influence of temperature on measurement accuracy

The performance of four Coriolis flow meters designed for use in hydrogen refuelling stations was evaluated with air and nitrogen by three members of the MetroHyVe JRP consortium; NEL, METAS and CESAME EXADEBIT.A wide range of conditions were tested overall, with gas flow rates ranging from (0.05–2) kg/min and pressures ranging from (20–86) bar. The majority of tests were conducted at nominal pressures of either 20 bar or 40 bar, in order to match the density of hydrogen at 350 bar and 20 °C or 700 bar and −40 °C. For the conditions tested, pressure did not have a noticeable influence on meter performance.When the flow meters were operated at ambient temperatures and within the manufacturer's recommended flow rate ranges, errors were generally within ±1%. Errors within ±0.5% were achievable for the medium to high flow rates.The influence of temperature on meter performance was also studied, with testing under both stable and transient conditions and temperatures as low as −40 °C.When the tested flow meters were allowed sufficient time to reach thermal equilibrium with the incoming gas, temperature effects were limited. The magnitude and spread of errors increased, but errors within ±2% were achievable at moderate to high flow rates. Conversely, errors as high as 15% were observed in tests where logging began before temperatures stabilised and there was a large difference in temperature between the flow meter and the incoming gas.One of the flow meters tested with nitrogen was later installed in a hydrogen refuelling station and tested against the METAS Hydrogen Field Test Standard (HFTS). Under these conditions, errors ranged from 0.47% to 0.91%. Testing with nitrogen at the same flow rates yielded errors of −0.61% to −0.82%.     

Accurate mass flow and density of bubbly liquids using speed of sound augmented Coriolis technology

Speed of sound augmented Coriolis technology utilizes a process fluid sound speed measurement to improve the accuracy of Coriolis meters operating on bubbly liquids. This paper presents a theoretical development and experimental validation of speed of sound augmented Coriolis meters. The approach utilizes a process fluid sound speed measurement, based on a beam-forming interpretation of a pair of acoustic pressure transducers installed on either side of a Coriolis meter, to quantify, and mitigate, errors in the mass flow, density, and volumetric flow reported by two modern, dual bent-tube Coriolis meters operating on bubbly mixtures of air and water with gas void fractions ranging from 0% to 5%. By improving accuracy of Coriolis meters operating on bubbly liquids, speed of sound augmented Coriolis meters offer the potential to improve the utility of Coriolis meters on many existing applications and expand the application space of Coriolis meters to address additional multiphase measurement challenges.The sources of measurement errors in Coriolis meters operating on bubbly liquids have been well-characterized in the literature. In general, conventional Coriolis meters interpret the mass flow and density of the process fluid using calibrations developed for single-phase process fluids which are essentially incompressible and homogeneous. While these calibrations typically provide sufficient accuracy for single-phase flow applications, their use on bubbly liquids often results in significant errors in both the reported mass flow, density and volumetric flow. Utilizing a process fluid sound speed measurement and an empirically-informed aeroelastic model of bubbly flows in Coriolis meters, the methodology developed herein compensates the output of conventional Coriolis meters for the effects of entrained gas to provide accurate mass flow, density, volumetric flow, and gas void fraction of bubbly liquids.Data presented are limited to air and water mixtures. However, by influencing the effective bubble size through mixture flow velocity, the bubbly liquids tested exhibit decoupling characteristics which spanned theoretical limits from nearly fully-coupled to nearly fully-decoupled flows. Thus, from a non-dimensional parameter perspective, the data presented is representative of a broad range of bubbly liquids likely to be encountered in practice.     

From disturbance to measurement: Application of Coriolis meter for two-phase flow with gas bubbles

Entrained gas has been regarded as disturbance to measurements based on Coriolis meters, since measurement accuracy can be degraded because of this disturbance. Recent research from Endress + Hauser has discovered that different types of gas bubbles, namely free bubbles and suspended bubbles, have various impact on the meter measurement performance. It is important to understand the error mechanism for different effects, namely bubble effect and resonator effect, which are introduced by different bubble types, and to take the corresponding measures to cope with the effects. It is also crucial to identify the bubble pattern in the measuring tube of a Coriolis meter to make a diagnosis and reduce the negative influence of the disturbance accordingly. For free bubbles that typically cause inhomogeneity of a medium, the fluctuation of the resonance frequency of the measuring tube in a Coriolis meter is directly correlated to the existence of this type of bubbles, since this medium under a flowing condition causes density fluctuation to the meter as gas density is typically much lower than that of a liquid. For homogenous suspended bubbles that lead to a significantly increased compressibility of a medium, the innovative Multi-Frequency Technology in Promass Q sensor offers the means to qualitatively detect the existence of this type of bubbles and quantitatively calculate the volume fraction of the gas phase, based on its ability to derive the speed of sound in a medium containing such bubbles. Identification of the type of bubbles helps not only for crediting the measurement reliability, but also for obtaining more detailed medium properties, and in turn a better process insight, with which a process optimization can be enabled to improve the quality of production.     

汽车仪表的识别、使用与发展趋势

本文介绍了汽车上的常见仪表及其正确使用。展望了汽车仪表的数字化发展趋势，重点介绍了步进式电动汽车仪表的特点和应用前景。     

Research on the dynamic characteristics of a turbine flow meter

In the hardware-in-loop simulation of aero-engine control system where the real fuel regulator is engaged, it's crucial to measure the real-time flow rate. In view of this, a flow meter with high precision and fast response is important. In this paper, modeling and experiments are conducted to verify the dynamic characteristics of a turbine flow meter (TFM). For the modeling part, driving torque and resistance torques are analyzed to derive the kinetic equation of TFM. Simulation with the kinetic equation shows good dynamic performance of TFM. In experiments, a workbench is designed to generate step-type flow and sine-type flow for identification in time domain and frequency domain. Results show that the settling time for TFM is no more than 100 ms and its band-with is over 4.61 Hz. Compared with the settling time of a main fuel valve and the band-width of a main fuel control loop, that is, 1.2 s and 2 Hz respectively, TFM is considered to be adaptive to measure the fuel of aero-engine.     

A Coriolis mass flowmeter based on a new type of elastic suspension

After a survey of the existing Coriolis mass flowmeters, all based upon the elastic deformation of the resonant sensor, this paper describes a new type of Coriolis mass flowmeter realised, in a prototypal way, in the DIME laboratories. The flowmeter prototype is composed of two attached elements: a stiff tube and an original system of independent elastic suspension which lets the whole sensor vibrate. In such a way, the new type of elastic suspension permits measurement independent from the elastic properties of the tube, not subject to deformation, realising a new mass flow sensor. The DIME prototype, which is described in the present paper, was studied and realised with the main aim of checking the mechanical behaviour of the new type of uncoupled elastic suspension.

Being the prototype and not a production-engineered version, for which it is possible to provide the metrological performances, the DIME flowmeter was tested on the DIME calibration facility, and the experimental results, which prove the linear behaviour of the prototype, are reviewed.     

The consistency of pressure effects between three identical Coriolis flow meters

Coriolis flow meters are one of the most popular flow measurement technologies in the world today for high accuracy measurement of single-phase liquids, gases and even slurries. They are capable of measuring both mass and density directly and can also infer the volume flow. They can be installed in challenging process environments and have been successfully deployed with non-Newtonian fluids, high viscosity fluids, pulsating flows and even at extreme temperatures and pressures.However, it is known that operating most Coriolis flow meters at a pressure which differs from the original calibration pressure requires compensation else significant measurement errors will occur. Pressure compensation coefficients appear to vary by manufacturer, meter geometry and sensor material. Furthermore, the manufacturer published pressure compensation coefficients are not fully traceable. To date, there has not been sufficient research exploring the consistency of the pressure compensation for identical Coriolis flow meters.This paper presents the findings of a research conducted at the TÜV SÜD National Engineering Laboratory (NEL) Elevated Pressure and Temperature (EPAT) oil flow facility to investigate the pressure effect uniformity for matching Coriolis devices. The first stage of the experimental programme calibrated three identical DN80 Coriolis flow meters at a range of pressures with no pressure compensation applied. A pressure compensation coefficient was then derived from the data and the Coriolis meters were then calibrated at two alternative pressures to ascertain the robustness of the coefficients and whether the compensation could be extrapolated successfully.From the experimental results, it can be concluded that the pressure effect for the three DN80 Coriolis flow meters was extremely repeatable and consistent with a discrepancy of less than 0.025% between the devices at 80 bar. Whilst the mass flow was significantly affected by fluid pressure, the fluid density did not appear to be influenced. The pressure corrected results were also well within the manufacturer specification of ±0.1%.     

浅谈石化装置流量仪表的选用

石化行业生产所用的原料及产品种类繁多。根据这些流体特点,需要采用不同的流量计进行测量。该文浅谈了针对不同性能的流体所采用的测量方法和流量计的选型。     

新型脉冲式热流计分析研究

现有热流计都需要流量计来计量流量.流量计很容易损坏并产生计量误差.为了解决这一问题,依据能量守恒提出了一种新型热量计,并对该装置的测量原理进行了理论分析和数值模拟,从而实现了只测量温差的情况下测出用户消耗的热量,摆脱了流量对测量结果的影响,从模拟和理论分析证明本方法能够较准确的计量热量值.     

Development of a turbine meter for two-phase flow measurement in vertical pipes

The performance of a turbine meter in two-phase (water/air) flow in a vertical pipe is assessed. If the single phase (water) meter factor is used in two-phase flow, the total (water and air) flowrate is found to be underpredicted. The error can be as much as 12.5% at a void fraction of 25%. A technique for using measurements of the fluctuations in the turbine meter rotor velocity to determine void fraction (= air flowrate/total flowrate) is described. A single meter is then used to measure, using this technique, both the water flowrate to an accuracy of ± 2% and void fraction to an accuracy of ±0.02.