Improvements in Coriolis flow measurement technology


Mass flow measurement based on the Coriolis principle has been expanding its presence in diverse applications throughout several industries. This technology has shown its outstanding performance in terms of low uncertainty, high repeatability, and long-term stability. However, new improvements for this technology have upgraded its results under specific process conditions usually considered as limiting. In this paper, a   summary of the newest developments for the Coriolis meter that appeared in previous publications is discussed, including Reynolds number compensation allows dynamic compensation the effect of low Reynolds number applications in the measurement results, as well as Multi-Frequency Technology (MFT) intended to compensate the meter errors introduced under entrained gas conditions. Finally, the direct viscosity measurement feature obtained with a straight pipe Coriolis meter is also discussed. The field of application for each new feature is also presented.


Mass Coriolis flowmeters have been one of the most attractive and consistent flow measurement choices during the last thirty years. Even though, its acceptance has been increasing gradually through all these years. But nowadays there is a consensus about their reliability in quite different industries, from crude oil after the primary phase separation up to hygienic food and beverage applications.

Probably, one most valuable features of the Coriolis technology is related to its capability to maintain low measurement uncertainty even under changing fluid properties These property changes include not only fluid density, which is also measured by the meter, but also viscosity.

However, further research has discussed the real effect of low Reynolds number conditions in the Coriolis meter. Low Reynolds regime in transport applications used to be related to high viscosity conditions. Compensations to the meter factor shift that occurred under low Reynolds conditions.

Coriolis flow meters are designed to measure a single-phase fluid. Multi-phase behavior, such as that produced by entrained gas in a liquid stream,

clearly affects the meter accuracy. improvements in their Coriolis sensors that allow them to compensate for errors associated with increased fluid compressibility when an entrained gas is present.

Viscosity measurement is also one of the most important contributions to the multivariable nature of Coriolis flow meters. Depending on the way that the driving force is exerted on the oscillating system of the flow meter, consistent information on the fluid viscosity can be obtained.

Coriolis principle of operation for mass flow measurement

A Coriolis mass flowmeter is probably one of the most known applications of the Coriolis force (named in honor of its discovery Gustave Coriolis). These flowmeters are basically conformed by an oscillating system with one, two, or four pipes and an array of the driver and pick-up coils, capable of imposing a vibrating frequency to the system close to its natural frequency, and detecting the phase shift of the anti-symmetric oscillation, appeared and detected between A and C when a fluid flows through the oscillating tubes, respectively

This phase shift is a direct function of the mass flow flowing through the oscillating tubes. But in addition to the mass flow, the density is also measured by the relation between this variable and the frequency of the oscillating system.

Low  Reynolds  number  application:  Inertial forces vs viscous forces

Reynolds number (Re) is one of the most important dimensionless numbers of fluid mechanics. Basically, it accounts for the relation between the major groups of forces acting in fluid transport applications: inertial and viscous forces.

Re = Vdr/m  (1)

Where V is the average velocity of the fluid stream; d is the internal diameter of the pipe; r is the mass density of the fluid and m is the fluid dynamic viscosity. One of the bigger influencers of Re in a fluid transport application in a pipeline is the fluid viscosity.

The effect of the viscosity changes, and consequently of Re in the flow meter accuracy is a fact recognized by the Coriolis meter developers and manufacturers. The Reynolds number of the fluid flow stream obtained inside the meter is relevant to detect and also to compensate for this effect.

TÜV/NEL conducted several independent experiments to analyze this behavior in Coriolis meters. Tests were carried out up to 300 CST. The higher the viscosity (and consequently the Reynolds number), the higher the negative deviations found during these tests. This result was consistent for all the types of meters employed.

This effect is quite related to the interaction between the oscillating Coriolis forces and the oscillating shear forces acting on the fluid. The lower the Re is (basically the higher the viscosity is), the higher the influence of this.

The mechanism

The mechanism acting in the effect is described in as a result of the axial flow profile as a result of an interaction between a) the oscillatory shear force and b) the inertial Coriolis force in the measuring tube, leading to an oscillatory secondary force. This secondary force moves in opposite directions on either side of the axial center of the tube but disappears at the center of the tube. The ratio between these two forces a) and b) is directly proportional to Re.

The alternating secondary force appeared at low Re and was expressed in the outer layer close to the tube wall. This effect is totally connected with the existence of the thin layer or boundary layer, where the viscous forces are preponderant compared to the inertial forces.  In this condition, the Coriolis force (that one who produces the phase shift) must overcome the oscillatory shear force and for that reason, part of its energy does not contribute to the deflection of the tube and consequently to the phase shift. That is the reason behind the underreading of the actual mass flow rate. The magnitude of the secondary circulation is proportionally inverse to the Reynolds number, thus this effect becomes negligible at high Re.

Real-time measurement correction based on Re

The only missing element to calculate the Re of the application is the fluid viscosity at actual conditions.  Coriolis flowmeters can measure the fluid viscosity in addition to density and mass flow rate measurements.

With this information, a correction algorithm is implemented to compensate for the deviations described above. This patented feature allows us to obtain the mass flow rate corrected value through a real-time compensation based on the Reynolds number.

the results obtained in witnessed measurements performed in  TÜV/NEL (3” – 6”) and SPSE (10”-14”) with totally different fluid viscosities, ranging from 0.7 to 1000 CST. Tests were developed under quite distant Reynolds numbers ranging from 100 to 5 million, this spread of values was obtained by changing the flow rate and the fluid viscosity.

Both results are consistent with the expected values and no deviations are observed at low Reynolds numbers.

Error of mass Coriolis meters with Reynolds number compensation algorithm plotted against viscosity and with different flow meter diameters. Error-values kept in the band of ±0.2%.

The error of mass Coriolis meters with Reynolds number compensation algorithm, plotted against Reynolds number and with different flow meter diameters. Error values kept in the band of ±0.2%

The Reynolds number compensation is standard on flow meters.  With this feature, those instruments can fulfill the maximum permissible error established in  OIML- 117-1 class 0.3 for a wide range of process conditions. This feature also guarantees to maintain the same metrological performance of the meter even under low Reynolds application and changing flow and fluid properties.

Improving the Coriolis meter accuracy under entrained gas conditions

The existence of a second phase in the fluid stream to be measured by a Coriolis meter has been a concerning topic for both manufacturers and end users. Mainly, for Custody Transfer for liquid applications entrained gas in the measured stream could represent an additional source of errors for the measurement system. The increased compressibility of the fluid in the presence of entrained gas is directly associated with this undesired but real and frequent condition.

Literature reports at least two main sources of error associated with a multi-phase condition in liquid fluid, the bubble effect and the resonator effect (which is more commonly named as compressibility effect).

The bubble effect can be summarized as the distortion or deviation from the oscillating system (tube and liquid fluid) generated by the bubbles, which is a portion of the fluid with a density value hundreds of times less than the liquid. Thus, a relative motion between the bubble and the liquid is generated, since the liquid cannot totally “hold” the bubble. A secondary flow is induced around the bubble and as a result its inertial effect finally affects the phase shift, which is sensed to measure the mass flow rate. The resultant consequence is an underestimation in mass flow rate and density.

In the ideal condition of free bubbles, there is no any “holding” effect from the liquid fluid. However, fluid viscosity and the presence of small-size bubbles deviate the field conditions from free bubble conditions. The ratio of the bubble and liquid oscillation amplitude quantifies the contribution of the bubble effect to the measurement error.

Resonator effect, in addition to free bubbles there are also suspended bubbles; they will oscillate together with the liquid fluid (amplitude and phase) so no bubble effect is generated. However, they will radically increase the fluid compressibility leading again to mass and density error.  This mechanism can be briefly described as the radical reduction of the resonance frequency of the fluid in the presence of a suspended bubble of gas, driving the system out of resonance and leading the flowmeter to again underestimate density and mass flow rate. However, if the acoustic resonance frequency of the system is known is possible to calculate the resonator effect on the mass Coriolis flowmeter.

Multi Frequency Technology

Endress+Hauser has developed the Multi-Frequency Technology (MFT), which allows to compensate for the measurement error caused by the resonator error on both, density and mass flow rate. This technology has been implemented in Coriolis flow meters

With this technology, the measuring tubes are excited simultaneously in two different oscillation modes using the same driver. In this case, the first and the third natural mode frequency were selected. The difference in frequencies between these two modes used to be typically by a factor of 5 or 6.

The meter, now excited at two different frequencies, can process the combined signal and simultaneously obtain the two independent vibrational properties of the two modes.

Since the ratio between the two resonance frequencies is known, as well as its deviation due to the presence of entrained gas, there is also a way to calculate the correction factor associated with this change of frequencies. This correction factor compensates for the deviation generated by the presence of entrained gas in the liquid stream.

developed to perform very well in applications such as crude oil or heavy oil where due to the fluid high viscosity, bubbles are held by the liquid and consequently the resonator effect is strongly generated.

MFT has recently been tested by measuring  WC  and GVF in an independent laboratory, DNV GL. In this case, entrained gas was introduced as a third phase, in addition to water volume fraction in oil.

DNV GL provided a highly reliable reference for WCs. Several WC values were generated. A comparison between the WC values obtained with and without MFT is shown in Figure 8 (right). Drastic deterioration related to the GVF increase is no longer present. Deviations are kept from 0 to – 4%, which is very a consistent value for this application.

Direct  viscosity measurement  with Coriolis flow meters

Direct viscosity measurement is an important variable for different applications. Viscosity measurement is a valuable approach to simplify control loops for product quality.

Online viscosity measurement included as part of the measured variables for a Coriolis meter is available.

The mechanism

Viscosity measurement implemented in a straight pipe oscillating tube design is not exactly a recent development, but worth mentioning this capability, considering that it also represents an important enhancement to the mass Coriolis meters.


The required power to maintain the oscillating tube with a steady torsional oscillation in amplitude and frequency will be affected by the fluid viscosity. The oscillating tube is simultaneously driven by two resonance frequencies, the standard lateral mode at 600-700 Hz and by the new torsional mode at 900 Hz, Figure 10. These oscillations are geometrically  orthogonal,  thus no interference between these two oscillations occurs.

The result of this combination of excitation conditions is two truly independent measurements of viscosity and mass flow without any cross-influence.

Measurement performance in mass flow and viscosity, as well as mass density, fulfills the requirements specified in process applications with high repeatability and long-term stability. Viscosity measurement has shown to be consistent with laboratory results, but differently from a discrete measurement, the variable is always available.

The benefits

Online viscosity measurement represents a direct way to control the blending process, fuel combustion, and product quality. In this case, the benefit is not only the knowledge of the variable but also to get that information continuously. This continuous approach will also prevent any consequence derived from undesired deviation to occur.

Applications such as heavy fuel oil preparation or combustion control in a burner are two typical examples where direct viscosity measurement represents important savings and improves safety.

The combination of mass flow, density viscosity, and temperature, results in an effective way to control in only one instrument basic process variables with low uncertainty and high reliability.


Coriolis’s principle of operation for mass flow measurement has been evolving to improve its primary results.

Current improvements in this technology expand the range of conditions and applications where these types of flowmeters could be used to fulfill the process requirements.

Online correction of the low Reynolds number effect allows maintaining the meter accuracy obtained in reference conditions and also under high viscosity fluid conditions. This capability has been tested on international calibration facilities with consistent results.

Multi-Frequency Technology application provides a reliable tool to compensate for the error associated with the presence of entrained gas in a liquid fluid stream. Water-cut as well as GVF calculations are also improved using this technology.

Direct viscosity measurement extends the multivariable nature of the Coriolis meters family and provides online information on an important process variable. The results obtained for this variable are totally consistent with the laboratory results.


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[4]Kumar, V; Tschabold, P; M, Anklin. Fluid-Structure Interaction (FSI) simulations on the sensitivity of Coriolis flow meter under low Reynolds flow, – 15th Flow Measurement Conference (FLOMEKO), Taipei, Taiwan, 2010

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[7]Zhu, H; Rieder, A. An innovative technology for Coriolis metering under entrained gas conditions. Endress+Hauser Flowtec AG, KägenStr, Reinach, 2016.

About the authors

Osmel Reyes Vaillant, Regional Industry Manager for Oil and Gas Market in Latin America Support Center, Panama. More than twenty years in the Oil and Gas Industry as an application engineer, project manager, and researcher. He worked for CUPET (Cuba) and as a researcher for USP/Petrobras (Brazil). He holds a BS in Automation Engineering from ISPJAE, Cuba, an MSc Degree in Electrical Engineering from São Paulo University, Brazil, and a PhD in Electrical Engineering from ISPJAE, Cuba/IPT, Brazil.

Erwin H. Doorenspleet, Business Development Manager Oil and Gas/Coriolis AG, Reinach, Switzerland. More than twenty years of experience with industrial measuring technology, from which 13 years specifically active in flow measurement technology. He holds degrees in Electronics, Marketing, and Business Administration from Netherland System University, Holland.