Coriolis meter density errors induced by ambient air and fluid temperature differentials
Introduction
The continued development of Coriolis flow metering technology (Fig. 1) has been well documented and summarised in Ref. [[1], [2], [3]]. During the evolution of this technology, a largely consistent device design has emerged. While manufacturer and application-specific variations exist, the common design principle entails a single or dual flow tube, which is manufactured in either a straight or curved configuration. The flow tube is mechanically driven to oscillate at its natural frequency. Displacement (or more usually velocity) sensors located upstream and downstream of the centre of the flow tube are used to determine the extent of Coriolis force exerting twist. The time delay measured by these sensors is proportional to the mass flow rate passing through the meter. If no mass flow is present there will be no Coriolis force, and therefore no time delay is detected between the upstream and downstream sensors.
As a secondary output, a Coriolis meter is also capable of determining the density of the fluid present within the vibrating pipe sections. This process value is determined from the resonant frequency of the flow tube and is defined in Ref. [4] asWhere
- -
is the resonant frequency
- -
is the mechanical stiffness/spring constant
- -
is the total mass
- -
is the mass of the oscillating flow tube
- -
is the mass of fluid within the oscillating flow tube
- -
is the volume of fluid within the oscillating flow tube
- -
is the density of the fluid
To calculate the density of the fluid within the flow tube, the following equation can be derived from equations (1), (2), (3):
The phenomenon of ambient air temperature affecting the quality of Coriolis meter measurements has been noted in earlier research. In Ref. [5], an examination of ‘zero drift’ highlighted ambient temperature variation as a contributing factor. In Ref. [6], where the suitability of Coriolis technology was assessed for a specific industrial application, it was again observed that ambient air fluctuations, which were intentionally introduced into the system by the research team, caused a detectable drift in the meter mass flow rate.
It should be noted that [5,6] do not address the effects of ambient air temperature on the fluid density output from Coriolis meters. It is this gap in knowledge that this research intends to address.
The diagnostic capabilities of Coriolis transmitters which are responsible for analogue signal interpretation, digitisation and process value correction have been discussed previously [7]. Significant research has also been conducted with respect to developing the capabilities of the transmitter. In particular, the research described in Ref. [8] developed a self-validating sensor, capable of fault detection and data correction to ensure measurement quality is upheld.
An initial investigation into the effects of air temperature on the density measurement from a Coriolis flow meter is reported in Ref. [9].
The results in Ref. [9] were presented to a Coriolis manufacturer and a partnership was formed, the research objective being to develop a new temperature correction model that would significantly reduce errors and which could readily be implemented in a conventional commercial transmitter [10,11].
Correct measurement and interpretation of data output from flow metering technologies is key to production forecasting, custody transfer and fiscal metering [[12], [13], [14], [15], [16]].
Section snippets
Test design
To ensure fine control over all variables, NEL's Very Low Flow Facility (VLFF) was used. The 8 mm pipe bore supports good temperature control on a minimised mass of fluid, compared to NEL's larger flow loops. The VLFF is housed in a small (4 m × 3 m x 2 m) laboratory, reducing the potential for uncontrolled ambient temperature fluctuation. Details of the VLFF and the test matrix are described in sections 2.1 Facility layout and equipment, 2.2 Test procedure.
Reference measurements and data analysis
Fig. 3, Fig. 4 show the test meter's ambient air temperature changes as measured by the enclosure thermocouple (Fig. 2) for tests 1 and 2 respectively. The reference fluid temperature as measured by the test section central PRT (Fig. 2) is also trended. The reference fluid temperature increased by 1 °C and 0.8 °C for water and kerosene respectively.
Fig. 5, Fig. 6 show the corresponding room temperatures. The intention was to maintain the room temperature to within ±1 °C of its initial value.
Meter B results
The experiments of section 3 were repeated using a different meter model from the same manufacturer. In addition, this meter was exposed to extreme changes in ambient air temperature. This was designed to be representative of conditions that may be encountered in the field, such as sudden increases and decreases in air temperature due to sunlight. The results of these experiments are presented and discussed below.
Discussion and conclusions
The results presented here have demonstrated the potential for error in Coriolis meter calculated density. The errors were induced by ambient air temperature changes. Specifically, as the differential between the flowing fluid and test meter ambient air temperature increased, the error in both the uncompensated and compensated fluid density was shown to increase. These results combined with our preceeding research [9] indicate that limitations exist within the temperature compensation models
CRediT authorship contribution statement
Gordon Lindsay: Conceptualization, Methodology, Software, Resources, Investigation, Validation, Formal analysis, Data curation, Writing - original draft, Visualization, Project administration, Funding acquisition. Norman Glen: Conceptualization, Validation, Resources, Writing - review & editing, Supervision. John Hay: Conceptualization, Validation, Resources, Writing - review & editing. Seyed Shariatipour: Conceptualization, Validation, Resources, Writing - review & editing, Supervision. Manus
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work was funded by the Department of Business, Energy and Industrial Strategy (BEIS). Project number - FPRE05.
References (19)
Coriolis flowmeters: industrial practice and published information
Flow Meas. Instrum.
(1994)- et al.
Coriolis mass flowmeters: overview of the current state of the art and Latest research
Flow Meas. Instrum.
(2006) - et al.
Coriolis flowmeters: a review of developments over the past 20 years, and an assessment of the state of the art and likely future directions
Flow Meas. Instrum.
(2014) - et al.
A self-validating digital Coriolis mass-flow meter: an overview
Contr. Eng. Pract.
(2000) - et al.
Profiling and trending of Coriolis meter secondary process value drift due to ambient temperature fluctuations
Flow Meas. Instrum.
(2018) Measurement of Fluid Flow in Closed Conduits – Guidance to the Selection, Installation and Use of Coriolis Meters (Mass Flow, Density and Volume Flow Measurement)
(2015)- et al.
Experimental investigation on zero drift effect in Coriolis mass flowmeters
- et al.
Are Coriolis mass meters suitable for fiscal liquid applications?
Flow meter diagnostics
Cited by (6)
Study and development of a technique for measuring concentration and mass flow rate for saline solutions
2024, Flow Measurement and InstrumentationMetering inaccuracy analysis and improvement measures of typical scenarios in hydrogen refueling station
2024, International Journal of Hydrogen EnergyEvaluating the measurement uncertainty at hydrogen refueling stations using a Bayesian non-parametric approach
2022, International Journal of Hydrogen EnergyCitation Excerpt :The measurement uncertainty of CMFs includes factors such as pressure effect, temperature measurement uncertainty, CMF zero stability, CMF repeatability, and flow rate measurement uncertainty [10]. The measurement errors of CMFs within stable pressure, temperature, and flow rate ranges in a laboratory setting were examined in Refs. [11–13]. A CMF is normally calibrated by a water flow calibration standard at room temperature.
A Bayesian method for on-line evaluation of uncertainty in measurement of Coriolis flow meters
2021, Measurement: Journal of the International Measurement ConfederationCitation Excerpt :Also, in high viscosity conditions, CMFs must be adjusted with suitable fluid effects. Lindsay et al. further showed that an increase in temperature difference between the fluid and the ambient environment resulted in increased errors in measurement for both uncompensated and compensated fluid density scenarios [26]. CMFs are used in hydrogen refueling stations for their accuracy in high pressure dispensing processes.
Current status and prospect of studies on mixed oils in batch transportation of multi-product pipelines in China
2023, Zhongguo Shiyou Daxue Xuebao (Ziran Kexue Ban)/Journal of China University of Petroleum (Edition of Natural Science)