# Systems for calibration testing of coriolis flowmeters

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DOI: 10.1007/s11018-012-0062-4

- Cite this article as:
- Mikheyev, M.Y., Gudkov, K.V., Yurmanov, V.A. et al. Meas Tech (2012) 55: 927. doi:10.1007/s11018-012-0062-4

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A method of in-situ calibration testing of flowmeters is proposed. The design of the system, operating principles, and results of a simulation of the action of pulse interference are considered.

### Keywords

Coriolis flowmetercalibrationcoarse distortions of measurement resultsCoriolis mass flowmeters are currently used to monitor transportation and assign tax assessments from the results of measurements of the flow of many different types of liquids, in particular, liquefied petroleum gas and other hydrocarbons. For these applications, the use of a measuring transducer must have an error of 0.5% or even 0.1%.

The use of systems based on a gravimetric diverter for calibration of flowmeters constitutes a relatively time-consuming and expensive process and the measurement benches themselves are relatively cumbersome. A calibration procedure with the use of reference measuring transducers calibrated on gravimetric systems and used in calibration of relatively less precise measuring instruments is of lesser precision but simpler. Most modern methods of calibration include the operation of extracting the flowmeter which is to be calibrated from the pipeline in which it functions. Automatic compensation of external effects that influence the precision and reproducibility of the results, such as mechanical action affecting the measuring instrument, the configuration of the pipeline, and variations in the properties and composition of the liquid and the environment, is needed for in-situ calibration of flowmeters.

Let us consider the steps involved in the application of such a construction.

First, each series of calibrations must last 1–2 min in order to minimize the error in counting the number of pulses and assure reproducibility of the results arriving from the output of measuring instruments on a base consisting of two calibrated flowmeters and a single Coriolis flowmeter which is to be calibrated. This presupposes a high level of stability of the parameters of the measured flow of substance in the course of the indicated time intervals, something which is difficult to achieve for a commercial pumping plant.

Second, at least two identical calibrating flowmeters are involved in the calibration procedure. The two flowmeters are calibrated in a special plant with error one-third that of the flowmeter which is to be calibrated and the scale division of these flowmeters is roughly one-tenth that of the flowmeter being calibrated. The readings of only the reference flowmeter are used in processing the information while the readings of the second flowmeter are used only in the operation of determining the reliability of the readings of the first flowmeter. Such an approach is in contradiction with the general assumptions of the theory of measurement.

The process of recording the response of the measurement system to pulse interference is a particular difficulty. Increases in anomalous measurement results can be expected for calibrating flowmeters having one-third lesser error.

Third, the calibrating flowmeters, which are mounted on a common platform, are connected to the pipeline at a site that is upstream or downstream relative to the flowmeter which is being calibrated. Correspondingly, the pipeline experiences vibratory mechanical effects produced by the calibration plant, which leads to an increase in the measurement error. If the calibrating flowmeters are connected on only one side this is equivalent to some damping of the vibrations precisely from this side. Such a difference leads to bias in the estimates of the calibration coefficient of a measurement of the mass flow rate of the flowmeter which is being calibrated.

Fourth, vibration of the flowmeter pipe at the resonance frequency occurs in any flowmeter based on the Coriolis effect. Because of different effects described, for example, in [2–4], the nodal points of this vibration are displaced according to the design of the flowmeter. Thus, the control and reference flowmeter are sources of additional vibration effects, moreover at nearly the same, essentially equal resonance frequencies. Consequently, there arises a mutual influence of two (or three) devices functioning at the same resonance frequency. Theoretically, such a regime induces an additional measurement error; the present authors are not aware of any quantitative estimation of this error.

To eliminate this type of drawback, we wish to propose a method of calibration based on a plant of *N* mass flowmeters based on the Coriolis effect. The calibrating flowmeters are situated both downstream and upstream relative to the flowmeter which is being calibrated and the control system assures delivery of flow of matter to the measurement and reference flowmeters. Correction factors are obtained by processing the results of measurements of all *N* mass flowmeters.

*Y*(

*t*), which constitutes a single realization of a nonstationary process, may be represented as a sum of information-bearing and non-informationbearing components:

*M*(

*t*) is an information-bearing component that describes the value of the mass flow rate as a function of time;

*M*

_{n}(

*t*), noise component of measurement results; and

*M*(

*t*), coarsely distorted measurement results.

Increasing the precision of the calibration entails synthesis of a procedure for processing the measurement results *Y*(*t*) in order to determine the information-bearing component *M*(*t*) against the background of the two non-information-bearing components *M*_{n}(*t*) and *M*_{c}(*t*).

We will use a method that is best under the present conditions to minimize the influence of *M*_{n}(*t*) – averaging over nan ensemble of realizations *y*_{j}(*t*_{i}) obtained from *N* mass flowmeters, where *j* = 2, …, *N* is the index of a flowmeter and *i* the index of a realization. The root-mean-square error of the measurement results will be 1/*N*^{1/2} times that obtained with the use of a single mass flowmeter. This assertion is more theoretical than practical in nature, since the cost of the system grows in proportion to the number of reference Coriolis flowmeters. Therefore, variants for *N* = 2 or 4 were considered in [4] and the expected effect amounts to 1/2^{1/2} and 1/2. However, this result may be attained only in the absence of correlation between the analyzed signals, i.e., under the condition that *N* simultaneously functioning mass flowmeters do not affect each other to within the specified precision. The operation of preliminary joint calibration of *N* flowmeters in a special reference pipeline that assures successive transfer of matter through all the flowmeters is introduced in order to eliminate this influence. In order to support this regime, the entrance and escape holes of the calibration device are connected to branch pipes situated further downstream than the functioning flowmeter and on opposite sides of the pipeline’s shutoff and drain valves.

In the course of calibration, the phase relations between the vibrations of the operating regimes of the flowmeters are regulated until a minimal error is attained. Because of the proximity of the working frequencies of the flowmeters, the mutual influence of the flowmeters is eliminated through introduction of a phase shift between the resonance frequencies; this serves to compensate for the interference created by the flowmeters.

In addition to the set of the indicated regimes caused by the generated excitation of the flowmeter pipes, regimes that arise due to vibration that is external relative to the flowmeters are possible in the course of calibration of a flowmeter in a pipeline under operating conditions. A priori information about the characteristics of the external vibrations is not available. To reduce the influence of these vibrations on the result of a calibration, the flowmeters that are being utilized are divided into two groups, preferably equal, and arranged symmetrically relative to the flowmeter which is being calibrated. Thus, bias in the estimates of the calibration coefficient in measurements of the mass flow rate is minimized.

Let us now discuss the component *M*_{c}(*t*). Before performing the operation of averaging over an ensemble, the coarsely distorted measurement results must be eliminated. For this purpose, the maximal value *y*_{max} is determined and some threshold α*y*_{max}is established in accordance with a specified level of significance α, where 0 < α≤ 1 on each interval of random length for the difference process Δ_{j}(*t*_{i}). A specific weight, for example, 1 is assigned to each value of the difference process Δ_{j}(*t*_{i}) that has exceeded the threshold value. The procedure is repeated for all *L* difference processes. A build-up of the values of the weights occurs and the density function of the values is constructed. For a given level of significance, which results of the measurements must be excluded from further processing are determined from the density function. Thus the effect of pulse interference leading to the appearance of strongly distorted measurement results is eliminated.

The proposed method of calibration of flowmeters under operating conditions has certain drawbacks. A calibration of a flowmeter may yield a valid estimate of its precision characteristics over a lengthy interval of time only where the pattern of noise components of the interference acting on the flowmeter from the direction of the environment is fully invariant. This assumption is impossible to achieve when a flowmeter is functioning outside the laboratory.

In the course of the development of a calibration complex based on Coriolis flowmeters it must be borne in mind that the working frequency of a flowmeter is a resonance frequency. All the noise components of the interference with frequency close to the operating frequency will increase its amplitude and, consequently, reduce the operating precision of the system. It is practically impossible to eliminate this interference.

Calibration complexes based on Coriolis flowmeters suffer from a major drawback associated with the production of information about the density of the flow. It is possible to eliminate this constraint only through the creation of Coriolis flowmeters based on entirely different methods of obtaining information about flow rate and not related to the use of resonance frequencies along with the use of flowmeters exhibiting interference and noise immunity as viewed from the pipeline.

Existing models of Coriolis flowmeters with the use of polymer materials lead us to conclude that materials with elevated indicators of the damping factor and reduced indicators of the stiffness coefficient may be used in the construction.

The process of determining the density of a flow in such a construction is based on measurement of the inertial force of the pipe as matter is traveling through the pipe. This method of measurement is independent of the resonance frequency. Therefore, we wish to propose that operating frequencies that are not in direct proximity to the flowmeter’s resonance frequency be selected.

Calibration of a flowmeter is easier and more appropriate to carry out with the use of a mass standard. Since the construction of a flowmeter is based on direct measurement of the forces acting on the device and since the effect produced by a load with previously known mass may be calculated analytically, sites for attaching a system of calibrated loads with standard mass must be provided in the structure of the flowmeter. When a flowmeter is functioning without the passage of a flow of matter traveling through the pipe, the inertial forces which thereby arise may be calculated. If reference standard masses are subsequently installed in the pipe, this will alter the inertial force. The response of the system to reference mass sources may be established from the difference in the inertial forces before and after insertion of these mass sources. The correction factor of the sensors may be derived precisely if the indicators are adjusted with the use of previously calculated analytic data.

Thus, starting with the proposed design of a Coriolis flowmeter, it becomes possible to implement in-situ calibration of a flowmeter together with minimization of the influence of interference on the indicators of the flow of the calibrating flowmeter. Graphs that describe the operation of the plant for subsequent compilation of a chart of correction factors may also be constructed.

The present article has been prepared within the framework of the project “Development of Methods and Means of Nondestructive Diagnostics of Onboard Radio Engineering Devices for Space Systems” (State Contract No. 14.740.11.0840) and the Federal Targeted Program on Scientific and Teaching Staff for an Innovative Russia in 2009–2013.