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New Developments to Improve Natural Gas Custody Transfer Applications with Coriolis Meters

Including Application of Multi-Point Piecewise Linear Interpolation (PWL)

Marc Buttler, Midstream O&G Marketing Manager

Tonya Wyatt, Process Gas and Chemical Industry Marketing Manager

Karl Stappert, Americas Flow Solutions Advisor

Emerson Process Management – Micro Motion

Ron Gibson, Senior Engineer

Gary McCargar, Senior Engineer

ONEOK Partners

Abstract

This paper provides an update on the growing use of Coriolis flow meters for natural gas wholesale

custody transfer measurement. Practical applications of provisions found within the 2nd

Edition of the

American Gas Association Report No. 11 (AGA 11) will be covered that deal with calibration fluid

flexibility, compensation for the effect of pressure on the meter, automatic multi-point piecewise linear

interpolation, and in-situ secondary verification methods that can be used after meters are installed in

service as an ongoing check of the calibration accuracy. This paper expands upon a paper previously

presented at the 9th International Symposium of Fluid Flow Measurement (ISFFM)

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1. Calibration Adjustment Factors Employed in Natural Gas Custody Transfer The 2

nd Edition of the American Gas Association Report No. 11 (AGA 11)

2 refers to four different

methods for applying adjustment factors to minimize any observed bias errors in meter calibration results.

These include:

Flow-Weighted Mean Error (FWME)

Polynomial Algorithm

Multi-point Linear Interpolation

Piecewise Linearization

The purpose of applying adjustment factors is to allow for the meter to be adjusted to as close to zero

error as possible at flow rates that cover the full expected service flow range.

Any type of calibration adjustment factor relies upon taking laboratory measurements on a flow device

and applying a correction factor(s) to the results in order to reduce the residual differences between the

flow device and the reference. The difference between the four adjustment methods listed above are that

they may be a single adjustment factor for the entire flow range (like the FWME) or multiple factors

applied for the range that both adjust any bias compared to the laboratory reference and adjust the

performance to provide a more linear result. When multiple correction factors are applied, they can

implement a best fit algorithm such as a polynomial fit, can implement multiple individual correction

factors for each point (Piecewise Linearization or Step-wise correction), or can implement multiple

correction factors with interpolation between the points.

Historically, the most common method for adjusting the indication of a typical early flow meter design

(e.g., turbine gas flow meter) was the application of a single FWME correction factor (a.k.a.

Flow-Weighted Final Meter Factor). Although this method provided a single flow-weighted best fit

correction suitable for a narrow range of flow rates, when a meter was applied over a wider flow range,

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the linearity of some meter types could vary by more than the accuracy requirements for the application

as shown in Figure 1.

Fig.1. Example of a Traditional Flowmeter Potential Non-Linearity

With the advent of microprocessor-based flow computers, the piecewise linearization method was

developed. This method allowed for the improvement of a meter’s performance across the whole flow

application range. Piecewise linearization provides the ability to linearize a flow meter indication so that

it closely tracks the measurement of the calibration flow reference over a wider range of flow rates.

The first implementations of multi-point piecewise linearization were in turbine and positive displacement

flow computers in the 1980s. An example of piecewise multi-point linearization adjustment is shown in

Figure 2. This correction is a step-wise correction process. In liquids standards terminology, this type of

corrections is sometimes called Piecewise Linearization (note that for the remainder of this paper,

Piecewise Linearization will not be used to describe this step-wise correction method) or Multi-Point

Calibration.

Fig.2. Example of Piecewise Linearization Adjustment with No Interpolation

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Flow Rate, lbm per second

As Found Error

Step-wise Correction

Corrected Data

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This and other linearization methods have since been applied and are widely accepted in the use of

ultrasonic flow meters and other highly repeatable flow meters. Ultrasonic flow meters very commonly

employ a multi-point piecewise linear interpolation adjustment. With this method, the adjustment that is

applied between each neighboring pair of the piecewise points is the linear interpolation between those

points as shown in Figure 3. When used with ultrasonic meters, this type of adjustment is commonly

referred to as just “piecewise linearization” or “PWL” for short. Note that this may be confusing because

turbine and positive displacement meter correction using the step-wise correction can be called the same

thing. The ability to linearize flow meter performance utilizing a piecewise linearization function has

become so widely accepted that this functionality can be commonly found in the designs of most

ultrasonic flow meter transmitters and flow computers.

Fig.3. Example of Multi-Point Piecewise Linear Interpolation (PWL) Adjustment

2. Coriolis Meter Calibration Options from AGA 11

Coriolis meters continue to grow in natural gas custody transfer applications. The wide range of flow

rates, high level of accuracy, ease of use, low maintenance, and long-term stability of Coriolis meters

make them quite useful in applications ranging from smaller industry and city gates to larger transmission

lines. A typical installation of a Coriolis meter in a natural gas custody transfer application is shown in

Figure 4. To support this growth, studies are being conducted to explore and develop new options for

Coriolis meter calibration to achieve further improvements in accuracy and efficiency.

Fig.4. Typical Natural Gas Custody Transfer Station with Coriolis Meter Installed

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Flow Rate, lbm per second

As Found Error

Multi-Point Piecewise Linear Interpolation Correction

Corrected As Found Data

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a. Calibration Fluid Flexibility

AGA 11 states in the beginning of Section 7 Gas Flow Calibration Requirements that it can be valid to

use an alternative calibration fluid, such as water, to calibrate Coriolis meters for gas measurement, so

long as transferability of the calibration from the alternative fluid to gas has been demonstrated by the

meter manufacturer through tests conducted by an independent flow calibration laboratory.

Transferability of the calibration from an alternative fluid will include an added uncertainty relative to gas

measurement that must be quantified by the manufacturer and verified by the independent flow

calibration laboratory.

Emerson has verified transferability of water calibration to gas flow measurement for the Micro Motion®

ELITE® CMF series of flow meters through testing at multiple independent flow calibration laboratories.

The maximum difference observed during testing between the original water calibration and the tests on

natural gas and nitrogen was ±0.5%3. No linearization or adjustment was applied after the original

factory calibration on water was performed. Compensation for the known effect of pressure on the meter

was applied. A Coriolis meter installed in an independent gas calibration laboratory for testing is shown

in Figure 5.

Fig.5. Coriolis Meter Installed for Independent Gas Laboratory Testing4

Coriolis meter designs that have not yet demonstrated transferability of calibration fluids are required to

be flow calibrated on gas as prescribed in Section 7.1 of AGA 11.

b. Pressure Effect Compensation

AGA 11 describes the effect that internal line pressure can have on some Coriolis meter designs and sizes.

AGA 11 includes the equation that is used to perform a linear correction which applies the compensation

factor (PEffect - in units of % of flow rate per unit of pressure) that is required to compensate accurately as

the line pressure deviates from the calibration pressure (PCal). It is important to note that not all Coriolis

meters exhibit a measurable effect. As the size of the meter increases, the likelihood also increases that a

pressure effect will occur. Compensation factors are published for all Micro Motion meters that exhibit a

pressure effect and Micro Motion meters have the ability to automatically apply compensation as it is

described in AGA 11.

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The pressure compensation applied by a Micro Motion meter is optional and may be activated or

deactivated through the device configuration. When activated, pressure compensation can be

implemented in one of two ways. The first method allows the operator to manually enter the service line

pressure as a fixed value. This is a simple method that can be employed when it is known that the line

pressure will be relatively constant. In cases where it is expected that the line pressure will vary

considerably, the second method can be employed in which a pressure reading is read as a live input by

the Coriolis meter and used for dynamic pressure compensation.

An example of independent laboratory as-found test data that is both uncompensated and then

compensated for pressure effect is shown in Figure 6. The meter was initially calibrated at the factory on

water at approximately 20 psig. The application of the correct pressure effect compensation (applying

correction from 20 psig to 740 psia) causes the measurements to meet the manufacturer’s published

specifications.

Fig.6. Large Coriolis Meter Test Data Uncorrected and Corrected for Pressure Effect

For any specific meter design and size, if the Coriolis meter manufacturer has not provided a pressure

correction value or declared that the meter in question has no pressure effect, then it is necessary for an

independent gas test laboratory to ensure that any pressure effect is addressed. This can be done either by

calibrating the meter at the service average line pressure, if known, or by testing to characterize the

pressure effect compensation that will need to be applied to the meter while it is in service.

c. Multi-Point Piecewise Linear Interpolation

Coriolis meters have traditionally used the technique of applying a single factor over the entire flow range

to adjust meters during calibration. This single factor may often come from the original factory

calibration or by using the FWME method. The original factory calibration is typically established at a

single flow rate and subsequently verified across the range of the flow meter. The FWME method applies

a single factor to all flow rate measurements and is usually applied after testing a meter against an

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Erro

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% of QMax

Natural Gas at 740 psiaTest Results - CMFHC2M - Pigsar

Uncompensated

Pressure Effect Compensated

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independent reference. A single-factor adjustment method for calibration is usually quite acceptable

because many Coriolis meters are inherently linear within AGA 11 limits over a wide range of flow rates.

Although gas flow measurement with Micro Motion ELITE CMF meters will meet both the AGA 11

maximum allowable error requirements of ±0.70% and the published manufacturer’s specifications of

±0.35% without the benefit of any form of piecewise linearization adjustment, recent work is showing

that the application of the multi-point piecewise linear interpolation method (PWL) has the potential to

achieve even greater accuracy during calibration than is otherwise possible. ONEOK and Emerson

Process Management have worked together on a program of testing with independent labs to determine

whether or not, and by how much, the accuracy of gas meter test results can be improved.

3. Implementation of PWL and Pressure Compensation of Coriolis Meters by Independent Gas

Calibration Laboratories

Emerson has developed an optional software feature in the Micro Motion ELITE CMF meters that

provides qualified independent gas calibration laboratories with the capability to program the meter with

up to ten adjustment points that will thereafter be applied for PWL adjustment of the meter flow

indication. The adjustment applied by this method is identical to that shown earlier in Figure 3. Meters

must be specially ordered with the necessary software option for PWL capability before they are sent to a

qualified laboratory for the calibration to be performed.

All ELITE CMF meters are equipped with a standard feature that may be configured and activated to

perform pressure compensation.

To date, Emerson has qualified three independent gas calibration laboratories in North America to

perform multi-point linear interpolation calibrations of Micro Motion ELITE CMF meters; Colorado

Engineering Experiment Station, Inc. (CEESI), Southwest Research Institute (SwRI), and TransCanada

Calibrations (TCC). These labs have received the tools, procedures, and training that are needed to

determine and program the PWL settings.

The procedure to perform PWL calibrations of Micro Motion ELITE CMF meters follows these basic

steps:

1. The meter is installed in the laboratory to meet or exceed manufacturer and operating company

recommendations.

2. The meter zero setting is verified and adjusted, if needed, according to manufacturer and

operating company recommendations and policies.

3. The meter pressure compensation is activated, if needed, and configured appropriately to apply

the correct compensation during the collection of all as-found and as-left data.

a. (Alternative method with no pressure compensation activated)

An alternative method for calibrating the meter is possible with the pressure

compensation deactivated. When this method is used, the laboratory calibration pressure

(PCal) value should be changed at the end of the procedure from the original factory

calibration pressure to the independent laboratory calibration pressure. For meters that

do not require pressure compensation, it is not necessary to adjust the PCal value.

4. The initial (as-found) data is collected covering the flow range for the application.

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5. The initial (as-found) data is reviewed and up to ten flow rates are selected where the

linearization adjustment points will be set so as to optimize the overall results. The correction

values to be applied at the selected flow rates are then determined based on the average error of

the as-found data that was recorded at each of these flow rates. Linearization points will not be

selected at flow rates below the Qt flow rate because adjustment in the range of the lowest flow

rates of the meter is better accomplished with the meter zero setting.

6. The established PWL points are programmed into the meter configuration.

7. Verification test data is collected and reviewed to assess the successful implementation of the

PWL adjustment. Often, flow rates that are different than the flow rates selected for linearization

will be chosen for the verification tests in order to thoroughly test the effectiveness of the

adjustment.

Following the installation of the meter in service, overall system metrics will be monitored to ensure that

no bias shift in the performance of the meter has occurred to adversely impact the flow measurement.

Examples of the resulting improvements that are being realized with PWL adjustment can be seen in

Figures 7 through 12. The “as-found” data shown in these figures represents the meter performance in the

gas calibration laboratory as it was received following the initial factory calibration on water. The

“verification” data shown represents the data that was collected later after the PWL adjustments were

completed.

Fig.7. Example of PWL Results with a CMF100 1-inch meter

Complete Data Set

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Verification Data

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Fig.8. Example of PWL Results with a CMF100 1-inch meter

Averages at Each Flow Rate

Fig.9. Example of PWL Results with a CMF200 2-inch meter

Complete Data Set

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As Found Averages by Flow Rate

Verification Averages by Flow Rate

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Verification Data

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Fig.10. Example of PWL Results with a CMF200 2-inch meter

Averages at Each Flow Rate

Fig.11. Example of PWL Results with a CMF300 3-inch meter

Complete Data Set

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As Found Averages by Flow Rate

Verification Averages by Flow Rate

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Fig.12. Example of PWL Results with a CMF300 3-inch meter

Averages at Each Flow Rate

a. Importance of the Correct Implementation of Pressure Compensation and PWL Together

During Coriolis Meter Calibration

The best practice is to apply PWL adjustment independently of pressure correction. This is achieved by

activating pressure compensation during the collection of the initial (as-found) data that is to be used to

establish the set of adjustment point values. With this method, the linearization can be subsequently

applied regardless of the service line pressure, while the pressure correction can be adjusted

independently and applied with flexibility to accommodate line pressure changes and live pressure

compensation.

An alternative method combines pressure compensation together with linearization as part of the PWL

adjustment. This can be done by collecting the initial (as-found) data at the service line pressure with the

meter pressure effect compensation deactivated. In this implementation, the resulting multi-point

adjustment values will include both linearization and pressure compensation for that service pressure.

The value of PCal will henceforth become the pressure that was applied during the collection of the initial

(as-found) data in the gas calibration laboratory instead of the pressure that was applied during the initial

factory calibration on water. As a result, there will be zero pressure compensation when the line pressure

is equal to this new PCal value, and future pressure compensation will be based on the difference between

any new line pressure and this new PCal calibration pressure baseline.

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As Found Averages by Flow Rate

Verification Averages by Flow Rate

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4. In-Situ Secondary Verification of Coriolis Meter Calibration

One of the most sought-after benefits of Coriolis meters is that the calibration remains very constant over

time if nothing occurs to damage the meter flow tubes structurally. This is why diagnostic tools that

accurately monitor the structural health of a Coriolis meter are useful as a tool for secondary verification

of the meter calibration that can be relied on, even after lengthy periods of time have passed since the

most recent calibration against a primary or secondary flow reference standard.

Micro Motion ELITE CMF meters can be equipped with an optional diagnostic feature called Smart

Meter Verification (SMV) that uses a sophisticated analysis the Coriolis meter flow tube vibration

response characteristics to assess and trend the structural consistency of the meter flow tubes. If the

structure of the meter is found by the SMV tool to be consistent over time, this result indicates that the

meter’s flow calibration has remained unchanged.

As discussed earlier in this paper, a Coriolis meter may be installed directly into service for natural gas

custody transfer after the factory calibration on water, or it may be sent to an independent gas calibration

laboratory for calibration that may or may not implement PWL adjustments. In either case, the value of

the investment in equipment and calibration can be prolonged and preserved by using an automated

secondary verification diagnostic tool like the Micro Motion Smart Meter Verification feature.

5. Impact of Zero

For a flow metering device, there are three potential types of offset; zero, span, and linearity. When the

zero of the flow metering device is offset, that specific amount of error results in a consistent bias across

the entire flow range (see figures 13 and 14). The flow calibration, on the other hand, impacts the

measurement by the same percentage across the entire flow range (see figures 13 and 15).

Fig.13. Example of linear device with a positive meter zero offset

and flow calibration factor applied for slope adjustment

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Fig.14. Example of linear device where the slope or flow calibration

factor (from Fig. 13) remains unchanged, but the zero has shifted down

Fig.15. Example of linear device where the meter zero (from Fig. 13)

remains unchanged, but the flow calibration factor has changed

The meter zero typically will have little effect in terms of percentage of rate offset at high flow rates, but

can become very important at low flow rates where the zero offset is a much higher percentage of the

flow. Since gas applications have low density, the mass flow rates through the meter are typically much

smaller than liquid mass flow rates through a similar line size, so achieving a proper meter zero is

especially important for gas.

All Micro Motion Coriolis meters are zeroed during the factory calibration. In most installations, that

initial zero that is captured may be the best zero for the meter and should not be changed. However, some

things can occasionally impact the zero including temperature, mounting conditions, etc. Some

manufacturers recommend always capturing an installed meter zero, while others claim there is never a

need to zero. Micro Motion offers a zero verification tool that looks at eight parameters to determine if

the flow is stopped and the process conditions are stable enough to determine whether or not the currently

captured zero is the best zero. If conditions are found to be stable and the current zero is not the best zero

for the application, the tool will recommend the user on the appropriate actions. This is a simple way

with a touch of a button to insure the meter has the best zero without having to change the zero value.

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6. Conclusions

Coriolis meters that are properly designed and constructed for natural gas custody transfer service will

meet the basic AGA11 maximum allowable error requirements of ±0.70% above the Qt flow rate without

the need for any form of linearization. Micro Motion ELITE CMF meters are designed to achieve

±0.35% accuracy in mass flow measurement of natural gas based on the initial factory calibration using

water and without any further adjustment or linearization other than the application of published pressure

compensation, when it is needed.

However, it has been found that accuracy improvements beyond the AGA 11 requirements and the

manufacturer’s specifications can be achieved in independent laboratory tests by applying the PWL

adjustment method over the range of flow rates tested. Results of testing to date have shown that PWL

adjustment of Micro Motion ELITE CMF Coriolis meters during calibration by independent gas

calibration laboratories consistently yields results as good as ±0.10% or better in the averages at each

flow rate over the calibrated flow range during the verification tests and Emerson offers an option to

make this correction in the transmitter. It is important to note that the overall combined uncertainty will

always include the uncertainty of the laboratory reference standards.

The next logical step in this work to further confirm the potential value of PWL adjustment of Coriolis

meters will be to conduct round robin testing of meters that have been calibrated with this method

between multiple independent accredited gas calibration laboratories in order to demonstrate that PWL

adjustment results are transferrable from one lab to the next. Parties interested in learning more about this

ongoing work are invited and encouraged to contact the authors.

1 Buttler, M., Gibson, R., McCargar, G., Stappert, K., Wyatt, T., The Practical Application of Multi-

Point Piecewise Linear Interpolation (PWL) and Other Developing Trends with Coriolis Meters for

Natural Gas Custody Transfer Applications, April 2015 2 AGA Report No. 11, API MPMS Chapter 14.9, Measurement of Natural Gas by Coriolis Meter,

American Gas Association, 400 N. Capitol Street, N.W., 4th Floor, Washington, DC 20001 3 Test Report Number NMi-12200340-02, Project Number 12200340, NMi Certin B.V., Hugo de

Grootplein 1, 3314 EG Dordrecht, The Netherlands 4 Wyatt, T., Stappert, K., Large Coriolis Meters and the Applicability of Water Calibrations for Gas

Service