PS-G-13 — Provisional Specifications and Procedures for the Approval of Correction Devices and Linearization Functions Incorporated in Meters and Flow Computers

PS-G-13 — Provisional Specifications and Procedures for the Approval of Correction Devices and Linearization Functions Incorporated in Meters and Flow Computers (PDF, 125.6 KB, 8 pages)

Date: 2006-03-31
Provisional Specification: PS-G-13
Category: Natural Gas

Table of Contents

1.0 Scope

This document provides specification requirements and test procedures for the approval evaluation of meter performance enhancement schemes based on the linearization or curve fitting of uncorrected or raw flow calibration data. This document applies to schemes which are incorporated in electronic flow computers, correction devices, flow meters and supporting software external to the device, and are intended to be user accessible and programable at the time of initial verification.

This document shall be read in conjunction with the specifications particular to each type of meter.

These recommendations address two specific types of meter performance enhancement schemes. These are:

  1. The selection of K or meter factors as a function of flowrate and,
  2. The selection of correction factors based on 4-20 ma inputs from transmitters.

2.0 Authority

These specifications are issued under the authority of section 12 of the Electricity and Gas Inspection Regulations.

3.0 References

3.1 Measurement Canada's "Principles for Correction Devices Used in the Measurement of Natural Gas".

3.2 Measurement Canada's "Provisional Specifications for the Verification of Correction Devices andLinearization Functions Incorporated in Meters and Flow Computers".

4.0 Introduction to Meter Performance Enhancement Schemes

There are a number of meter performance enhancement schemes commonly available in flow computers and correction devices. For discussion purposes, these schemes can be divided into the following three general categories:

4.1 Linear Interpolation

In this scheme, sometimes also referred to as "point-to-point linearization", separate and discreet straight lines of the form Y = mX + b are drawn between adjacent predetermined calibration values. The meter performance correction values (either meter factors or K factors) are selected by the flow computer or correction device relative to its determination of the fluid flowrate. These values are used to correct the raw meter pulse signal and provide an estimate of the true value of flow.

4.2 Modelling Equation

This scheme employs the reduction of calibration data (meter or K factor vs. flowrate) using a preselected modelling equation. One model commonly chosen is a 4th order equation. Data manipulation is usually performed using software external to the flow computer or correction device, and results in a series of coefficients (a, b, c, d, e, etc.) and an estimate of the uncertainty of the curve fit being provided. The equation coefficients are then programmed into the correction device or flow computer. Corrections are then calculated using the same form, by the flow computer or correction device, and used to correct the "raw meter pulse signal" Footnote 1 and provide an estimate of the true value of flow.

4.3 Discreet Step Interpolation

A third and now uncommon scheme is "discreet step interpolation". This scheme involves the application of a single correction factor for each specific range of flowrates.

5.0 Evaluation of Linear Interpolation Schemes

Meters which contain electronics containing user-programmable linearization schemes (unique coefficients for each individual meter) shall first be evaluated against the accuracy tolerances (specified in the applicable meter specification) with the meter's linearization function disabled. The meter shall then be retested in the manner described below, with the linearization function enabled. For ultrasonic meters, the linearity tolerance (specified in PS-G-06) shall be applied using test results for which the meter's linearization function was enabled.

5.1 Recommended Test Points for the Evaluation of Linear and Discreet Step Interpolation Using Simulated Inputs

Standard test protocols require the meter to be evaluated at a minimum of five flowrates (10 percent, 25 percent, 50 percent, 75 percent, and 100 percent of Qmax). These cardinal points, with slight modifications, shall be used as the data points to be programmed into the flow computer for testing. Table 1 lists the recommended values to be entered in the flow computer.

Table 1 — Values to be programmed into correction devices for evaluation purposes
Cardinal points (% Qmax) Error value to be programmed (%) Meter factor to be programmed K factors to be programmed
10 -1.00 1.01000 1.01000 x Base K
25 1.00 0.99000 0.99000 x Base K
50 0.50 0.99500 0.99500 x Base K
75 0.01 0.99990 0.99990 x Base K
90 0.05 0.99950 0.99950 x Base K

The evaluation procedure shall then be used to determine if the meter or flow computer is able to correctly calculate the intermediate values between the cardinal points in Table 1, and to determine if the values applied above and below the limiting values were determined in accordance with the requirements of Measurement Canada's "Principles for Correction Devices Used in the Measurement of Natural Gas".

Table 2 — Expected correction values as a function of Qmax
Test points Table 2, note 1 (% Qmax) Expected value (%) Expected Meter factor Expected K factor
Table 2, note 1 The selected flow rate shall be within ±5% of the recommended flow rate. Return to Table 2, note 1 reference
5 -1.00 1.01000 1.01000 x Base K
15 0.00 1.00000 1.00000 x Base K
35 0.75 0.99250 0.99250 x Base K
60 0.30 0.99700 0.99700 x Base K
95 0.05 0.99950 0.99950 x Base K

Generally, the value applied from zero flowrate to the first cardinal point shall be equal to the value at the first cardinal point. Similarly, the value applied from the last cardinal point to Qmax and beyond, shall be the value of the last cardinal point. Alternatively the values applied outside the bounds of the cardinal points can be the mean of the cardinal points.

The method to determine which correction factor has been applied will vary depending on the flow computer's configuration and design. The maximum expected frequency and voltage signal shall be determined from the flow computer's nameplate or manufacturer's literature. In the case of a pulse input, the average value of the K factor of the meter to be used with the flow computer is also required. Once this has been determined, the maximum frequency of input (Qmax) can be determined. Knowing the above, a suitable pulse generator and counter can then be selected for use in the evaluation.

5.2 Accuracy Test Procedure for Linearized Flowrates using Simulated Inputs

This method assumes that the effects of other correction factors can be determined and isolated from the determination of the metered volume (or mass). It does not apply to devices that do not use pulse inputs signals from a metering element. In these cases, the meter and linearization equipment will need to be flow tested as per section 6.1.

This method is also based on the assumption that the linearization value determined and applied by the flow computer cannot be directly displayed. This value must therefore be calculated based on the input pulse count and the associated frequency. From this data, the expected meter volume (or mass) indication and the value determined by the flow computer can be determined and compared. The specifics of the calculation will again be based on the methods used in the flow computer. These methods can generally be broken down into two types, as shown by equations 1 and 2 below:

V expected = Pulse count ÷ Calculated Linearizing K factor

V expected = (Pulse count × Calculated Linearizing Mf) ÷ Base K factor

Where, Mf = Meter Factor

In both cases the frequency of the simulated pulse input must be known in order to determine the value of the K factor or Mf which should have been used by the flow computer. Once the frequency has been determined, the corresponding value in Table 2 can be used in equation 1 or 2 to determine the expected indicated volume (Vexpected) from the flow computer. It is unlikely that the exact flow or pulse rate value in Table 2 can be achieved, and in these cases the measured input frequency shall be used to calculate the corresponding K factor or meter factor. The equation shall be the same linearization equation used in the flow computer. This procedure shall then be repeated for each value of flowrate in Table 2.

Linearization Error (%) = ((V indicated - V expected) ÷ V expected) × 100

The performance of the flow computer's linearization function shall then be determined by comparing the mathematically determined volume throughput to the indicated throughput.

The error in the linearization shall not exceed ±0.1 percent Footnote 2.

6.0 Evaluation of Modelling Equations for Curve Fitting

Unless otherwise approved by Measurement Canada Engineering & Laboratory Services, the modelling equation for turbine, rotary and ultrasonic meter performance shall take the general form of:

Y = a + b (1 ÷ X) + c(X) + d(X^2) + e(X^3)

Other equations may be approved depending on their suitability for the particular meter's performance curve. The curve model used shall be stated in the Notice of Approval.

6.1 Evaluation of Curve Fitting Interpolation Schemes using the Flow Testing Method

This method is usually applied to meters which incorporate curve fitting interpolation schemes which cannot be tested using a simulated input. This method can also be applied to flow computers when they are included as part of the metering assembly during flow testing. This scheme would typically apply to some types of ultrasonic meters.

The evaluation of the flow computer's ability to determine the volumetric output, given a predetermined set of coefficients, is divided into three basic steps. The first is the evaluation of the software and the suitability of the modeling equation, the second is the ability of the equation to predict meter performance using standard test points, and the third is the ability of the device to apply the coefficients during operation.

6.2 Policy for the Application of Linearization Schemes to Ultrasonic Meters

Meters which have user-programmable linearization factors (which will differ for each individual meter), must be first evaluated against the specified error tolerance with the meter's linearization function disabled, and then retested (as outlined in the steps below) with the linearization function enabled. Both of these two sets of test results must fall within the error tolerance of ±1.0 percent. The linearity error tolerance specified in PS-G-06 will then be applied using test results for which the meter's linearization function was enabled.

Step 1 Evaluation of the Software and the Suitability of the Modeling Equation

Although standard test protocols require the meter to be evaluated at a minimum of five flowrates (10 percent, 25 percent, 50 percent, 75 perent, and 100 percent of Qmax), these cardinal points are not sufficient for the determination of the flow equation's coefficients. Generally, three data points are required per coefficient. Therefore, if the equation takes the form of the 4th order equation in the general form below, a total of 3 x 5 =15 points will be needed

Dev (i) = a + b (1 ÷ Qi) + c(Qi) + d(Qi^2) + e(Qi^3)

Where, Dev(i) is the predicted meter deviation, and Q, is the meter flowrate or Reynolds Number.

Because the slope of the performance curve for most meter types fluctuates dramatically below 20 percent of Qmax, the distribution of the test points should not be evenly distributed as a function of flowrate. The majority of the calibration points need to be concentrated at the lower flows and in areas of rapidly changing slope. In the case of meters exhibiting typical performance curves with 15 points, this can be accomplished by distributing the calibration points in accordance with the function below. (Here, the same specification as used in OIML R 117 [6] is adopted, after modification, for use in approval evaluation work.)

Qi = (Qmin ÷ Qmax)^((i - 1) ÷ (N - 1)) × Qmax

Where, i is the rank number of the test flowrate, N is the minimum number of test points, and j is the number of variables in the evaluation equation, according to:

N = 1 + 5 · log(Qmax ÷ Qmin)

Where, Qmin is the minimum flowrate the meter will be operated at, Qmax is the maximum rated meter flowrate, and N is rounded to the nearest integer.

Once the flowrate and deviation values from the calibration certificate have been entered into the software package under evaluation and the coefficient values have been predicted, the precision of the prediction shall be evaluated. This shall be done by comparing the values of meter deviation predicted by equation 5 to those supplied on the certificate of calibration. For each flowrate listed in the certificate of calibration, the predicted correction value shall be determined using this equation. The difference or residual between the predicted value and the value listed in the certificate of calibration shall then determined. Two times the standard deviation of all the differences shall not exceed 0.2 percent. Also, any one value shall not exceed 0.5 percent.

Step 2 The Ability of the Equation to Predict Meter Performance Using Standard Test Points

To accomplish this, the values of the coefficients for the modelling equation shall be determined using the standard test points stipulated in the specific specification applicable to the meter. These usually are 10 percent, 25 percent, 50 percent, 75 percent, and 100 percent of Qmax Footnote 3 , and shall be selected from the 15 points provided on the certificate of calibration. Once computed, the new coefficients shall be programmed into the flow computer or meter. Again, the difference or residual between the predicted value and the value listed in the certificate of calibration shall then be determined. Two times the standard deviation of all the differences shall not exceed 0.2 percent.

Step 3 Ability of the Device to Apply the Coefficients During a Simulated Meter Run

The final step in the evaluation is to evaluate the flow computer's ability to apply the coefficients during operation. To accomplish this, the performance of the flow computer or meter shall be evaluated using the values of the coefficients previously determined in step 2.

In this step and in some cases, inputs to flow computers can be simulated. In most cases for flow meters, additional flow data will be required. Here again, the test points stipulated in the particular specification for the meter shall be applied. These usually are 10 percent, 25 percent, 50 percent, 75 percent, and 100 percent of Qmax Footnote 4.

In addition to the meter performance criteria, the result shall indicate a reduction in the meter error relative to the uncorrected values.

Where it is practical to simulate the input to the flow computer, use the method in section 6.0 above.

7.0 Introduction to the Selection of Minimum Values for Meter Flow Rates

There are a number of criteria to be considered when selecting the minimum flowrate for a metering system. Of principal importance are the accuracy, repeatability and reproducibility of the meter output, and the accuracy, repeatability and reproducibility of the standard used to determine the performance of the meter.

The most common approach used to determine the meter's minimum flowrate is to set bounds for the acceptable meter accuracy, and then limit the flowrate to the range in which the meter's performance curve remains within those bounds. The resulting number is commonly referred to as the "turndown ratio". This method usually applies well to meters without linearization schemes.

When the linearization schemes discussed above are employed, meter accuracy is no longer the primary factor to be considered in the selection of the minimum meter flow rate. In these cases, two factors take precedence. The first is the uncertainty of the test data at low flow rates and the second is the ability of the flow computer to correctly determine the meter flow rate. For the purpose of ease of application, reasonable bounds for these values have been established based on maximum acceptable uncertainty values. The minimum flow rate of a meter then becomes the rate at which:

  1. the uncertainty in the determination of the accuracy value by the standard exceeds ±0.3 percent,Footnote 5.
  2. prior to correction, the change in the raw meter correction does exceed 0.3 percent per 5 percent change in flowrate.
  3. prior to correction, the meter performance exceeds the legal bounds of ±1.0 percent Footnote 6, Footnote 7 between 10 and 100 percent Qmax, and,
  4. the meter repeatability exceeds the prescribed limits.

8.0 Introduction to Linearization Test Requirements for Transmitters

There are also a number of linearization schemes available in flow computers for transmitter inputs. Here the linear interpolation of correction factors as a function of the input value is common. In some instances the flow computer can also use a predetermined mathematical function which models the transmitte's performance.

Typically, transmitters require a three-point calibration. This process differs from meter linearization schemes in that the values are usually sensed by the transmitter and the corresponding true value programmed into the flow computer or transmitter. These points are typically zero, span, and one intermediate value.

The evaluation procedure will determine if the instrument is able to correctly calculate the intermediate values between the three(3) calibration points. This can be done simply by determining the performance of the transmitter at 10 percent, 25 percent, 50 percent, 75 percent, and 100 percent of full scale, in an increasing and decreasing manner. The values determined by the flow computer shall be within the acceptable limit of error.

9.0 Additional Information for Inclusion in the Notice of Approval

In order to verify or reverify the performance of the linearization function once the metering device is placed in service, it is recommended that the Notice of Approval contain the following additional information:

  1. the form(s) of the equation(s) and/or method used for the interpolation,
  2. the type of meter(s) the equation(s) is modelling, if the function resides in the flow computer or correction device; and,
  3. the minimum flowrate applicable for each meter type modelled.

Alan E. Johnston
President

Footnote 1 Note that the term "raw meter pulse signal" does not imply that the signal has not been processed from the inferred measurement to a volumetric (or mass) output. (Return to footnote 1 reference)

Footnote 2 Note that this determines the correctness of the mathematical model. For ultrasonic meters, the linearization error tolerance specified in PS-G-06 is to be applied after the linearization function is programmed and functionning, in order to meet this requirement. (Return to footnote 2 reference)

Footnote 3 Note that the Linearization specification values stipulated in PS-G-06 are applied after the linearization function is programmed and functionning. (Return to footnote 3 reference)

Footnote 4 Note that the Linearization specification values stipulated in PS-G-06 are applied after the linearization function is programmed and functionning. (Return to footnote 4 reference)

Footnote 5 The Laboratory providing the calibration data for review shall provide uncertainty values for each of the test flowrates as well as an overall estimate. Unless otherwise authorized by Measurement Canada Engineering and Laboratory Services, the data shall be provided by a laboratory recognized by Measurement Canada in Bulletin G-16. (Return to footnote 5 reference)

Footnote 6 This requirement is consistent with Measurement Canada's "Principles for Correction Devices Used in Natural Gas Measurement", but does not apply to reference meters. (Return to footnote 6 reference)

Footnote 7 Note that no data should be collected or correction points calculated below minimum flowrate specified by the manufacturer of the measuring element or that specified in the Notice of Approval. (Return to footnote 7 reference)