Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids— Concentric, Square-edged Orifice Meters

Part 1: General Equations and Uncertainty Guidelines

AGA Report No. 3 Part 1

Manual of Petroleum Measurement Standards Chapter 14.3.1

American Gas Association 400 North Captiol Street, NW Washington, DC 20001

American Petroleum Institute 1220 L Street, NW Washington, DC 20005

FOURTH EDITION, SEPTEMBER 2012 ERRATA, JULY 2013

An American National Standard

ANSI/API MPMS Ch. 14.3.1/AGA Report No. 3, Part 1

Special Notes

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Foreword

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iii

1. Introduction 1

   1. Scope 1

   2. Organization of Standard 1

2. Normative References 2

3. Terms, Definitions, and Symbols 3

   1. Terms and Definitions 3

   2. Symbols 7

4. Field of Application 8

   1. Applicable Fluids 8

   2. Types of Meters 9

   3. Uncertainty of Measurement 10

5. Method of Calculation 10

6. Orifice Flow Equation 10

   1. Velocity of Approach Factor (Ev) 12

   2. Orifice Plate Bore Diameter (d) 12

   3. Meter Tube Internal Diameter (D) 12

7. Empirical Coefficient of Discharge 13

   1. Regression Database 14

   2. Empirical Coefficient of Discharge Equation for Flange-tapped Orifice Meters 15

   3. Reynolds Number (ReD) 16

   4. Flow Conditions 16

   5. Pulsating Flow 17

8. Empirical Expansion Factor (Y ) for Flange-tapped Orifice Meters 19

   1. Upstream Expansion Factor (Y1) 20

   2. Downstream Expansion Factor (Y2) 21

9. In-situ Calibration 22

   1. General 22

   2. Meter Factor (MF) 22

10. Fluid Physical Properties 23

    1. Viscosity (μ) 23

    2. Density (ρt,p, ρb) 23

    3. Isentropic Exponent () 24

11. Unit Conversion Factors 24

    1. Orifice Flow Equation 24

    2. Reynolds Number Equation 25

    3. Expansion Factor Equation 25

    4. Flow Rate per Unit of Time Conversion 25

12. Practical Uncertainty Guidelines 28

    1. General 28

    2. Uncertainty Over a Flow Range 28

    3. Uncertainty of Flow Rate 28

    4. Typical Uncertainties 31

    5. Example Uncertainty Calculations 37

Annex A (informative) Discharge Coefficients for Flange-tapped Orifice Meters 40

Annex B (informative) Adjustments for Instrument Calibration and Use 51

Annex C (informative) Buckingham and Bean Empirical Expansion Factor (Y) for Flange-tapped

Orifice Meters 52

Bibliography 56

Figures

1. Orifice Tapping Location 5

2. Orifice Meter Elements 9

3. Contribution to Flow Error Due to Differential Pressure Instrumentation 29

4. Empirical Coefficient of Discharge: Uncertainty at Infinite Reynolds Number 32

5. Relative Change in Uncertainty: Dependence on Reynolds Number 32

6. Practical Uncertainty Levels. 34

Tables

1. Linear Coefficient of Thermal Expansion 13

2. Orifice Flow Rate Equation: Unit Conversion Factor (N1). 26

3. Reynolds Number Equation: Unit Conversion Factor (N2) 27

4. Empirical Expansion Factor Equation: Unit Conversion Factor (N3) 27

5. Uncertainty Statement for Empirical Expansion Factor 33

6. Example Uncertainty Estimate for Liquid Flow Calculation 38

7. Example Uncertainty Estimate for Natural Gas Flow Calculation 39

1. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 2-in. (50-mm) Meter

   [D = 1.939 in. (49.25 mm)] 40

2. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 3-in. (75-mm) Meter

   [D = 2.900 in. (73.66 mm)] 41

3. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 4-in. (100-mm) Meter

   [D = 3.826 in. (97.18 mm)] 42

4. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 6-in. (150-mm) Meter

   [D = 5.761 in. (146.33 mm)] 43

5. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 8-in. (200-mm) Meter

   [D = 7.625 in. (193.68 mm)] 44

6. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 10-in. (250-mm) Meter

   [D = 9.562 in. (242.87 mm)] 45

7. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 12-in. (300 mm) Meter

   [D = 11.374 in. (288.90 mm)] 46

8. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 16-in. (400-mm) Meter

   [D = 14.688 in. (373.08 mm)] 47

9. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 20-in. (500-mm) Meter

   [D = 19.000 in. (482.60 mm)] 48

10. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 24-in. (600-mm) Meter

    [D = 23.000 in. (584.20 mm)] 49

11. Discharge Coefficients for Flange-tapped Orifice Meters: Nominal 30-in. (750-mm) Meter

[D = 29.000 in. (736.60 mm)] 50

Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids— Concentric, Square-edged Orifice Meters

Part 1: General Equations and Uncertainty Guidelines

1. Introduction

   1. Scope

      
      

      This standard provides a single reference for engineering equations, uncertainty estimations, construction and installation requirements, and standardized implementation recommendations for the calculation of flow rate through concentric, square-edged, flange-tapped orifice meters. Both U.S. customary (USC), and international system of units (SI) units are included.

      
      

   2. Organization of Standard

      
      

      The standard is organized into four parts. Parts 1, 2, and 4 apply to the measurement of any Newtonian fluid in the petroleum and chemical industries. Part 3 focuses on the application of Parts 1, 2, and 4 to the measurement of natural gas.

      
      

      1. Part 1—General Equations and Uncertainty Guidelines

         
         

         The mass flow rate and base (or standard) volumetric flow rate equations are discussed, along with the terms required for solution of the flow equation.

         
         

         The empirical equations for the coefficient of discharge and expansion factor are presented. However, the basis for the empirical equations are contained in other sections of this standard or the appropriate reference document.

         
         

         In several sections of this revision of Part 1, identified errata have been changed relative to previous editions. In addition, this revision includes a change to the empirical expansion factor (Y) calculation for the flange-tapped orifice meters.

         
         

         For all existing installations, the decision as to which expansion factor equation to use shall be at the discretion of the parties involved. However, the parties should be cognizant of the following:

         
         

         1. If the calculated difference between previous revision (1990) Buckingham and Bean expansion factor equation (Annex C or API MPMS Ch. 14.3.3/AGA Report No. 3, Part 3, Annex G) and the new revised expansion factor equation is less than or equal to 0.25 %, then the expansion factor values produced by either expansion factor equation will be within the uncertainty of the new expansion factor database and the existence of any flow bias will be uncertain.

            
            

         2. However, if the calculated difference between expansion factor equations exceeds 0.25 %, then a variable flow

1

bias, which is a function of diameter ratio (β), isentropic exponent (, and ΔP  Pf

unless the new expansion factor equation is utilized.

ratio (x1), will be experienced

For the proper use of this standard, a discussion is presented on the prediction (or determination) of the fluid’s properties at flowing conditions. The fluid’s physical properties shall be determined by direct measurements, appropriate technical standards, or equations of state.

Uncertainty guidelines are presented for determining the possible error associated with the use of this standard for any fluid application. User-defined uncertainties for the fluid’s physical properties and auxiliary (secondary) devices are required to solve the practical working formula for the estimated uncertainty.