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

Part 4—Background, Development, Implementation Procedure, and Example Calculations

AGA Report No. 3 Part 4

Manual of Petroleum Measurement Standards Chapter 14.3.4

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

American Petroleum Institute

200 Massachusetts Avenue, Street, NW Washington, DC 20001

FOURTH EDITION, OCTOBER 2019

An American National Standard

ANSI/API MPMS Ch. 14.3.4/AGA Report No. 3, Part 4

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iii

1. Scope 1

2. Normative References 1

3. Symbols, Units, and Terminology 1

   1. General 1

   2. Symbols and Units 1

4. History and Development 4

   1. Background 4

   2. Historical Database 6

   3. Recent Data Collection Efforts 6

   4. Basis for Equation 12

   5. Reader-Harris/Gallagher Equation 14

   6. Expansion Factor Revision 21

   7. Rigorous Method for Calculation of Mass Flow Uncertainty 24

   8. Research on Installation Effects 26

5. Implementation Procedures 26

   1. Introduction 26

   2. Solution for Mass or Volume Flow Rate 27

   3. Special Procedures and Example Calculations for Natural Gas Applications 39

   4. Example Calculations 55

Annex A (informative) Development of Flow Equation Algorithm 97

Bibliography 104

Figures

1. Flange Tap Data Comparison-Mean Deviation (%) versus Nominal Beta Ratio 17

2. Flange Tap Data Comparison-Mean Deviation (%) versus Nominal Pipe Diameter 18

3. Flange Tap Data Comparison-Mean Deviation (%) versus Reynolds Number Ranges 18

4. Corner Tap Data Comparison-Mean Deviation (%) versus Nominal Beta Ratio 18

5. Corner Tap Data Comparison-Mean Deviation (%) versus Reynolds Number Ranges 19

6. D-D/2 (Radius) Tap Data Comparison-Mean Deviation (%) versus Nominal Beta Ratios 19

7. D-D/2 (Radius) Tap Data Comparison-Mean Deviation (%) versus Reynolds Number Ranges 19

8. Scatter Diagram Based on Buckingham Equation 20

9. Scatter Diagram Based on Reader-Harris/Gallagher Equation 20

1. Number of Iterations Required to Solve for Orifice Plate Coefficient of Discharge-Direct Substitution Method 102

2. Number of Iterations Required to Solve for Orifice Plate Coefficient of Discharge-Newton-Raphson Method 103

Tables

1. Nominal Tube Diameters and Beta Ratios Included in API/GPA Discharge Coefficient Research 8

2. Regression Data Points by Tapping Configuration 10

3. Regression Database Point Distribution for Flange Taps 10

4. Regression Database Point Distribution for Corner Taps 11

5. Regression Database Point Distribution for D-D/2 (Radius Taps) 11

6. Example Y1 Calculated Values Where k = 1.1 22

7. Example Y1 Calculated Values Where k = 1.3 23

8. Example Y1 Calculated Values Where k = 1.5 23

   
   

9. Typical Values of Linear Coefficients of Thermal Expansion 29

10. Units, Conversion Constants, and Universal Constants 30

11. Example Test Case Abbreviations 55

Introduction

This part of the standard for Concentric, Square-edged Orifice Meters provides the background and history of the development of the standard and recommends a method to solve the flow equations for mass and volumetric flow.

vii

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

Part 4—Background, Development, Implementation Procedures, and Example Calculations

1. Scope

   Chapter 14.3, Part 4 describes the background and development of the equation for the coefficient of discharge of flange-tapped, square-edged, concentric orifice meters, and recommends a flow rate calculation procedure. The recommended procedures provide consistent computational results for the quantification of fluid flow under defined conditions, regardless of the point of origin or destination, or the units of measure required by governmental customs or statute. The procedures allow different users with different computer languages on different computing hardware to arrive at almost identical results using the same standardized input data.

   
   

2. Normative References

   The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

   
   

   API Manual of Petroleum Measurement Standards

   
   

   Chapter 12.2.1, Calculation of Petroleum Quantities Using Dynamic Measurement Methods and Volume Correction Factors, Part 1—Introduction

   
   

   Chapter 14.2/AGA Report No. 8, Compressibility Factors of Natural Gas and Other Related Hydrocarbon Gases

   
   

   Chapter 14.3.1/AGA Report No. 3, Part 1, Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids— Concentric, Square-edged Orifice Meters, Part 1—General Equations and Uncertainty Guidelines

   
   

   Chapter 14.3.2/AGA Report No. 3, Part 2, Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids— Concentric, Square-edged Orifice Meters, Part 2—Specification and Installation Requirements

   
   

   Chapter 14.3.3/AGA Report No. 3, Part 3, Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids— Concentric, Square-edged Orifice Meters, Part 3—Natural Gas Applications

   
   

3. Symbols, Units, and Terminology

   1. General

      
      

      The symbols and units used are specific to API MPMS Chapter 14.3.3/AGA Report No. 3, Part 3 and were developed based on the USC inch—pound system of units. Regular conversion factors can be used where applicable; however, if SI units are used, the more generic equations in API MPMS Chapter 14.3.1/AGA Report No. 3, Part 1 should be used for consistent results.

      
      

   2. Symbols and Units

Cd orifice plate coefficient of discharge

Cd  FT 

Cd

o

Cd

1

coefficient of discharge at a specified pipe Reynolds number for flange-tapped orifice meter first flange-tapped orifice meter coefficient of discharge constant within iteration scheme second flange-tapped orifice meter coefficient of discharge constant within iteration scheme

1