Api mpms 14 3 4 1992 (2006) scan (american petroleum institute)

A P I MPMS*L4-3-4 92 W 0732290 0506280 O31 W

Manual of Petroleum
Measurement Standards
Chapter 14-Natural Gas Fluids
Measurement
Section 3-Concent ric, Square-Edged
Orifice Meters
Part 4-Background, Development,
Implementation Procedures and
Subroutine Documentation
THIRD EDITION, NOVEMBER, 1992
REAFFIRMED, FEBRUARY 2006

AGCI

American Gas Association

Report No. 3, Part 4

Gas Processors Association

GPA 8185-92, Pari 4

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American Petroleum Institute
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Washington, D.C. 20005

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A P I M P M S * L 4 - 3 = 4 92 9 0732290 0506283 T78

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Manual of Petroleum
Measurement Standards
Chapter 14-Natural Gas Fluids
Measurement
Section 3-Concentric, Square-Edged
Orifice Meters
Part 4-BackgroundY Development,
Implementation Procedures and
Subroutine Documentation
THIRD EDITION, NOVEMBER, 1992

American
Petroleum
Institute

Copyright American Petroleum Institute
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API MPMS*L4.3*V 7 2

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0732270 050b282 904

SPECIAL NOTES
1. API PUBLICATIONS NECESSARILY ADDRESS PROBLEMS OF A GENERAL
NATURE. WITH RESPECT TO PARTICULAR CIRCUMSTANCES, LOCAL, STATE,
AND FEDERAL LAWS AND REGULATIONS SHOULD BE REVIEWED.

2. API IS NOT UNDERTAKING TO MEET THE DUTIES OF EMPLOYERS, MANUFACTURERS, OR SUPPLIERS TO WARN AND PROPERLY TRAIN AND EQUIP
THEIR EMPLOYEES, AND OTHERS EXPOSED, CONCERNING HEALTH AND
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UNDER LOCAL, STATE, OR FEDERAL LAWS.

3. INFORMATION CONCERNING SAFETY AND HEALTH RISKS AND PROPER
PRECAUTIONS WITH RESPECT TO PARTICULAR MATERIALS AND CONDITIONS SHOULD BE OBTAINED FROM THE EMPLOYER, THE MANUFACTURER
OR SUPPLIER OF THAT MATERIAL, OR THE MATERIAL SAFETY DATA SHEET.
4. NOTHING CONTAINED IN ANY API PUBLICATION IS TO BE CONSTRUEDAS
GRANTING ANY RIGHT, BY IMPLICATION OR OTHERWISE, FOR THE MANUFACTURE, SALE, OR USE OF ANY METHOD, APPARATUS, OR PRODUCT
COVERED BY LETTERS PATENT. NEITHER SHOULD ANYTHING CONTAINED
IN THE PUBLICATION BE CONSTRUED AS INSURING ANYONE AGAINST
LIABILITY FOR INFRINGEMENTOF LE'ITERS PATENT.

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5. GENERALLY, API STANDARDS ARE REVIEWED AND REVISED, REAFFIRMED, OR WITHDRAWN AT LEAST EVERY FIVE YEARS. SOMETIMES A ONETIME EXTENSION OF UP TO TWO YEARS WILL BE ADDED TO THIS REVIEW

CYCLE. THIS PUBLICATION WILL NO LONGER BE IN EFFECT FIVE YEARS
AFTER ITS PUBLICATIONDATE AS AN OPERATIVEAPI STANDARD OR, WHERE
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MATERIALS IS PUBLISHED ANNUALLY AND UPDATED QUARTERLY BY API,
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FOREWORD
This foreword is for information and is not part of this standard.
Chapter 14, Section 3, Part 4 of the Manual of Petroleum Measurement Standards
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 quantificationof 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.
This standard has been developed through the cooperative efforts of many individuals
under the sponsorship of the American Petroleum Institute, API, and the American Gas
Association, A.G.A., with contributions from the Gas Processors Association, GPA, and
others.
API publications may be used by anyone desiring to do so. Every effort has been made
by the Institute to assure the accuracy and reliability of the data contained in them; however, the Institute makes no representation, warranty, or guarantee in connection with this
publication and hereby expressly disclaims any liability or responsibility for loss or damage
resulting from its use or for the violation of any federal, state, or municipal regulation with
which this publication may conflict.
Suggested revisions are invited and should be submitted to the director of the Measurement Coordination Department, American Petroleum Institute, 1220 L Street, N.W.,
Washington, D.C. 20005.

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I

ACKNOWLEDGMENTS
From the initial data-collection phase through the final publication of this revision of
Chapter 14, Section 3, of the Manual of Petroleum Measurement Standards, many individuals have devoted time and technical expertise. However, a small group of individuals has
been very active for much of the project life. This group includes the following people:

H. Bean, El Paso Natural Gas Company (Retired)
R. Beaty, Amoco Production Company, Committee Chairman
D. Bell, NOVA corporation
T. Coker, Phillips Petroleum Company
W. Fling, OXY USA, Inc. (Retired), Project Manager
J. Gallagher, Shell Pipe Line Corporation
L. Hillburn, Phillips Petroleum Company (Retired)
P. Hoglund, Washington Natural Gas Company (Retired)
P. LaNasa
G. Less, Natural Gas Pipeline Company of America (Retired)
J. Messmer, Chevron U.S.A. Inc. (Retired)
R. Teyssandier, Texaco Inc.
E. UPP
K. West, Mobil Research and Development Corporation
During much of the corresponding time period, a similar effort occurred in Europe. The
following individuals provided valuable liaison between the two efforts:
D. Gould, Commission of the European Communities
F. Kinghorn, National Engineering Laboratory

M. Reader-Harris, National Engineering Laboratory
J. Sattary, National Engineering Laboratory
E. Spencer, Consultant
J. Stolz, Consultant
P. van der Kam, Gasunie
The American Petroleum Institute provided most of the funding for the research project.
Additional support was provided by the Gas Processors Association and the American Gas
Association. Special thanks is given to the Gas Research Institute and K. Kothari for
providing funding and manpower for the natural gas calculations used in this project and to
the National Institute of Standards and Technology in Boulder, Colorado, for additional
flow work.
J. Whetstone and J. Brennan were responsible for the collection of water data at the
National Institute of Standards and Technology in Gaithersburg, Maryland. C. Britton,
S . Caldwell, and W. Seid1 of the Colorado Engineering Experiment Station Inc. were responsible for the oil data. G. Less, J. Brennan, J. Ely, C. Sindt, K. Starling, and R. Ellington
were responsible for the Natural Gas Pipeline Company of America test data on natural gas.
Over the years many individuals have been a part of the Chapter 14.3 Working Group
and its many task forces. The list below is the roster of the working group and its task forces
at the time of publication but is by no means a complete list of the individuals who participated in the development of this document.
R. Adamski, Exxon Chemical Americas-BOP
R. Bass
M. Bayliss, Occidental Petroleum (Caldonia) Ltd.
R. Beaty, Amoco Production Company
D. Bell, NOVA Corporation
B. Berry
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J. Bosio, Statoil
J. Brennan, National Institute of Standards and Technology
E. Buxton
S. Caidweli
R. Chittum, American Petroleum Institute
T. Coker, Phillips Petroleum Company
H. Colvard, Exxon Company, U.S.A.
L. Datta-Bania, United Gas Pipeline Company
D. Embry, Phillips Petroleum Company
W. Fling
J. Gallagher, Shell Pipe Line Corporation
V. Gebben, Kerr-McGee Corporation
B. George, Amoco Production Company
G. Givens, CNG Transmission Corporation
T. Glazebrook, Tenneco Gas Transportation Company
D. Goedde, Texas Gas Transmission Corporation
D. Gould, Commission of the European Communities
K.Gray, Phillips Petroleum Company
R. Hankinson, Phillips 66 Natural Gas Company
R. Haworth
E. Hickl, Union Carbide Corporation
L. Hillburn

P. Hoglund, Washington Natural Gas Company
J. Hord, National Institute of Standards and Technology
E. Jones, Jr., Chevron Oil Field Research Company
M. Keady
K. Kothari, Gas Research Institute
P. LaNasa
G. Less
G. Lynn, Oklahoma Natural Gas Company
R. Maddox
G. Mattingly, National Institute of Standards and Technugy
E, McConaghy, NOVA Corporation
C. Mentz
L. Norris, Exxon Production Research Company
K.Olson, Chemical Manufacturers Association
A. Raether, Gas Company of New Mexico
E. Raper, OXY USA, Inc.
W. Ryan, El Paso Natural Gas Company
R. Segers
J. Sheffield
S. Stark, Williams Natural Gas Company
K. Starling
J. Stolz
J. Stuart, Pacific Gas and Electric Company
W. Studzinski, NOVA/Husky Research Company
M. Sutton, Gas Processors Association
R. Teyssandier, Texaco Inc.
V. Ting, Chevron Oil Field Research Company
L. Traweek, American Gas Association
E. VPP
E Van Orsdol, Chevron U.S.A. Inc.

N. Watanabe, National Research Laboratory of Metrology, Japan

V
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K. West, Mobil Research and Development Corporation
P. Wilcox, Total of France
J. Williams, Oryx Energy Company
M. Williams, Amoco Production Company
E. Woomer, United Gas Pipeline Company
C. Worrell, OXY USA, Inc.

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CONTENTS
Page

CHAPTER 14--NATW
GAS FLUIDS MEASUREMENT
SECTION 3.CONCENTRIC.
SQUARE-EDGED
ORIFICE METERS

APPENDIX 4-A-DEVELOPMENT OF FLOW EQUATION
SOLUTIONALGOEUTHM .......................................................
APPENDIX 4-B-RECOMMENDED ROUNDING PROCEDURES....................
APPENDIX 4-C-ROUND ROBIN TESTING .......................................................
Figures
4-1-Flange Tap Data Comparison-Mean Deviation (%) versus
Nominal Beta Ratio ......................................................................................
4-2-Flange Tap Data Comparison-Mean Deviation (%) versus
Nominal Pipe Diameter ................................................................................
4-3-Flange Tap Data Comparison-Mean Deviation (%) versus
Reynolds Number Ranges ............................................................................
4-4-Corner Tap Data Comparison-Mean Deviation (%) versus
Nominal Beta Ratio ......................................................................................
4-5-Corner Tap Data Comparison-Mean Deviation (%) versus
Reynolds Number Ranges ............................................................................
4-6-0-D/2 (Radius) Tap Data Comparison-Mean Deviation (%)
versus Nominal Beta Ratios .........................................................................

4-7-0-0/2 (Radius) Tap Data Comparison-Mean Deviation (%)
versus Reynolds Number Ranges .................................................................
4-8Ccatter Diagram Based on BuckinghamEquation .......................................
4-9Ccatter Diagram Based on Reader-HarridGallagherEquation ....................
4-A-1-Number of Iterations Required to Solve for Orifice Plate
Coefficient of Discharge-Direct Substitution Method .............................
4-A-2-Number of Iterations Required to Solve for Orifice Plate
Coefficient of Discharge-Newton-Raphson Method ...............................
Tables
4- 1-Regression Database Point Distribution for flange Taps .............................
4-2-Regression Database Point Distribution for Corner Taps .............................
4-3-Regression Database Point Distribution for D-D/2 (Radius) Taps...............

vii
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1

3

5
6
10
13
20

20
31
48

63
71
75

16
16
16
17
17
18
18
19
19
68
70
9
10
11

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4.1 Introduction and Nomenclature
4.1.1 Introduction ................................................................................................
4.1.2 Nomenclature .............................................................................................
4.2 History and Development
4.2.1 Background .................................................................................................

4.2.2 Historical Data Base...................................................................................
4.2.3 Recent Data Collection Efforts ..................................................................
4.2.4 Basis for Equation ......................................................................................
4.2.5 Reader-Harris/Gallagher Equation.............................................................
4.3 Implementation Procedures
4.3.1 Introduction .................................................................................................
4.3.2 Solution for Mass or Volume Flow Rafe ....................................................
4.3.3 Special Procedures and Example Calculations for Natural Gas
Applications ...............................................................................................
4.3.4 Example Calculations.................................................................................


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4-4-Typical Values of Linear Coefficients of Thermal Expansion ......................
4.5-Units. Conversion Constants. and Universal Constants ...............................

22

23

Tables (continued)
4-&Input Parameters for Six Example Test Cases (US. IP.Metric.
and SI Units) .................................................................................................
4-7-Intermediate Output for Example Test Case Number 1................................
4-8-Intermediate Output for Example Test Case Number 2 ................................
4-9-Intermediate Output for Example Test Case Number 3................................
4-10-Intermediate Output for Example Test Case Number 4 ..............................
4-11-Intermediate Output for Example Test Case Number 5 ..............................
4-12-Intermediate Output for Example Test Case Number 6 ..............................
4-B- 1-Recommended Rounding Tolerances .......................................................
4-C-1-Round Robin Test Parameters (US Units) ................................................
4-C-2-Round Robin Test Parameters (IP Units) ..................................................
4-C-3-Round Robin Test Parameters (Metric Units)...........................................
4-C-”Round Robin Test Parameters (SI Units) ..................................................
4-C-5-Selected Round Robin Test Results Matrix (US Units)............................
4 - C d S e l e c t e d Round Robin Test Results Matrix (SI Units) .............................

.

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49
51
53

55
57
59
61
74
76
77
78
79
81
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Chapter 14-Natural Gas Fluids Measurement
SECTION 3-CONCENTRIC,

SQUARE-EDGED ORIFICE METERS

PART 4-BACKGROUND, DEVELOPMENT, IMPLEMENTATION
PROCEDURES AND SUBROUTINE DOCUMENTATION
4.1
4.1.1

Introduction and Nomenclature
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.

4.1.2

NOMENCLATURE

The symbols used have, in some cases, been given a more general definition than that
used in other parts of API 2530. Some symbols have a different meaning than that defined
elsewhere in the standard. Care should therefore be given to the meaning of variables used
in this document.
Represented Quantity
Line& coefficient of thermal expansion of the orifice plate material.
Linear coefficient of thermal expansion of the meter tube material.
Ratio of orifice plate bore diameter to meter tube internal diameter (&I)
calculated at flowing temperature, $.
Ratio of orifice plate bore diameter to meter tube internal diameter (dD)
calculated at measured temperature, T,t.
Ratio of orifice plate bore diameter to meter tube internal diameter (d/D)
calculated at reference temperature, T,.
Orifice plate coefficient of discharge.
Coefficient of discharge at a specified pipe Reynolds number for flange-tapped
orifice meter.
First flange-tapped orifice plate coefficient of discharge constant within iteration
scheme.

Second flange-tapped orifice plate coefficient of discharge constant within
iteration scheme.
Third flange-tappedorifice plate coefficient of discharge constant within iteration
scheme.
Fourth flange-tapped orifice plate coefficient of discharge constant within iteration scheme.
Fifth flange-tapped orifice plate coefficient of discharge constant within iteration
scheme.
Orifice plate coefficient of discharge bounds flag within iteration scheme.
Orifice plate bore diameter calculated at flowing temperature $.
Meter tube internal diameter calculated at flowing temperature $.
Orifice plate bore diameter calculated at reference temperature T,.
Meter tube internal diameter calculated at reference temperature T,.
Orifice plate bore diameter calculated at measured temperature Tm.
Meter tube internal diameter calculated at measured temperature T,,.
Orifice plate coefficient of discharge convergence function derivative.

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A P I M P M S * 1 4 - 3 * 4 92

CHAPTER 14-NATURAL

GAS FLUIDS MEASUREMENT

Orifice differential pressure.
Napierian constant, 2.71828.
Velocity of approach factor.
Orifice plate coefficient of discharge convergence function.
Iteration flow factor.
Iteration flow factor pressure-independent factor.
Iteration flow factor pressure-dependent factor.
Mass flow factor.
Ideal gas relative density (specific gravity).
Real gas relative density (specific gravity).
Real relative density (specific gravity), % carbon dioxide, and % nitrogen.
Isentropic exponent.
Mass.
Absolute viscosity of flowing fluid.
Molar mass (molecular weight) of dry air.
Dimensionless downstream dam height.
Number of moles.
Unit conversion factor (orifice flow).
Unit conversion factor (Reynolds number).
Unit conversion factor (expansion factor).
Unit conversion factor (discharge coefficient).
Unit conversion factor (absolute temperature).
Base pressure.
Static pressure of fluid at the pressure tap.
Absolute static pressure at the orifice upstream differential pressure tap.
Absolute static pressure at the orifice downstream differential pressure tap.
Measured air pressure.

Measured gas pressure.
Pi, 3.14159... .
Mass flow rate.
Volume flow rate per hour at base conditions.
Volume flow rate flowing (actual) conditions.
Universal gas constant.
Pipe Reynolds number.
Density of the fluid at base conditions, (6,G).
Air density at base conditions, (8,G).
Gas density at base conditions, (4,Tb).
Density at standard conditions, (P, ,TJ.
Density at flowing conditions, (9,Tf).
Base temperature.
Measured orifice plate bore diameter temperature.
Measured meter tube internal diameter temperature.
Measured temperature of air.
Measured temperature of gas.
Rowing temperature.
Reference temperature of the orifice plate bore diameter and/or meter tube
internal diameter.
Downstream tap correction factor.
Small meter tube correction factor.

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SECTION &CONCENTRIC.

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SQU RE-EDGED ORIFICE METERS. PART 4-43

CKGROUND

I;, Upstream tap correction factor.
X Reduced reciprocal Reynolds number (4,000/ReD).

X, Value of X where change in orifice plate coefficient of discharge correlation
occurs.
Y Expansion factor.
Yp Expansion factor pressure constant.
Zb Compressibility (base conditions).
2, Compressibility at flowing conditions (9,Tf>.
Air compressibility at air measurement conditions.
Z"leir
ZnlgOs Gas compressibility at gas measurement conditions.

4.2
4.2.1

History and Development
BACKGROUND

In May 1924, the Board of Directors of the Natural Gas Association (this later became
the Natural Gas Departmentof the American Gas Association') directed its Main Technical
and Research Committee to establish a new subcommitteeto be known as the Gas Measurement Committee. The duties of this new committee were outlined by the directors as:
Determinethe correct methods of installing orifice meters for measuring natural gas.
Determine the necessary corrective factors and operative requirementsin the use of
orifice meters, using natural gas in all experimentalwork.
Secure the cooperation and assistance of the National Bureau of Standards2and the
United States Bureau of Mines3, and secure, if possible, the assignmentof members
of their staffs to the Gas MeasurementCommittee to assist in this work.
The Gas Measurement Committee held ifs first meefing in November 1924 and discussed
various features of the work assignedto it. Beginning in the summer of 1925, and extending
over a period of six years, this committee conducted several research projects on orifice
meters.
The Gas Measurement Committee published a preliminary report in 1927, which was
revised in 1929, and Report No. 1 was issued in 1930. In the introduction to Report No. 1,
the following statement was made:
'This is not a final report, but it is made with the understandingthat the committee will continue its analytical studies of the data already developed, The committee also fully expects
that it will be necessaryfor it to conduct further work of its own. This will make necessary
one or more supplemental reports, in which the data will be summarized and the mathematical principles announced, which are thebasis for the present report, and such modifications
and extensions will be made as additional data and further study may require."

rn September 1931, this committeejoined with the Special Research Committee of Fluid
Meters of the American Society of MechanicalEngineers4 in the formation of a Joint Committee on Orifice Meters so that future publications on orifice meters by these two parent

committees might be in harmony. This joint committeefound that a few additional research
projects on orifice meters, especially for the determination of the absolute values of orifice
coefficients, were needed. Thereafter, the committee formally requested representatives of
the National Bureau of Standardsto review the data obtainedin these later research projects
and report their findings to the committee.
Gas Measurement Committee Report No. 2 was published on May 6, 1935 and was
intended to supplement Report No. 1. Within certain limits explained in that report, any
orifice meter installed in accordance with the recommendations in Report No. 1 would
'American Gas Association, 1515Wilson Boulevard, Arlington, Virginia 22209.
'National Bureau of Standards (is now the National institute of Standards and Technology). NiST publications
are available from the US. Government Printing Office, Washington, D.C. 20402.
3United States Bureau of Mines. Bureau of Mines publications are available from the U.S. Government Printing
Office, Washington, D.C. 20402.
4American Society of Mechanical Engineers,345 East 47th Street, New York, New York 10017.
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3


CHAPTER 14-NATURAL

GAS FLUIDS MEASUREMENT

fulfill all the requirements stated in Report No. 2. The use of factors given in Report No. 2

made possible the use of orifice meters over a much wider range of conditions than had
been possible before.
The material in Report No. 2 was based on a special engineering report made by the Joint
American Gas AssociatiodAmerican Society of Mechanical Engineers Committee on
Orifice Coefficients to the Gas Measurement Committee in October 1934 and was presented to and accepted by the Main Technical and Research Committee in January 1935. The
analysis of the data presented in the report of that joint committee was made by Dr. Edgar
Buckingham and Mr. Howard S. Bean of the National Bureau of Standards and checked by
Professor Samuel R. Beitler for the committee. The report of the joint committee in its
original form passed through the editorial committee of the bureau and was approved for
publication by the director of the bureau.
Since publication of Report No. 2, new types of equipment have been made available for
use in the constructionof orifice meter stations, Further, the need developed for larger meter
tube diameters and heavier wall pipe to measure the larger volumes of gas at higher metering pressures. It was recognized by the industry that Report No. 2 should be brought up to
date. Thus, early in 1953, the PAR Plan’s Pipeline Research Committee appointed the
Supervising Committee for PAR Project NX-7, for the purpose of developing Gas Measurement Committee Report No. 3. To maintain cooperation between the American Society
of Mechanical Engineers and the American Gas Association in the development of publications on orifice meters, the members of the supervising committee had dual membership
on the American Society of Mechanical Engineers Research Committee on Fluid Meters,
Subcommittee No. 15, as well as the NX-7 Committee.
Report No. 3 supplemented Report No. 2. Generally, all of the data in this report were
the same as included in Report No. 2, except that it was expanded to cover a wider range
of conditions. In many instances, slight changes were made and statements added to clarify
some of the conditions brought about from practical application of Reports No. 1 and 2. In
Report No. 3, a pressure base of 14.73 pounds per square inch absolute was adopted to
replace the former pressure base of 14.4 pounds per square inch absolute. The results are
consistent with those obtained from Report No. 2.
Since the publication of Report No. 3 in 1955, there have been refinements and new
developments in the measurement of natural gas. The 1969 revision updated the report and
provided additional information which had been developed since the original publication.
The basic concepts in Report No. 3 were not changed. The use of large pipe diameters and
new manufacturing techniques as well as the use of computers, required additional material

to make the report more useful. Fundamentally, however, these revisions did not make any
appreciable changes. The compressibility material presented was abstracted from the
Manual for Determining SupercompressibilityFactors for Natural Gas.
During 1975, the American Petroleum Institute’s Committee on Petroleum Measurement
adopted Report No. 3 and approved it as API Standard 2530, and for publication as Chapter
14.3 of the American Petroleum Institute’s Manual of Petroleum Measurement Standards.
Subsequently, Report No, 3 was submitted by the American Petroleum Institute to the
American National Standards Institute’ for endorsement as an American National Standard. The American National Standards Institute approved Report No. 3 as an American
National Standard on June 28, 1977, identified as ANSUAPI 2530.
During 1982-1983, API’s Committee on Petroleum Measurement worked in cooperation
with the American Gas Association and the Gas Processors Association‘ to revise the
standard. API adopted the revised standard by ballot of its Committee on Petroleum Measurement on November 23, 1983. The 1983 revision updated the standard and altered the
format to improve its clarity and ease of application. Several forms of the flow equations
5American National Standards Institute, 1430 Broadway, New York, New York 10018.
6Gas Processors Association, 6526 East 60th Street, Tulsa, Oklahoma 74145.

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SECTION &CONCENTRIC,

0732290 0506293 7 9 T M

SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND

were provided. The calculated flow rate results were equivalent for any of the forms
presented and were also equivalent to those obtained with the first edition.
The empirical equation of state for natural gas, or compressibility factors was also
updated in the 1983 revision. Gas compressibility work was completed on an expanded list
of gas compositions and for pressures up to 20,000 pounds per square inch. These experiments were supported with facilities, technology, expertise, and funds supplied by the
National Bureau of Standards, the University of Oklahoma, Texas A & M University, the
Compressed Gas Association7,the Gas Research Institute*, the American Gas Association,
and others. The resultant empirical equation of state for natural gas was adopted as A.G.A.
Transmission Measurement Report No. 8. No other substantive technical revisions to the
standard were undertaken at that time. The American National Standards Institute approved
the 1983 revision as an American National Standard on May 16, 1985.
The empirical coefficient of discharge equation for flange-tappedorifice meters has been
updated in the present revision. Extensive test work on orifice meters using oil, water, air,
and natural gas as test fíuids was conducted by an international set of laboratories. Two sets
of meter tubes in nominal 2 , 3 , 4 , 6 , and 10 inch sizes with two sets of eight orifice plates
in nominal beta (ß) ratios from 0.05 to 0.75 were tested. The U.S. experiments were supported with facilities, technology, expertise, and funds supplied by the National Bureau of
Standards, the American Petroleum Institute, the Gas Processors Association, the Gas
Research Institute, the American Gas Association, and others. The new coefficient of
discharge equation is based on the most extensive, high quality data ever collected.
The approach length, piping configuration, and flow conditioning recommendations are
unchanged from the 1983 revision. A restatement of uncertainty will result from the current
installation research and will offer a basis for future changes in this standard.

4.2.2
4.2.2.1

HISTORICAL DATA BASE

OSU Data Base

The largest single collection of industry-sponsored experiments to determine orifice
discharge coefficients was conducted from 1932 to 1933 under the direction of Professor
S.R. Beider at Ohio State University (OSU). These experiments used water in seven pipe
diameters ranging from 25 to 350 millimeters (1 to 14 inch). The test results are commonly
referred to as the OSU data base.
Orifice plates with a wide range of diameters were studied in each of the pipe sizes.
While little is known of the detail of the pipework condition or of the plates themselves, the
tests were undertaken with considerable care. All flange-tapped orifice metering standards
published prior to 1990 (A.G.A. Report No. 3, ANSI/API 2530, and IS09 5167) were based
on this sixty year old OSU data base.
The results from these experiments were used by Dr. Edgar Buckingham and
Mr, Howard Bean of NBS to develop a mathematical equation to calculate the flow coefficient for orifice meters. They derived the equation by cross-plotting the data on large sheets
of graph paper to obtain the best curve fit. The quality of the work done by Beitler, Buckingham, and Bean is obvious from the fact that their results were used for almost 60 years.

4.2.2.2

Data Reevaluation

In the late 1960s and early 1970s, attempts were made to mathematically rationalize the
variety of discharge coefficient data then available. Equations using a power series form
evolved. These provided excellent fits to specific data bases, but could not be used for
7Compressed Gas Association, 1725 Jefferson Davis Highway, Arlington, Virginia 22202.
*Gas Research Institute, 8600 West Bryn Mawr Avenue, Chicago, Illinois 60631.
'International Organization for Standardization.IS0 publications are available from ANSI.

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--`,,```,,,,````-`-`,,`,,`,`,,`---

A P I MPMS*L4*3*4 92


A P I MPMS*L4.3-4 % 2

CHAPTER 14-NATURAL

6

m 0732270 0506274 626 m

GAS FLUIDS MEASUREMENT

extrapolations.These attempts did not replace the Buckingham equation for flange-tapped
orifice meters.
In the early 1970s, a joint committee of the American Gas Association, the American
Petroleum Institute, and the International Organization for Standardization (ISO) was
formed to address perceived problems associated with the OSU data base. Wayne Fling of
the USA and Jean Stolz of France were selected to evaluate the OSU data base.
In their evaluation, Stolz and Fling discovered a number of physical reasons to question
some of the data points of the OSU Data Set. Several installations and plates were found
that did not meet the requirements of ANSUAPI 2530 and I S 0 5 167. The F%ng/Stolz analysis identified 303 technically defensible data points from the OSU experiments.

Unfortunately, it is not known which points were selected by Buckingham/Beanto generate
the discharge coefficient equation. The 303 defensible data points were from 4 meter tubes
covering a p ratio range of 0.2 to 0.75 and a pipe Reynolds number range of 16,000 to
1,600,000.This data was developed using water.
4.2.3

RECENT DATA COLLECTION EFFORTS

In the late 1970s, recognizing from the Fling/Stolz analysis the availability of only a
small amount of definitive data, API and GPA initiated a multimillion dollar project to
develop a new archival discharge coefficient data base for concentric, square-edged, flangetapped, orifice meters. At about the same time, a similar experimentalprogram was initiated
by the Commission of European Communities'' (CEC). The goal of both research efforts
was to develop a high quality archival data base of orifice meter discharge coefficients
covering the broadest possible range of pipe Reynolds numbers. The data base was generated over a ten year period at eleven laboratories using oil, water, air, and natural gases as
test fluids.
The experiments were randomized to eliminate experimental bias within a laboratory.
Randomization assured valid estimates of the experimental error and allowed the application of statistical tests of significance, confidence levels, and time-dependent analyses.
Replication of independent bivariate data points (Cd,ReD)was conducted to measure precision and to assess uncontrolled variables which could affect the find results. By using
different laboratories, the possibility of systematic bias originating from any one laboratory
could be identified, investigated, and corrected.
The experimental pattern was designed to vary in a controlled fashion the correlating
parameters of p, pipe size, and Reynolds number for a given tapping system. All orifice
plates were quantified with respect to concentricity, flatness, bore diameter, surface roughness, edge sharpness, and other characteristics. The edge sharpness was quantified by lead
foil, casting, beam of light, and fingernail methods. The meter tubes were quantified with
respect to circularity, diameter, stepdgaps, pipe wall roughness, and so forth. The wall
roughness was quantified by the profilometer and the artifact methods.
The experimental design recognized the importance of the data taken on each of the four
basis fluids. The water data were viewed as the most important of the research effort. The
water experiments occupied the intermediate Reynolds number range. It was decided not
to test all tube/plate combinations in all four fluids. The API/GPA experiments were

restricted to flange-tapped orifice meters, using oil, water, and natural gas as the test fluids,
The CEC experiments covered orifice meters equipped with corner, radius (D-D/2), and
flange tappings. Test fluids included water, dry air, and natural gas.
The combined data base which resulted is based on a combination of 12 meter tubes
covering five nominal pipe diameters. It contains data from 106 orifice plates covering
eight p ratios for both liquids and gases. The data base was collected from eleven different
laboratories over a pipe Reynolds number range of 100 to 35,000,000.
"Commission of European Communities, rue de la Loi, B-1049, Brussels, Belgium.

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SECTION SCONCENTRIC. SQUARE-EDGED ORIFICE METERS. PART 4-BACKGROUND

Full descriptions of the research projects may be found in the documents referenced in
the appendix to Pari 1.
4.2.3.1

APVGPA Discharge Coefficient Research

--`,,```,,,,````-`-`,,`,,`,`,,`---

The API/GPA discharge coeffficient research was restricted to flange-tapped orifice
meters. Only those experiments conducted using oil and water were used in the final regression data base. For several technical reasons, the originators of the high Reynolds number

experiments at Joliet considered the natural gas experiments to be comparison quality,
rather than regression quality.
Since theresults of the project were to be applied in commerce, the experimental pattern
included two sets of five nominal pipe diameters (2,3,4,6, and 10 inches). A three-section
meter tube design was selected to facilitate inspection of internal surface conditions and for
future experiments on installation conditions. Tube roughness values were representative
of commercial installations.
Two sets of orifice plates having nominal p ratios (0.050, 0.100, 0.200, 0.375, 0.500,
0.575, 0.660, 0.750) were selected to produce a statistically consistent data base which
could be used to develop an equation for the discharge coefficient. Plates were replaced
when they were damaged or when the edge sharpness had deteriorated beyond acceptable
levels. The nominal pratios and nominal tube diameters for the experimental patterns were:

0.050
o.100
0.200
0.375
0.500
0.575
0.660
0.750

x
x
x
x
x
x
x

x
x
x
x
x
x
x
x

x
x
x
x
x
x
x
x

x
x
x
x
x
x
x

x
x
x
x

x
x
x

To ensure uniformity of the velocity profile at each laboratory, Sprenkle flow conditioners were constructed by the NBS mechanical shop in accordance with the original specifications of the Bailey Meter Company. These Sprenkle flow conditioners assured isolation
from laboratory induced piping configurations. Additionally, velocity profile tests were
performed to confirm the presence of uniform, fully-developed, swirl-free flow profiles.
Flow rates were selected for each pipe size and plate combination to produce Reynolds
numbers spread equally over the relevant range of the laboratories' capabilities. The resulting test matrix sought to correct any possible bias in the existing OSU data base and
minimize or eliminate aíl sources of bias in the new experimental data.

4.2.3.1.1

Low Reynolds Number Experiments

The low Reynolds number experiments were conducted at the Colorado Engineering
Experimental Station Incorporated (CEESI) Flow Laboratory located in Nunn, Colorado.
The viscous fluid selected was a white mineral oil with a nominal viscosity of 8 centipoise.
The mass flow rate for the oil experiments was calculated using a traditional liquid
turbine meter, small volume prover, and empirical density arrangement. The density and
viscosity of the white mineral oil was characterized to empirically predict flowing density
and viscosity.

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8

CHAPTER 14-NATURAL

GAS FLUIDS MEASUREMENT

4.2.3.1 -2 Intermediate Reynolds Number Experiments
The intermediateReynolds number experiments were conducted at the National Institute
of Science and Technology (NIST) Flow Laboratory located in Gaithersburg, Maryland.
The test fluid was potable water with a nominal viscosity of 1 centipoise.
The mass flow rate was calculated using the traditional weigh tank and empirical density
method. Water density as a function of temperature was predicted using George S. Kell’s
water density equation, combined with a zero offset attributable to dissolved minerals in
the sump water.

4.2.3.1.3

High Reynolds Number Verification Experiments

The high Reynolds number experiments were conducted at Natural Gas Pipeline of
America’s (NGPLA) Natural Gas Facility located at Joliet, Illinois. f i o natural gases were
utilized, Gulf Coast and Amarillo, both having a nominal viscosity of 0.01 centipoise.
The mass flow rate was determined using sonic flow nozzles and an empirical PVT
arrangement.The density and viscosities of the natural gases were continuously characterized by an on-line gas chromatograph which reported the composition in mole percent.

4.2.3.2

CEC Discharge Coefficient Research

The CEC Discharge Coefficient Research experiments used two tube sizes (100 millimeters and 250 millimeters) over a prange of 0.2 to 0.75 at eight laboratories.
To ensure a uniform velocity profile at each laboratory, long upstream lengths of straight
pipe (greater than SOD) and flow conditioners were used to assure isolation from laboratory
induced piping configurations. Again, velocity profile tests were performed to confirm the
presence of uniform, fully-developed, swirl-free flow profiles.
Flow rates were selected for each pipe size and plate combination to produce Reynolds
numbers spread equally over the relevant range of the laboratories’ capabilities. As in the
APUGPA experiments, the resulting test matrix was designed to correct any possible bias
in the existing OSU data base and to minimize or eliminate all sources of bias in the new
experimental data.
The combined data base includes data from eleven different laboratories, for four basic
fluid types with different sources, on twelve different meter tubes of differing origins, and
over one-hundred orifice plates of differing origins.
4.2.3.3

Laboratory Bias

Before proceeding with equation regression, the researchers analyzed laboratory bias
within the individual data bases as weil as the combined API/GPA and CEC data bases.
Laboratory bias would be evident if the discharge coefficient curve for a given p ratio
exhibited offsets between fluid data or between laboratories.
The traceability chain and method of determining mass flow, instrumentationcalibration,
and operating procedures were unique for each laboratory. Pipe sizes and p ratios common
to both the APUGPA and CEC data bases were used to test the assumption that laboratory
bias within the regression data set has been randomized.
Analysis of the APUGPA data base exhibited no laboratoq bias between the low and
intermediate Reynolds number laboratories.A statistical analysis by the AEWGPA technical
experts confirmed the lack of bias. Graphical analysis of the CEC data base indicated that
the laboratory biases were randomized.

Comparison of the APUGPA and CEC data graphically confirmed the assumption of
randomized laboratory bias between data bases. Additionally, a statistical comparison
using any of the candidate equations confirmed the extremely compatible level between
data bases.

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SECTION %-CONCENTRIC,

4.2.3.4

SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND

Regression Data Set

A meeting of interested international orifice metering experts in November, 1988,
mutually agreed that the Regression Data Set be defined as follows:
T h e Regression Data Set shall consist of those data points contained in the APWGPA and
CEC discharge coefficient experiments which were performed on orifice plates whose
diameter was greater than 11.4 millimeters (0.45 inches) and if the pipe Reynolds number
was equal to or greater than 4,000 (furbulent flow regime).”

Tests which contained uncontrolled independent variables and operator errors were

excluded from the data base. Points were discarded only if a physical cause could be identified and both the laboratory and APUGPA or CEC experts concurred on the evidence.
Questionable points which were considered to be statistical outliers were not discarded
from the data base.
This does not mean that other data were of inferior qualify. Insufficient information
existed for other data sets to determine if the independent variables were controlled and
quantified. Examples of comparison quality data include the OSU 303 points, the 1983
NBS Boulder Experiments, the AFWGPA Joliet Data, and the Japanese Water data base.
The Regression Data Set defined above consists of data generated on orifice meters
equipped with flange and D-D/2 (radius) tappings. The number of regression data points
are summarized as follows:
Tapping
Number of points
flange
comer
D-D/2
Total Poinfs

5,734
2,298
2,160
10,192

--`,,```,,,,````-`-`,,`,,`,`,,`---

Tables 4-1 through 4-3 show the range of data used to generate the RG correlation.
Table 4-I-Regression Database Point Distribution
for Flange Taps
Tube Size
Beta

o. 100

2
inches

3
inches

4
inches

6
inches

10
inches

summary
bvBeta

O
60
104
113

29
83
122
109
136

92
130

79
257
202
164
390
303
490

108
728
821
619
1123
944
1391

701

1885

5734

lo6
to

io7

0.200
0.375
0.500
0.575
0.660
.0.750

90

O
57
106
69
72

196
212

101

O
27 1
287
164
435
289
458

Summary
by Tube

775

469

1904

4000
to

io4

io5

to

loo00

lo5

to
lo6

2.000
3.000
4.000
6.000
10.000

112

22
95
68
41

414
209
622
275
300

summary
byReD

338

1820

64

Reg

Pipe

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to

io7

io8

249
238
1004
328
927

O
O
183
30
467

O
O
O
O
150

2746

680

150

Not for Resale

summary
by Pipe
775
469
1904
701
1885

5734

9


A P I N P N S * L 4 - 3 = 4 92

10

CHAPTER 14-NATURAL

4.2.3.5

0732290 0506298 2 7 1

GAS FLUIDS MEASUREMENT

Interpretation of Research Data

For high values of p, the data follows a pattern similar to the Moody Friction Factor
Diagram. This similarity is greatest at a p of 0.750 and continuously diminishes and
becomes imperceptible at a p ratio of 0.500.

For low p ratios, the data is erratic. Closer examination indicated that the ability to
reproduce an orifice plate with a sharp edge decreases with decreasing plate bore diameter.
Based upon lead foil and video imaging analyses, a reasonable low limit for commercial
plates was thought to be 11.4 millimeters (0.45 inches).
Data associated with the 50 millimeter and 75 millimeter (2 inch and 3 inch) tubes
exhibit an anomaly. Further analysis indicated that this anomaly may be caused by the
dimensionless tap hole size and dimensional location for flange taps.
The experiments confirmed the uncertainty guidelines used by the petroleum, chemical,
and natural gas industries, Improvement in accuracy below this level under normal operating conditions is unrealistic without in situ calibration of the device and secondary
instrumentation.
4.2.4

BASIS FOR EQUATION

--`,,```,,,,````-`-`,,`,,`,`,,`---

The underlying principle for present day theoretical and experimental fluid mechanics
is dynamic similarity. This principle states that two geometrically similar meters, with
identical dimensionless flow parameters will display geometrically similar streamlines
regardless of differences in density, viscosity, flow rate, and so forth, between the two
fluids.
Dynamic similarity implies a correspondence of fluid forces between the two metering
systems. Within the application limitations of this standard, the inertial and viscous forces
are those considered to be significant for the orifice meter. As a result, the Reynolds number, which measures the ratio of the inertial to viscous forces, is the term which correlates
dynamic similarity in all empirical coefficient of discharge and flow coefficient equations.
Table 4-2-Regression Database Point Distribution
for Corner Taps
Tube Size
Beta

o. 100

2
inches

3
inches
O
O
O

4
inches

6
inches

10
inches

Summary
by Beta

O
O
O
O
O
O

182
96
89
275
199
361

374
174
162
575
382
63 1

o

1202

2298

io6

io7
10'

0.200
0.375
0.500
0.575
0.660

0.750

O
O
O
O
O
O

O
O

192
78
73
300
183
270

Summary
byTube

O

O

1096

o

Reg
4000
to
10000

io4
to
lo5

lo6

to
lo7

27

278

629

162

O

1096

1o.Ooo

12

166

519

371

134

1202

Summary
by Reg

39

444

1148

533

134

2298

Pipe
2.000
3.000
4.000
6.000

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lo5
to

Not for Resale

to

Summary
byPipe


A P I M P M S * L 4 - 3 e 4 92

SECTION &CONCENTRIC.
~

0732290 0506299 L O B

SQUARE-EDGED ORIFICE METERS. PART &BACKGROUND

~

Table 4-3-Regression Database Point Distribution
for 0-012 (Radius) Taps
Tube Size

Beta

2
inches

3
inches

4
inches

6
inches

10
inches

summary
by Beta

o. 100
0.200
0.375
0.500
0.575
0.660
0.750

O
O

O
O
O
O

O
O
O
O
O
O

169
50
48
276
158
243

O
O
O
O
O
O

186
97
90
274

198
37 1

355
147
138
550
356
614

Summary
byTube

O

o

944

O

1216

2160

Ren

io4

io5

to
loo00

:i5

to

24

lo6

lo6
to
lo7

io7
to
lo8

summary
bypipe

229

529

162

O

944

12

167

534

367

i36

1216

36

396

1063

529

136

2160

4000

Pipe

--`,,```,,,,````-`-`,,`,,`,`,,`---

2.000
3.000
4.000
6.000
10.000

Summary
byReg

Provided the physics of the fluid does not change, the Reynolds number correlation
provides a rational basis for extrapolation of the empirical equation.
The originators of the APVGPA and CEC experiments considered fully developed velocity profiles as the foundation for the experiments. This decision was discussed extensively,
as were the definition and determination of fully developed flow. Fully developed flow
conditions were assured by the use of straight lengths of meter tube both upstream and
downstream from the orifice and by the use of flow sfraighteners.
The theoretical definition of fully developed velocity profiles is based largely on the
accumulated results of experimental observations of time-averaged velocity profile and,
parficularly, of the pressure gradient (or friction factor). It is well established that both the
velocity profile and the pressure gradient are sensitive to the condition of the pipe wall,
whether smooth, partially rough, or fully rough, and the nature of the roughness.

4.2.4.1

Form of Equation

Previous discharge coefficient equation forms (Buckingham, Murdock, Dowdell, and
others) were empirically derived expressions with minimal mathematical correlation to

fluid dynamic phenomena. In 1978, Jean Stolz derived an empirical orifice equation based
on the physics of an orifice meter. Stolz postulated that discharge coefficients obtained with
different sets of near field pressure tappings must be related to one another based on the
physics. The expression has been termed the Stolz linkage form. The coefficient of
discharge (C,) equation for the concentric, square-edged orifice plafe developed by
M. J. Reader-Harris and J. E. Gallagher, the RG equation, evolved from the work of Stolz.
The RG equation contains a coefficient of discharge at Reynolds number for corner taps,
C;,(CT),a slope term consisting of a throat Reynolds Number term and velocity profile term,
the near field tap t e m , and a “tap” size term for meter tubes less than 2.8 inches. A brief
description of the physical understanding for the equation is presented in 4.2.4.2 and
4.2.4.3.

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12

CHAPTER 14-NATURAL

4.2.4.2

GAS FLUIDS b%EASUREMENT

Tap Terms

The near field tap terms were derived first since it was necessary to determine them
before regression of the slope and q(CT) terms. The best-fit terms were derived statistically using the Regression data base and the Gasunie 600 millimeter flange tapping term data.
The total tapping term data set consisted of 11,346 points, nominal diameter ratios (j)
from
0.10 to 0.75, nominal pipe diameters from 50 to 600 millimeters, and pipe Reynolds
numbers which ranged from approximately 200 to 50,000,000.
Stolz's postulate states that the near field tapping terms are equal to the difference
between the discharge coefficient for the corner taps and the flange (or radius taps). The
values of the terms were determined from the CEC data which included all three sets of
tappings. However, the form of the tapping terms was based on data collected by several
researchers. Because the data aplied to only one pair of tappings (flange), the value of the
tapping terms in the APUGPA data could only be calculated for comparison.
The upstream term has a form which is essentially identical to that of IS0 5167. The
downstream form is based on a suggestion by R. G. Teyssandier and Z. D. Husain. Also,
it was agreed that the upstream and downstream tap terms should have a continuous first
derivative.
No effect of Reynolds number on the tap terms is evident from analysis of the CEC data.
However, data in the low Reynolds number range in the API/GPA experiments show the
effect of Reynolds number on the tap term. The effect of low Reynolds number on the
upstream and downstream wail pressure gradient has been reported by Witte, Schroeder,
and Johansen. Perfect low Reynolds number tapping terms cannot be produced due to lack
of data. However, it is important to produce the best ones possible.

4.2.4.3

Ci(CT) Term

The infinite discharge coefficient for corner taps, q(CT), increases with pratio to a maximum near p of 0.55 and then decreases rapidly with increasing p. The form of the equation,
without taking into account the tap hole diameter term, is:

Ci (CT) = A,, + A l p 2 +A-#'

The constant exponents of 2 and 8 were chosen to enable a good fit to the data while
keeping the exponents reasonable.
The 50 millimeter flange tap data differed significantly from the radius tap terms by as
much as 0.4 percent for small values of b. Gallagher and Teyssandier postulated that this
difference was a result of dimensional tap effects, An additional term was added to account
for the tap hole diameter effect for 50 millimeter tubes. It is debatable whether this term
should be in the tap term or G(CT) term. A proposal by Reader-H&s to add a tap hole
diameter term to the C,(CT) term was accepted and has been implemented.

4.2.4.4

Slope Term

Intuitively, for small p ratios, the Cd should depend only on throat Reynolds Number
(Re,). However, for large p ratios the velocity profile or friction factor is the correlating
parameter.
Several scientists have attempted to correlate C, as a function of friction factor. While
theoretically correct, the practical application would be unpopular. Also, the ability to
measure friction factor is impractical in the field and difficult in the laboratory.
The slope term form should also provide a transition from laminar to turbulent flow
because the velocity profile changes rapidly in the transitional flow regime. The data indicated that the slope for pipe Reynolds number (ReD)greater than 3,500 was very different
from the slope for pipe Reynolds number (Re,) less than 3,500.
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SECTION 3-CONCENTRIC,

SQUARE-EDGED ORIFICE METERS, PART 4-BACKGROUND

The final slope term form is as follows:

The '%" term for Re, c 3,500 is different from Re, > 3,500 to correct for the velocity
profile changes from laminar to turbulent flow regime.

4.2.5

READER-HARRIWGALLAGHER EQUATION

The equation for the coefficient of discharge (C,) for concentric square-edged orifice
plates developed by Reader-HarridGallagher (RG) is structured into distinct linkage terms
and is considered to best represent the current regression data base. The RG equation, as
ballotted within API in 1989, is valid for the three tappings represented by the regression
database and is acceptable for low flow conditions if a higher uncertainty is acceptable. The
bailoted equation is given below.

c,

=

ci + SIX] + s,x,

+

Ci = Ci(CT) Tap Term

C;:(CT) = 0.5961 + 0.0291ß2- 0.2290ß8+ 0.003 (1 - ß) Ml

Tap T e m = Upstrm + Dnstrm
Upstrm =

[ 0.0433 + 0.0712e-8'5L'- 0.1145e-6'0L1] (1 - 0.23A) B

Dnstrm = -0.0116

S2X, = (0.0210 + 0.0049A)ß4C
Also,

A =

[

19, Wß
ReD

0.8

]

For Re, greater than or equal to 3,500,

[E]
0.35

c=

--`,,```,,,,````-`-`,,`,,`,`,,`---

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13


CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

14

For Re, less than 3,500,

C = 30.0-6,500

Diameter ratio.
d1D.
Coefficient of discharge at a specified pipe Reynolds number.
Coefficient of discharge at infinite pipe Reynolds number.
Coefficient of discharge at infinite pipe Reynolds number for corner-tapped
orifice meter.
Orifice plate bore diameter calculated at Tf.
Meter tube internal diameter calculated at Tf.

Naperian constant, 2.71828.
O for corner taps.
N4/D for flange taps.
1 for 0-012 (radius) taps.
O for corner taps.
N4/Dfor flange taps.
0.47 for 0-012 (radius) taps.
1.0 when D is in inches; 25.4 when D is in millimeters,
pipe Reynolds number.
By restricting the RG equation to flange-tapped orifice meters with pipe Reynolds
numbers greater than or equal to 4,000, the RG equation becomes:
c
d

=

cj + SIXI + S2x2

Ci = Ci(CT) + Tap Term
C;(CT) = 0.5961 + 0.0291ß2- 0.2290ß8+ 0.003 (1 - ß) Ml
Tap Term = Upstrm iDnstrm
Upstrm =

[ 0.0433 + 0.07 12

Dnstrm = -0.0116

- O. 1145e-6'oL'] ( 1 - 0.23A) B

M2 - 0.52M:.3

lß'J

1 -0.14A)

S2X, = (0.0210 + 0.0049A)ß4C
Also,

D
M1 = max (2.8--,O.O)
N4

--`,,```,,,,````-`-`,,`,,`,`,,`---

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API flPMS*14*3.4

--`,,```,,,,````-`-`,,`,,`,`,,`---

SECTION &CONCENTRIC,

A =

[

19, Oooß
Re,

9 2 W 0732290 0506303 469 W

SQUARE-EDGED ORIFICE METERS, PART &BACKGROUND

0.8

]

Where:

A = Small throat Reynolds number correlation function.
B' = Fluid momentum ratio.
ß = Diameter ratio.
- dlD.
C = Generalized Reynolds number correlation function.
c, = Coefficient of discharge at a specified pipe Reynolds number.
c. = Coefficient of discharge at infinite pipe Reynolds number.
G(CT) = Coefficient of discharge at infinite pipe Reynolds number for corner-tapped
orifice meter.
d = Orifice plate bore diameter calculated at ïj.
D = Meter tube internal diameter calculated at Tf.
e = Naperian constant, 2.71828.
LI = N41D for flange taps.
4 ! = N,lD for flange taps.
N4 = 1.0 when D is in inches; 25.4 when D is in millimeters.
Re, = pipe Reynolds number.

The downstream tap term, M,, is the distance between the downstream face of the plate
and the downstream tap location. The tap hole term, M , , is significant only for nominal
meter tubes less than 75 millimeter (3 inch) equipped with 9.525 millimeter (0.375 inch)
flange taps holes.
The equation is applicable to nominal pipe sizes of 2 inches (50 millimeters) and larger,
diameter ratios (p)of 0.10 through 0.75 provided the orifice plate bore diameter,d,, is greater than 0.45 inches (11.4 millimeters), and for pipe Reynolds numbers greater than or equal
to 4,000. Those interested in applications with Re, less than 4000, d, less than 0.45 inches,
or for corner or 0-012 (radius) taps, all of which are outside the range of this standard, are
referred to Appendix 4-A.

4.2.5.1

Statistical Analysis

Since the mid 1930's, the correlation published by Dr. E. Buckingham and Mr. Howard
S. Bean has been used by A.G.A. Report No. 3 (ANSUAPI 2530). In 1980, IS0 replaced
the Buckingham equation with the Stolz linkage equation in the international orifice standard (IS0 5167). Statistical analysis of the Regression Data Set showed that in several
regions, neither the Buckingham nor Stolz equations accurately represented the data for
flange-tapped orifices (Figures 4-1 through 4-3). The figures indicate that the data does not
substantiate the uncertainty statementpublished in both the IS0 and 1985ANSI standards.
The figures show that the RG equation provides an excellent fit to the data for flange-tapped
orifice meters. Figure 4-9 shows that the RG equation fits the data much better over the
entire Reynolds number range than the previous equation (Figure 4-8).
Figures 4-4,4-5,4-6, and 4-7 show the superior fit of the RG equation to the corner and
0-012 (radius) tap data.
(text continued on page 20)

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15


16

CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT

0.8
0.6
0.4

op

Y

c 0.2

.
9
c
m
‘5

o

a”

g -0.2

’
a

-0.4

(LI

~-

-0.6

Buckingham

I S 0 5167-Stolz

-0.8
0.2

0.1

0.375

0.5

0.575

0.66

0.75

Beta ratio

Figure 4-1-Flange Tap Data Comparison-Mean Deviation (“A)versus
Nominal Beta Ratio
o’8
0.6
0.4

*

op

Y

.-8m

0.2

c

o

‘5
--`,,```,,,,````-`-`,,`,,`,`,,`---

a>
U

.‘

I

’

-0.4

-

-0.6
-n
R
V.”

I

I

I

I

I

Buckingham

~~

ISO5167-Stolz

I

I

4

3

2

RG Equation

.

10

6

Pipe diameter (inches)

Figure 4-2-Flange Tap Data Comparison-Mean Deviation (“h)versus
Nominal Pipe Diameter
0.8

.

0.6

0.4

Oe

v

.-8

0.2

g

o

.-;a
U

5a> -0.2

’

-0.4
I

-0.6

i

1IS0 5167-Stolz

I

104

I

I 05

I

I

106

II

I

107

108

Reynolds number ranges

Figure 4-3-Flange Tap Data Comparison-Mean Deviation (“YO) versus
Reynolds Number Ranges
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