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Natural Gas Measurement Handbook James E. Gallagher Houston, Texas
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Page 1: Natural Gas Measurement her Front Matter-FINAL

Natural Gas Measurement

Handbook

James E. Gallagher

Houston, Texas

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Copyright © 2006 by Gulf Publishing Company, Houston, Texas. All rights reserved. No part of this publication may be reproduced or transmitted in any form without the prior written permission of the publisher.

Gulf Publishing Company2 Greenway Plaza, Suite 1020Houston, TX 77046

10 9 8 7 6 5 4 3 2 1

Printed in the United States of America.

Printed on acid-free paper.

Text design and composition by Ruth Maassen.

Library of Congress Cataloging-in-Publication Data

Gallagher, James E.Natural gas measurement handbook / James E. Gallagher.

p. cm.Includes bibliographical references and index.ISBN 1-933762-00-4 (acid-free paper)1. Natural gas—Measurement. 2. Gas-meters—Handbooks, manuals, etc.I. Title. TH6870.G35 2006665.7'4—dc22

2006016759

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To my wife Patricia,

my sons Ryan and Daniel,

and my parents

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Contents

List of Tables xiList of Figures xiiiPreface xixSymbols xxiUnit Conversions xxvii

1 Introduction 11.1 Transportation System 21.2 Measurement 91.3 Fluid Classification, Commercial 121.4 Material Quality 141.5 Risk Management 15

2 Composition and Quality 192.1 Assay 202.2 Quality Parameters and Tolerances 222.3 Potential Impacts of Gas Quality 262.4 Typical Streams 29

3 Physical Properties and Process Conditions 393.1 Natural Gas 393.2 Fluid Classification: Technical 423.3 Phase Envelope 43

v

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3.4 Fluid Properties 473.5 Process (or Operating) Conditions 543.6 Typical Natural Gas Physical Properties 65

4 Measurement Concepts 794.1 Applicable Fluids 804.2 Base Conditions 804.3 Flowmeters (or Primary Devices) 814.4 Flowmeter Calibration Concepts 824.5 Law of Similarity 884.6 Single-Phase Fluid Flow in Pipes 924.7 Multiphase Fluid Flow in Pipes 1024.8 Secondary Devices 1074.9 Tertiary Device 108

4.10 Uncertainty 1084.11 Total Cost of Measurement 110

5 Orifice Flowmeter 1115.1 General Principles 1115.2 Mass Flow Equation 1155.3 Artifact Calibration 1215.4 Uncertainty Roadmap 1255.5 Sources of Error 1295.6 Risk Management 129

6 Ultrasonic Flowmeter 1356.1 General Principles 1356.2 Mass Flow Equation 1396.3 Central Facility Calibration 1416.4 In Situ Calibration 1426.5 Uncertainty Roadmap 1436.6 Sources of Error 1486.7 Risk Management 158

7 Turbine Flowmeter 1637.1 General Principles 1637.2 Mass Flow Equation 1667.3 Central Facility Calibration 166

vi Contents

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7.4 In Situ Calibration 1677.5 Uncertainty Roadmap 1687.6 Sources of Error 1737.7 Risk Management 174

8 Rotary Displacement Flowmeter 1778.1 General Principles 1778.2 Mass Flow Equation 1808.3 Central Facility Calibration 1818.4 In Situ Calibration 1828.5 Uncertainty Roadmap 1838.6 Sources of Error 1878.7 Risk Management 188

9 Calculations 1919.1 Base Conditions 1919.2 Physical Properties 1929.3 Natural Gas Density 2029.4 GPA 2172 versus A.G.A.8 2099.5 Mass Flow Rate in Pipes 2149.6 Mass Flow Rate for Orifice Flowmeter 2159.7 Mass Flow Rate for Ultrasonic Flowmeter 2229.8 Mass Flow Rate for Turbine Flowmeter 2279.9 Mass Flow Rate for Rotary Displacement Flowmeter 230

9.10 Volumetric Flow Rate at Base Conditions 2319.11 Energy Flow Rate at Base Conditions 2319.12 Quantities 233

10 Secondary and Tertiary Devices 23510.1 General 23610.2 Differential Pressure (dP) 24810.3 Static Pressure 25110.4 Temperature 25310.5 Multivariable Transmitter 25510.6 Online Densitometer 25710.7 Moisture Analyzer 25910.8 Online Gas Chromatograph 26310.9 Other Analyzers 268

Contents vii

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10.10 Flow Computers 26910.11 Gas Sampling Systems 270

11 Electronic Gas Measurement 27911.1 Description of an Electronic Gas Measurement System 27911.2 System Accuracy 28011.3 Definitions 28111.4 Sampling Flow Variables 28211.5 Low Flow Detection 28211.6 Averaging Techniques 28211.7 Compressibility, Density, and Heating Values 28211.8 Hourly and Daily Quantity Calculations 28311.9 Data Availability 283

11.10 Audit and Reporting Requirements 28611.11 Equipment Verification, Calibration, and Certification 29411.12 Security 296

12 Uncertainty 29912.1 Uncertainty Terms 30112.2 Measurement Uncertainty 30312.3 Examples of Flowmeter Uncertainties 30712.4 Statistical Weighting 312

13 Measurement System Design 31913.1 Targeted Uncertainty 31913.2 Fluid Physical Properties 32013.3 Operating Design Data 32013.4 Other Process Conditions 32113.5 General Equipment Redundancy 32213.6 Site Requirements 32413.7 Structures 32513.8 Piping Requirements 32613.9 Pressure Regulation and Control 329

13.10 Flare and Vent Facilities 33013.11 Overpressure Protection 33013.12 Thermal Relief Valves 33113.13 Headers 33113.14 Strainers 332

viii Contents

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13.15 DB&B Valves 33313.16 Check Valves 33413.17 Pulsation Control 33413.18 Primary Device 33413.19 Secondary Devices 33513.20 Tertiary Device (Flow Computer) 34413.21 Control Valves 34513.22 Wiring and Grounding 34513.23 Measurement Control Panel 34713.24 Power Supplies 34713.25 Satellite Panels 34813.26 Supervisory Control and Leak Detection 34813.27 Security 34913.28 Factory Acceptance Testing 35013.29 Dewatering, Cleaning, and Drying 35013.30 Commissioning 351

14 Orifice Flowmeter Design 35314.1 General 35314.2 Velocity and Piping Insulation 35414.3 Strainers 35514.4 Flowmeter Assembly 35514.5 Flowmeter, Mechanical 35814.6 Piping Spools, Mechanical 35814.7 Secondary and Tertiary Devices 358

15 Ultrasonic Flowmeter Design 36115.1 General 36115.2 Velocity and Piping Insulation 36315.3 Acoustic Filter 36315.4 Flowmeter Assembly 36315.5 Flowmeter, Mechanical 36615.6 Piping Spools, Mechanical 36715.7 Flowmeter: SPU, Electrical, and Software 36715.8 Secondary and Tertiary Devices 369

16 Turbine Flowmeter Design 37116.1 General 371

Contents ix

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16.2 Velocity and Piping Insulation 37216.3 Strainer and Lubrication 37316.4 Flowmeter Assembly 37316.5 Flowmeter, Mechanical 37516.6 Piping Spools, Mechanical 37516.7 Flowmeter: SPU, Electrical, and Software 37616.8 Secondary and Tertiary Devices 377

17 Rotary Displacement Flowmeter Design 37917.1 General 37917.2 Velocity and Piping Insulation 38017.3 Filtration and Lubrication 38117.4 Flowmeter Assembly 38117.5 Flowmeter, Mechanical 38217.6 Piping Spools, Mechanical 38217.7 Flowmeter: SPU, Electrical, and Software 38317.8 Secondary and Tertiary Devices 384

18 Inspection, Testing, Verification, Calibration, and Certification 387

18.1 Inspection 38918.2 Testing 38918.3 Verification 39018.4 Calibration 39118.5 Certification 39218.6 Equipment 39218.7 Equipment Information 39518.8 Records 406

Appendix: Standards, Publications, and Regulations 407

A.1 Mechanical Standards and Publications 408A.2 Electrical Standards and Publications 409A.3 Measurement Standards and Publications 410A.4 U.S. Government Regulations 418

Glossary 421Index 453

x Contents

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List of Tables

2 Composition and Quality2–1 Typical Assay 212–2 Additional Information 222–3 Quality Parameters and Tolerances 232–4 GOM Production Sales Gas Composition 302–5 GOM Inlet to Gas Plant Composition 322–6 GOM Outlet of Gas Plant Composition 332–7 Outlet of LNG Plant Composition 35

4 Measurement Concepts4–1 Multiphase Classifications, Horizontal and

Vertical Pipes 103

5 Orifice Flowmeter5–1 Mass Flow, Reynolds Number, and Expansion Factor

Equations 1225–2 Errors in Orifice Flowmeters 130

6 Ultrasonic Flowmeter6–1 Sensitivity Analysis Due to Buildup and Decay 1506–2 Chordal Path Angle Error 1526–3 Reflective Timing Measurements, 4-in. (100 mm)

Flowmeter 154

xi

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6–4 Reflective Timing Measurements, 12-in. (300 mm)Flowmeter 155

6–5 Nonreflective Timing Measurements, 4-in. (100 mm)Flowmeter 156

6–6 Nonreflective Timing Measurements, 12-in. (300 mm)Flowmeter 157

9 Calculations9–1 GPA 2172 versus A.G.A.8, GOM Production

Sales Gas 2109–2 GPA 2172 versus A.G.A.8, GOM Inlet to Gas Plant 2119–3 GPA 2172 versus A.G.A.8, GOM Outlet of

Gas Plant 2129–4 GPA 2172 versus A.G.A.8, Outlet of LNG Plant 213

12 Uncertainty12–1 Summary of Flowmeter Uncertainty Calculations

for a Pf of 1385 psig and a Tf of 100°F 30812–2 Summary of Flowmeter Uncertainty Calculations

for a Pf of 985 psig and a Tf of 70°F 30912–3 Summary of Flowmeter Uncertainty Calculations

for a Pf of 585 psig and a Tf of 100°F 31012–1 Summary of Flowmeter Uncertainty Calculations

for a Pf of 185 psig and a Tf of 70°F 311

13 Measurement System Design13–1 Components Analyzed by the Gas Chromatograph 342

xii List of Tables

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List of Figures

1 Introduction1–1 Transportation System 31–2 Simple Gas Gathering System 31–3 Complex Gas Gathering System 51–4 Gas Processing Plant 61–5 Transmission Pipeline System 81–6 Distribution System 91–7 Phase Envelope: Raw Material and Finished Product 15

3 Physical Properties and Process Conditions3–1 Multicomponent Gas Stream, PR EOS Phase Envelope 443–2 Typical Gulf Coast Gas, Phase Diagram 453–3 Predicted PhasePro Retrograde Generation, GOM

Production Sales Gas 463–4 Predicted PhasePro Envelope 463–5 Hydrate Disassociation Curves for Natural Gas 533–6 GOM Production Sales Gas: ρb, ρtp, μ, SOS, κr 673–7 GOM Production Sales Gas: Mass Density

versus Pressure for Various Isotherms 683–8 GOM Production Sales Gas: Absolute Viscosity versus

Pressure for Various Isotherms 683–9 GOM Production Sales Gas: Speed of Sound versus

Pressure for Various Isotherms 69

xiii

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3–10 GOM Production Sales Gas: Real Isentropic Exponentversus Pressure for Various Isotherms 69

3–11 GOM Inlet to Gas Plant: ρb, ρtp, μ, SOS, κr 713–12 GOM Inlet to Gas Plant: Mass Density versus

Pressure for Various Isotherms 723–13 GOM Inlet to Gas Plant: Absolute Viscosity versus

Pressure for Various Isotherms 723–14 GOM Inlet to Gas Plant: Speed of Sound versus

Pressure for Various Isotherms 733–15 GOM Inlet to Gas Plant: Real Isentropic Exponent

versus Pressure for Various Isotherms 733–16 GOM Outlet of Gas Plant: ρb, ρtp, μ, SOS, κr 753–17 GOM Outlet of Gas Plant: Mass Density versus

Pressure for Various Isotherms 763–18 GOM Outlet of Gas Plant: Absolute Viscosity versus

Pressure for Various Isotherms 763–19 GOM Outlet of Gas Plant: Speed of Sound versus

Pressure for Various Isotherms 773–20 GOM Outlet of Gas Plant: Real Isentropic Exponent

versus Pressure for Various Isotherms 77

4 Measurement Concepts4–1 Classification of Flowmeters 824–2 Classification of Calibration Concepts 834–3 Calibration Systems, Central Facility and In Situ 834–4 SwRI’s Metering Research Facility 854–5 CEESI’s Iowa Facility 864–6 TransCanada Calibrations’ Winnipeg Facility 864–7 Fully Developed Velocity Profiles, Laminar

and Turbulent 944–8 Fully Developed Turbulent Velocity Profile

(Hinze), Pipe Flows at Various Downstream PipeDiameters 97

4–9 Developing Flows, Swirl Free, Nonsymmetrical Pipe Flows at Various Downstream Pipe Diameters 98

4–10 Developing Flows, Moderately Swirling, Non-symmetrical Pipe Flows at Various Downstream Pipe Diameters 99

xiv List of Figures

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List of Figures xv

4–11 Developing Flows, High Swirling, Symmetrical Pipe Flows at Various Downstream Pipe Diameters 100

4–12 Multiphase Flow for Horizontal Pipes 1044–13 Sources of Uncertainty for Flowmeters 109

5 Orifice Flowmeter5–1 Classification of Orifice Flowmeters 1125–2 Dual-Chamber Orifice Fitting 1145–3 Orifice Plate 1155–4 Sources of Uncertainty for Orifice Meters,

a Broad Overview 1265–5 Sources of Uncertainty Using Artifact Compliance

Calibration 1265–6 Sources of Uncertainty for Orifice Meters, a

Detailed Overview 1275–7 Deficiencies of Geometric Similarity 1285–8 Deficiencies of Dynamic Similarity 128

6 Ultrasonic Flowmeter 1356–1 Classification of Ultrasonic Flowmeters 1366–2 Multipath Ultrasonic Flowmeters 1386–3 Sources of Uncertainty for Ultrasonic Meters,

a Broad Overview 1446–4 Sources of Uncertainty Using Central Facility

Calibration 1446–5 Sources of Uncertainty Using In Situ Calibration 1456–6 Sources of Uncertainty for Ultrasonic Meters,

a Detailed Overview 1466–7 Deficiencies of Geometric Similarity 1476–8 Deficiencies of Dynamic Similarity 147

7 Turbine Flowmeter 7–1 Gas Turbine Flowmeter 1647–2 Sources of Uncertainty for Gas Turbine Meters,

a Broad Overview 1697–3 Sources of Uncertainty Using Central Facility

Calibration 1697–4 Sources of Uncertainty Using In Situ Calibration 170

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7–5 Sources of Uncertainty for Gas Turbine Meters, a Detailed Overview 171

7–6 Deficiencies of Geometric Similarity 1727–7 Deficiencies of Dynamic Similarity 172

8 Rotary Displacement Flowmeter8–1 Rotary Displacement Flowmeter 1798–2 Sources of Uncertainty for Rotary Displacement

Meters, a Broad Overview 1838–3 Sources of Uncertainty Using Central Facility

Calibration 1848–4 Sources of Uncertainty Using In Situ Calibration 1858–5 Sources of Uncertainty for Rotary Displacement

Meters, a Detailed Overview 1868–6 Deficiencies of Geometric Similarity 1868–7 Deficiencies of Dynamic Similarity 187

9 Calculations9–1 GOM Production Sales Gas Phase Envelope 2009–2 GOM Production Sales Gas Retrograde

Generation, PR 2019–3 GOM Production Sales Gas Retrograde

Generation, SRK 2029–4 A.G.A.8’s Detailed Method, Uncertainties and

Limitations 2069–5 A.G.A.8’s Gross Characterization Method,

Uncertainties and Limitations 2089–6 Orifice Calculations of GOM Production Sales Gas 2219–7 Orifice Calculations for GOM Outlet of a Gas Plant 2219–8 Ultrasonic Calculations for GOM Outlet from a

Gas Plant 2259–9 Turbine Calculations for GOM Outlet of a Gas Plant 228

9–10 Rotary Displacement Calculations for GOM Outlet of a Gas Plant 232

10 Secondary and Tertiary Devices10–1 Differential Pressure Transmitter 249

xvi List of Figures

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List of Figures xvii

10–2 Static Pressure Transmitter 25210–3 Temperature Transmitter 25410–4 Multivariable Transmitter 25610–5 Online Gas Chromatograph 26410–6 Flow Computer 27010–7 Sampling System Overview 27210–8 Automatic Flow-Weighted Sampling System 27610–9 Manual (or Spot) Sampling System 277

12 Uncertainty12–1 Roadmap of Sources of Uncertainty for Flowmeter

Estimations 30412–2 Interlaboratory Results of a MUSM Flowmeter

Assembly (Artifact) 30512–3 Statistical Weighting Example 315

13 Measurement System Design13–1 Header Configurations 332

14 Orifice Flowmeter Design14–1 Orifice Flowmeter Assembly 356

15 Ultrasonic Flowmeter Design15–1 Ultrasonic Flowmeter Assembly 364

16 Turbine Flowmeter Design16–1 Turbine Flowmeter Assembly 374

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Preface

Measurement is the basis of commerce between producers, royaltyowners, transporters, process plants, marketers, state and federalgovernment authorities, and the general public. In fact, accuratemeasurement of hydrocarbon fluids and materials has a significantimpact on the Gross National Product of exporting and importingcountries, the financial performance and asset base of global com-panies, and the perceived efficiency of operating facilities. The needfor accurate fiscal measurement is obvious.

Given the present or future levels of the cost of natural gas, onecan quickly quantify the material and economic value unaccountedfor that is associated with each ±0.01% of systematic uncertaintythat might unknowingly exist in the measurement systems.

Measurement errors can have both immediate and long-termimpacts on profits. Inaccurate measurement may result in loss ofcustomers, adverse publicity, potential penalties, and legal liabili-ties. In short, equitable and accurate measurement is essential tobusiness. It affects the validity of financial and operating reports aswell as the corporate reputation (cash flow, profit and loss, balancesheet, royalties and taxes).

For reasons such as these, it is essential that material quantitymeasurements be precise and accurate with minimal bias errors.Furthermore, it is incumbent on those involved in custody transferto establish and maintain the traceability chains that link theirmeasurements to appropriate domestic and international standards.

xix

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xx Preface

In this manner, fiscal transfers can be done equitably with the confi-dence of both seller and buyer alike.

The capital and operating resources (CAPEX, OPEX) applied forfiscal transfers must be commensurate with the total cost of measure-ment: the capital cost of technology, the operating cost of technology,industry practice or standards, regulatory compliance and the total fis-cal exposure or risk (commodity value times throughput), the strategicand tactical business direction, and competitors’ strategy. The amountof uncertainty is governed by the investment of resources (CAPEXand OPEX) combined with the inherent uncertainty associated withthe method of measurement (primary, secondary, and tertiary devices)and the fiscal exposure or risk.

Measurement is a technically demanding, complex, state-of-the-art field with a significant impact on the profitability of anybusiness. As such, the field of measurement demands a highly tech-nical language of definitions, acronyms, and symbols that must befully understood and embraced by managers, supervisors, engi-neers, technicians, and operating personnel.

The combination of the “roadmaps” (sources of uncertainty)for each flowmeter technology, the uncertainty estimations (U 95),and the statistical weighting method are tools that can

• Identify error types and magnitude for the primary, secondary,and tertiary devices.

• Identify areas of improvement for existing facilities (upgradeor replacement).

• Set achievable loss performance based on the invested resources(CAPEX).

• Identify OPEX requirements for each flowmeter technology.

• Set priorities on OPEX resource allocation for each location.

• Set priorities on the loss investigation process.

The author’s desire is that the information contained in this hand-book provides a clear presentation of the measurement principles,state-of-the-art technology, and its applications in the real world.

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Symbols

Terms

A A term in the RG discharge coefficient equation Am Cross-sectional area of flowmeterAp Cross-sectional area of pipeAS Automatic samplerAT Analyzer transmitter (moisture analyzer, gas

chromatograph)B A term in the RG discharge coefficient equation Btu British thermal unitBtuIT British thermal unit, internationalC A term in the RG discharge coefficient equation Cd Coefficient of dischargeCd(CT) Coefficient of discharge for corner tapped orifice at

a ReD

Cd(FT) Coefficient of discharge for flanged tapped orifice ata ReD

Ci(CT) Infinite coefficient of discharge for corner tappedorifice

Ci(FT) Infinite coefficient of discharge for corner tappedorifice

CPS Correction for pressure on flowmeter body or pipeCTS Correction for temperature on flowmeter body or piped Orifice bore diameter at Tf

xxi

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xxii Symbols

dm Orifice bore diameter at Tm

dr Orifice bore diameter at Tr

dP Differential pressureD Internal diameter at Pf and Tf

Dm Internal diameter measured at Tm

Dr Internal diameter at Tr

e Naperian constant, 2.71828e Orifice bore thicknessE Orifice plate thicknessEm Modulus of elasticity of pipe or flowmeter bodyEv Velocity of approach factorFT Flow transmitter (i.e., preamp, dP transmitter)FQ Flow computergc Dimensional conversion constantG Specific gravity (identical to real relative density) Gid Ideal gravity (identical to ideal relative density)GC Gas chromatographGross HVid Gross heating value at 14.696 psia and 60ºFH Energy contentHHVb Higher heating value per base volume unit on a

“dry” basisJ JouleKF K-factor assigned to a flowmeterL1 Upstream tap location for orifice flowmeterL2 Downstream tap location for orifice flowmeterLi Chordal path length for an ultrasonic flowmeterLHV Lower heating valueMAOP Maximum allowable operating pressureM1 A term in the RG discharge coefficient equationM2 A term in the RG discharge coefficient equationMF Meter factorMS Manual samplerMW Molecular weightMWair Molecular weight of airMWgas Molecular weight of gasn Number of chordal paths for ultrasonic flowmeternm Number of parallel flowmeter assembly(s) for

uncertainty

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Symbols xxiii

N Number of flowmeter pulsesN1 Unit conversion factor (orifice flowrate equation)N2 Unit conversion factor (Reynolds number equation)N3 Unit conversion factor (expansion factor equation)N4 Unit conversion factor (for RG tap term) NKF Nominal K-factor assigned to a flowmeterNHV Net heating valueP PressurePb Base pressurePc Critical pressurePf Pressure at flowing conditionsPf

1Absolute static pressure at upstream orifice sensing tap

Pf2

Absolute static pressure at downstream orificesensing tap

PDROP Permanent pressure lossPT Pressure transmitterqH Energy flow rate at base conditionsqm Mass flow rateqav Actual volumetric flow rateqvb Volume flow rate at base conditionsQH Energy quantity at base conditionsQm Mass quantityQvb Volume quantity at base conditionsR Universal gas constantRD Real relative densityRDid Ideal relative densityReD Pipe Reynolds numberSCd Sensitivity coefficient for Cd

Sd Sensitivity coefficient for dSD Sensitivity coefficient for DSdP Sensitivity coefficient for dPSMF Sensitivity coefficient for MFSP Sensitivity coefficient for Pf

SRD Sensitivity coefficient for RDid

ST Sensitivity coefficient for Tf

SY Sensitivity coefficient for YSZ Sensitivity coefficient for Ztp

Sρtp Sensitivity coefficient for ρtp

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xxiv Symbols

SOS Speed of soundSOSb Speed of sound of fluid at base conditionsSOSi Speed of sound of fluid along chordal pathSOStp Speed of sound of fluid at flowing conditionstu Upstream transit time of the chordal pathtd Downstream transit time of the chordal pathT TemperatureTb Base temperatureTc Critical temperatureTf Temperature of fluid at flowing conditionsTm Temperature of diameter measurements (Dm) Tr Reference temperature (68ºF or 20ºC) for diameters

(Dr)TT Temperature transmitterTW ThermowellU UncertaintyUr Random uncertaintyUb Systematic (or bias) uncertaintyU 95 or U95 Uncertainty at 95% confidence intervalV VelocityVavg Average or mean velocity of the flowmeter or pipeVi Mean velocity measured by the chordal pathWi Weighting factor for individual ultrasonic chordWs Wobbe index of a given compositionx Ratio of differential pressure to absolute static

pressurexj Mole fraction of component jY Expansion factorZ CompressibilityZb Compressibility of gas at Pb and Tb

Zb of air Compressibility of air at Pb and Tb

Ztp Compressibility of gas at Pf and Tf

α Linear coefficient of thermal expansionαplate Linear coefficient of thermal expansion of orifice plateαpipe Linear coefficient of thermal expansion of pipe or

flowmeterβ Orifice diameter ratio (d/D) at Tf

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Symbols xxv

βr Orifice diameter ratio (dr/Dr) at Tr

κ Isentropic exponentκid Ideal isentropic exponentκr Real isentropic exponentρ Mass density of fluidρb Mass density of fluid at Pb and Tb

ρtp Mass density of fluid at Pf and Tf

τ Time periodθ Angle of the ultrasonic transducer or orifice plate

bevel angleμ Absolute viscosity of flowing fluid

Units of Measure

USC United States Customary units SI International System of unitsft Foot or feetin. Inchm Metermm MillemeterºF Degrees FahrenheitºC Degrees CelsiusºR Degrees RankineºK Degrees KelvinH2O @60 Inches of water at 60ºFpsi Pound per square inchbar Barmbar MillibarPa PascalkPa KilopascalMPa Megapascalfps Feet per secondmps Meters per secondlbm Mass in poundskgm Mass in kilogramsSCF Standard cubic footMSCF Thousand standard cubic feet

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xxvi Symbols

MM SCF Million standard cubic feetNm3 Normalized (standard) cubic meterBtu British thermal unitsDth Dekatherm, equivalent to MM BtuMM Btu Million Btu, equivalent to a Dth

J JouleMJ Megajoule

Subscripts

a Atmospheric or absoluteb Base conditionsd Differentialg Gaugei Chordal path i of ultrasonic flowmeterj Component j of a gas mixturer Reference conditions1 Upstream 2 Downstream

Powers

Factor Prefix Symbol 1012 tera T109 giga G106 mega M103 kilo k102 hecto h101 deka da10–1 deci d10–2 centi c10–3 milli m10–6 micro μ10–9 nano n10–12 pico p

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xxvii

Unit Conversions

The following unit conversions have been found useful for meas-urement engineers, technicians, and operating personnel.

Lengthm = ft × 0.3048 mm = in. × 25.4mm = m × 1E –03

Flowing Temperature (Tf )ºC = (ºF – 32) × (5/9)ºF = [(9/5) × ºC] + 32ºK = ºC + 273.15ºR = ºF + 459.67

Flowing Pressure (Pf )MPa = psi ×× 6.894 757E –03KPa = psi × 6.894 757E +00bar = psi × 6.894 757E –02mbar = bar × 1E –03KPa = Pa × 1E +03MPa = Pa × 1E +06

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Absolute Pressure (Pf )psia = psig + Patm

bara = barg + Patm

kPaa = kPag + Patm

MPaa = psig + Patm

Differential Pressure (dP)psid = in H2O at 60ºF/27.707 271psid = in H2O at 68ºF/27.729 760mbard = in H2O at 60ºF × 2.488 429kPad = in H2O at 60ºF × 0.248 842 9Pad = in H2O at 60ºF × 248.842 9

Mass (m)kgm = lbm × 4.535 924E –01grain= lbm/7.0E +03

Mass Density (ρ)kgm per m3 = lbm per ft3 × 1.601 846E +01

Volume (ρ)m3 = ft3 × 2.831 685E –02

Energy Content (H )J = BtuIT × 1.055 056E +03Calorie = BtuIT/3.968 3E –03Calorie = Joule/4.1869E +00

xxviii Unit Conversions

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