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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 Company
2 Greenway Plaza, Suite 1020
Houston, 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 2006
665.7'4—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
List of Figures
Preface
Symbols
Unit Conversions
xi
xiii
xix
xxi
xxvii
1
1.1
1.2
1.3
1.4
1.5
Introduction
Transportation System
Measurement
Fluid Classification, Commercial
Material Quality
Risk Management
1
2
9
12
14
15
2
2.1
2.2
2.3
2.4
Composition and Quality
Assay
Quality Parameters and Tolerances
Potential Impacts of Gas Quality
Typical Streams
19
20
22
26
29
3
3.1
3.2
3.3
Physical Properties and Process Conditions
Natural Gas
Fluid Classification: Technical
Phase Envelope
39
39
42
43
v
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Contents
3.4 Fluid Properties
3.5 Process (or Operating) Conditions
3.6 Typical Natural Gas Physical Properties
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
47
54
65
Measurement Concepts
Applicable Fluids
Base Conditions
Flowmeters (or Primary Devices)
Flowmeter Calibration Concepts
Law of Similarity
Single-Phase Fluid Flow in Pipes
Multiphase Fluid Flow in Pipes
Secondary Devices
Tertiary Device
Uncertainty
Total Cost of Measurement
79
80
80
81
82
88
92
102
107
108
108
110
5
5.1
5.2
5.3
5.4
5.5
5.6
Orifice Flowmeter
General Principles
Mass Flow Equation
Artifact Calibration
Uncertainty Roadmap
Sources of Error
Risk Management
111
111
115
121
125
129
129
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
Ultrasonic Flowmeter
General Principles
Mass Flow Equation
Central Facility Calibration
In Situ Calibration
Uncertainty Roadmap
Sources of Error
Risk Management
135
135
139
141
142
143
148
158
7
7.1
7.2
7.3
Turbine Flowmeter
General Principles
Mass Flow Equation
Central Facility Calibration
163
163
166
166
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Contents
vii
7.4
7.5
7.6
7.7
In Situ Calibration
Uncertainty Roadmap
Sources of Error
Risk Management
167
168
173
174
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
Rotary Displacement Flowmeter
General Principles
Mass Flow Equation
Central Facility Calibration
In Situ Calibration
Uncertainty Roadmap
Sources of Error
Risk Management
177
177
180
181
182
183
187
188
9
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
Calculations
Base Conditions
Physical Properties
Natural Gas Density
GPA 2172 versus A.G.A.8
Mass Flow Rate in Pipes
Mass Flow Rate for Orifice Flowmeter
Mass Flow Rate for Ultrasonic Flowmeter
Mass Flow Rate for Turbine Flowmeter
Mass Flow Rate for Rotary Displacement Flowmeter
Volumetric Flow Rate at Base Conditions
Energy Flow Rate at Base Conditions
Quantities
191
191
192
202
209
214
215
222
227
230
231
231
233
10
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
Secondary and Tertiary Devices
General
Differential Pressure (dP)
Static Pressure
Temperature
Multivariable Transmitter
Online Densitometer
Moisture Analyzer
Online Gas Chromatograph
Other Analyzers
235
236
248
251
253
255
257
259
263
268
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Contents
10.10 Flow Computers
10.11 Gas Sampling Systems
269
270
11
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11
11.12
Electronic Gas Measurement
Description of an Electronic Gas Measurement System
System Accuracy
Definitions
Sampling Flow Variables
Low Flow Detection
Averaging Techniques
Compressibility, Density, and Heating Values
Hourly and Daily Quantity Calculations
Data Availability
Audit and Reporting Requirements
Equipment Verification, Calibration, and Certification
Security
279
279
280
281
282
282
282
282
283
283
286
294
296
Uncertainty
Uncertainty Terms
Measurement Uncertainty
Examples of Flowmeter Uncertainties
Statistical Weighting
299
301
303
307
312
Measurement System Design
Targeted Uncertainty
Fluid Physical Properties
Operating Design Data
Other Process Conditions
General Equipment Redundancy
Site Requirements
Structures
Piping Requirements
Pressure Regulation and Control
Flare and Vent Facilities
Overpressure Protection
Thermal Relief Valves
Headers
Strainers
319
319
320
320
321
322
324
325
326
329
330
330
331
331
332
12
12.1
12.2
12.3
12.4
13
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
13.12
13.13
13.14
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Contents
13.15
13.16
13.17
13.18
13.19
13.20
13.21
13.22
13.23
13.24
13.25
13.26
13.27
13.28
13.29
13.30
ix
DB&B Valves
Check Valves
Pulsation Control
Primary Device
Secondary Devices
Tertiary Device (Flow Computer)
Control Valves
Wiring and Grounding
Measurement Control Panel
Power Supplies
Satellite Panels
Supervisory Control and Leak Detection
Security
Factory Acceptance Testing
Dewatering, Cleaning, and Drying
Commissioning
333
334
334
334
335
344
345
345
347
347
348
348
349
350
350
351
14
14.1
14.2
14.3
14.4
14.5
14.6
14.7
Orifice Flowmeter Design
General
Velocity and Piping Insulation
Strainers
Flowmeter Assembly
Flowmeter, Mechanical
Piping Spools, Mechanical
Secondary and Tertiary Devices
353
353
354
355
355
358
358
358
15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
Ultrasonic Flowmeter Design
General
Velocity and Piping Insulation
Acoustic Filter
Flowmeter Assembly
Flowmeter, Mechanical
Piping Spools, Mechanical
Flowmeter: SPU, Electrical, and Software
Secondary and Tertiary Devices
361
361
363
363
363
366
367
367
369
16 Turbine Flowmeter Design
16.1 General
371
371
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16.2
16.3
16.4
16.5
16.6
16.7
16.8
Velocity and Piping Insulation
Strainer and Lubrication
Flowmeter Assembly
Flowmeter, Mechanical
Piping Spools, Mechanical
Flowmeter: SPU, Electrical, and Software
Secondary and Tertiary Devices
372
373
373
375
375
376
377
17
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
Rotary Displacement Flowmeter Design
General
Velocity and Piping Insulation
Filtration and Lubrication
Flowmeter Assembly
Flowmeter, Mechanical
Piping Spools, Mechanical
Flowmeter: SPU, Electrical, and Software
Secondary and Tertiary Devices
379
379
380
381
381
382
382
383
384
18 Inspection, Testing, Verification, Calibration,
and Certification
18.1 Inspection
18.2 Testing
18.3 Verification
18.4 Calibration
18.5 Certification
18.6 Equipment
18.7 Equipment Information
18.8 Records
387
389
389
390
391
392
392
395
406
Appendix: Standards, Publications, and
Regulations
Mechanical Standards and Publications
Electrical Standards and Publications
Measurement Standards and Publications
U.S. Government Regulations
407
408
409
410
418
Glossary
Index
421
453
A.1
A.2
A.3
A.4
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List of Tables
2
2–1
2–2
2–3
2–4
2–5
2–6
2–7
Composition and Quality
Typical Assay
Additional Information
Quality Parameters and Tolerances
GOM Production Sales Gas Composition
GOM Inlet to Gas Plant Composition
GOM Outlet of Gas Plant Composition
Outlet of LNG Plant Composition
21
22
23
30
32
33
35
4 Measurement Concepts
4–1 Multiphase Classifications, Horizontal and
Vertical Pipes
103
5 Orifice Flowmeter
5–1 Mass Flow, Reynolds Number, and Expansion Factor
Equations
5–2 Errors in Orifice Flowmeters
122
130
6
6–1
6–2
6–3
Ultrasonic Flowmeter
Sensitivity Analysis Due to Buildup and Decay
Chordal Path Angle Error
Reflective Timing Measurements, 4-in. (100 mm)
Flowmeter
xi
150
152
154
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List of Tables
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 Calculations
9–1 GPA 2172 versus A.G.A.8, GOM Production
Sales Gas
9–2 GPA 2172 versus A.G.A.8, GOM Inlet to Gas Plant
9–3 GPA 2172 versus A.G.A.8, GOM Outlet of
Gas Plant
9–4 GPA 2172 versus A.G.A.8, Outlet of LNG Plant
12 Uncertainty
12–1 Summary of Flowmeter Uncertainty Calculations
for a Pf of 1385 psig and a Tf of 100°F
12–2 Summary of Flowmeter Uncertainty Calculations
for a Pf of 985 psig and a Tf of 70°F
12–3 Summary of Flowmeter Uncertainty Calculations
for a Pf of 585 psig and a Tf of 100°F
12–1 Summary of Flowmeter Uncertainty Calculations
for a Pf of 185 psig and a Tf of 70°F
13 Measurement System Design
13–1 Components Analyzed by the Gas Chromatograph
210
211
212
213
308
309
310
311
342
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List of Figures
1
1–1
1–2
1–3
1–4
1–5
1–6
1–7
Introduction
Transportation System
Simple Gas Gathering System
Complex Gas Gathering System
Gas Processing Plant
Transmission Pipeline System
Distribution System
Phase Envelope: Raw Material and Finished Product
3
3–1
3–2
3–3
Physical Properties and Process Conditions
Multicomponent Gas Stream, PR EOS Phase Envelope
Typical Gulf Coast Gas, Phase Diagram
Predicted PhasePro Retrograde Generation, GOM
Production Sales Gas
Predicted PhasePro Envelope
Hydrate Disassociation Curves for Natural Gas
GOM Production Sales Gas: ρb, ρtp, μ, SOS, κr
GOM Production Sales Gas: Mass Density
versus Pressure for Various Isotherms
GOM Production Sales Gas: Absolute Viscosity versus
Pressure for Various Isotherms
GOM Production Sales Gas: Speed of Sound versus
Pressure for Various Isotherms
3–4
3–5
3–6
3–7
3–8
3–9
xiii
3
3
5
6
8
9
15
44
45
46
46
53
67
68
68
69
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List of Figures
3–10 GOM Production Sales Gas: Real Isentropic Exponent
versus Pressure for Various Isotherms
3–11 GOM Inlet to Gas Plant: ρb, ρtp, μ, SOS, κr
3–12 GOM Inlet to Gas Plant: Mass Density versus
Pressure for Various Isotherms
3–13 GOM Inlet to Gas Plant: Absolute Viscosity versus
Pressure for Various Isotherms
3–14 GOM Inlet to Gas Plant: Speed of Sound versus
Pressure for Various Isotherms
3–15 GOM Inlet to Gas Plant: Real Isentropic Exponent
versus Pressure for Various Isotherms
3–16 GOM Outlet of Gas Plant: ρb, ρtp, μ, SOS, κr
3–17 GOM Outlet of Gas Plant: Mass Density versus
Pressure for Various Isotherms
3–18 GOM Outlet of Gas Plant: Absolute Viscosity versus
Pressure for Various Isotherms
3–19 GOM Outlet of Gas Plant: Speed of Sound versus
Pressure for Various Isotherms
3–20 GOM Outlet of Gas Plant: Real Isentropic Exponent
versus Pressure for Various Isotherms
4
4–1
4–2
4–3
4–4
4–5
4–6
4–7
Measurement Concepts
Classification of Flowmeters
Classification of Calibration Concepts
Calibration Systems, Central Facility and In Situ
SwRI’s Metering Research Facility
CEESI’s Iowa Facility
TransCanada Calibrations’ Winnipeg Facility
Fully Developed Velocity Profiles, Laminar
and Turbulent
4–8 Fully Developed Turbulent Velocity Profile
(Hinze), Pipe Flows at Various Downstream Pipe
Diameters
4–9 Developing Flows, Swirl Free, Nonsymmetrical
Pipe Flows at Various Downstream Pipe Diameters
4–10 Developing Flows, Moderately Swirling, Nonsymmetrical Pipe Flows at Various Downstream
Pipe Diameters
69
71
72
72
73
73
75
76
76
77
77
82
83
83
85
86
86
94
97
98
99
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List of Figures
4–11 Developing Flows, High Swirling, Symmetrical
Pipe Flows at Various Downstream Pipe Diameters
4–12 Multiphase Flow for Horizontal Pipes
4–13 Sources of Uncertainty for Flowmeters
5
5–1
5–2
5–3
5–4
5–5
5–6
5–7
5–8
6
6–1
6–2
6–3
6–4
6–5
6–6
6–7
6–8
Orifice Flowmeter
Classification of Orifice Flowmeters
Dual-Chamber Orifice Fitting
Orifice Plate
Sources of Uncertainty for Orifice Meters,
a Broad Overview
Sources of Uncertainty Using Artifact Compliance
Calibration
Sources of Uncertainty for Orifice Meters, a
Detailed Overview
Deficiencies of Geometric Similarity
Deficiencies of Dynamic Similarity
Ultrasonic Flowmeter
Classification of Ultrasonic Flowmeters
Multipath Ultrasonic Flowmeters
Sources of Uncertainty for Ultrasonic Meters,
a Broad Overview
Sources of Uncertainty Using Central Facility
Calibration
Sources of Uncertainty Using In Situ Calibration
Sources of Uncertainty for Ultrasonic Meters,
a Detailed Overview
Deficiencies of Geometric Similarity
Deficiencies of Dynamic Similarity
7 Turbine Flowmeter
7–1 Gas Turbine Flowmeter
7–2 Sources of Uncertainty for Gas Turbine Meters,
a Broad Overview
7–3 Sources of Uncertainty Using Central Facility
Calibration
7–4 Sources of Uncertainty Using In Situ Calibration
xv
100
104
109
112
114
115
126
126
127
128
128
135
136
138
144
144
145
146
147
147
164
169
169
170
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List of Figures
7–5 Sources of Uncertainty for Gas Turbine Meters,
a Detailed Overview
7–6 Deficiencies of Geometric Similarity
7–7 Deficiencies of Dynamic Similarity
8 Rotary Displacement Flowmeter
8–1 Rotary Displacement Flowmeter
8–2 Sources of Uncertainty for Rotary Displacement
Meters, a Broad Overview
8–3 Sources of Uncertainty Using Central Facility
Calibration
8–4 Sources of Uncertainty Using In Situ Calibration
8–5 Sources of Uncertainty for Rotary Displacement
Meters, a Detailed Overview
8–6 Deficiencies of Geometric Similarity
8–7 Deficiencies of Dynamic Similarity
9 Calculations
9–1 GOM Production Sales Gas Phase Envelope
9–2 GOM Production Sales Gas Retrograde
Generation, PR
9–3 GOM Production Sales Gas Retrograde
Generation, SRK
9–4 A.G.A.8’s Detailed Method, Uncertainties and
Limitations
9–5 A.G.A.8’s Gross Characterization Method,
Uncertainties and Limitations
9–6 Orifice Calculations of GOM Production Sales Gas
9–7 Orifice Calculations for GOM Outlet of a Gas Plant
9–8 Ultrasonic Calculations for GOM Outlet from a
Gas Plant
9–9 Turbine Calculations for GOM Outlet of a Gas Plant
9–10 Rotary Displacement Calculations for GOM Outlet
of a Gas Plant
10 Secondary and Tertiary Devices
10–1 Differential Pressure Transmitter
171
172
172
179
183
184
185
186
186
187
200
201
202
206
208
221
221
225
228
232
249
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List of Figures
10–2
10–3
10–4
10–5
10–6
10–7
10–8
10–9
Static Pressure Transmitter
Temperature Transmitter
Multivariable Transmitter
Online Gas Chromatograph
Flow Computer
Sampling System Overview
Automatic Flow-Weighted Sampling System
Manual (or Spot) Sampling System
xvii
252
254
256
264
270
272
276
277
12 Uncertainty
12–1 Roadmap of Sources of Uncertainty for Flowmeter
Estimations
12–2 Interlaboratory Results of a MUSM Flowmeter
Assembly (Artifact)
12–3 Statistical Weighting Example
305
315
13 Measurement System Design
13–1 Header Configurations
332
14 Orifice Flowmeter Design
14–1 Orifice Flowmeter Assembly
356
15 Ultrasonic Flowmeter Design
15–1 Ultrasonic Flowmeter Assembly
364
16 Turbine Flowmeter Design
16–1 Turbine Flowmeter Assembly
374
304
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Preface
Measurement is the basis of commerce between producers, royalty
owners, transporters, process plants, marketers, state and federal
government authorities, and the general public. In fact, accurate
measurement of hydrocarbon fluids and materials has a significant
impact on the Gross National Product of exporting and importing
countries, the financial performance and asset base of global companies, and the perceived efficiency of operating facilities. The need
for accurate fiscal measurement is obvious.
Given the present or future levels of the cost of natural gas, one
can quickly quantify the material and economic value unaccounted
for that is associated with each ±0.01% of systematic uncertainty
that might unknowingly exist in the measurement systems.
Measurement errors can have both immediate and long-term
impacts on profits. Inaccurate measurement may result in loss of
customers, adverse publicity, potential penalties, and legal liabilities. In short, equitable and accurate measurement is essential to
business. It affects the validity of financial and operating reports as
well as the corporate reputation (cash flow, profit and loss, balance
sheet, royalties and taxes).
For reasons such as these, it is essential that material quantity
measurements be precise and accurate with minimal bias errors.
Furthermore, it is incumbent on those involved in custody transfer
to establish and maintain the traceability chains that link their
measurements to appropriate domestic and international standards.
xix
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Preface
In this manner, fiscal transfers can be done equitably with the confidence of both seller and buyer alike.
The capital and operating resources (CAPEX, OPEX) applied for
fiscal transfers must be commensurate with the total cost of measurement: the capital cost of technology, the operating cost of technology,
industry practice or standards, regulatory compliance and the total fiscal exposure or risk (commodity value times throughput), the strategic
and tactical business direction, and competitors’ strategy. The amount
of uncertainty is governed by the investment of resources (CAPEX
and OPEX) combined with the inherent uncertainty associated with
the method of measurement (primary, secondary, and tertiary devices)
and the fiscal exposure or risk.
Measurement is a technically demanding, complex, state-ofthe-art field with a significant impact on the profitability of any
business. As such, the field of measurement demands a highly technical language of definitions, acronyms, and symbols that must be
fully understood and embraced by managers, supervisors, engineers, 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 (upgrade
or 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 handbook 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
Am
Ap
AS
AT
B
Btu
BtuIT
C
Cd
Cd(CT)
Cd(FT)
Ci(CT)
Ci(FT)
CPS
CTS
d
A term in the RG discharge coefficient equation
Cross-sectional area of flowmeter
Cross-sectional area of pipe
Automatic sampler
Analyzer transmitter (moisture analyzer, gas
chromatograph)
A term in the RG discharge coefficient equation
British thermal unit
British thermal unit, international
A term in the RG discharge coefficient equation
Coefficient of discharge
Coefficient of discharge for corner tapped orifice at
a ReD
Coefficient of discharge for flanged tapped orifice at
a ReD
Infinite coefficient of discharge for corner tapped
orifice
Infinite coefficient of discharge for corner tapped
orifice
Correction for pressure on flowmeter body or pipe
Correction for temperature on flowmeter body or pipe
Orifice bore diameter at Tf
xxi
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dm
dr
dP
D
Dm
Dr
e
e
E
Em
Ev
FT
FQ
gc
G
Gid
GC
Gross HVid
H
HHVb
J
KF
L1
L2
Li
LHV
MAOP
M1
M2
MF
MS
MW
MWair
MWgas
n
nm
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Symbols
Orifice bore diameter at Tm
Orifice bore diameter at Tr
Differential pressure
Internal diameter at Pf and Tf
Internal diameter measured at Tm
Internal diameter at Tr
Naperian constant, 2.71828
Orifice bore thickness
Orifice plate thickness
Modulus of elasticity of pipe or flowmeter body
Velocity of approach factor
Flow transmitter (i.e., preamp, dP transmitter)
Flow computer
Dimensional conversion constant
Specific gravity (identical to real relative density)
Ideal gravity (identical to ideal relative density)
Gas chromatograph
Gross heating value at 14.696 psia and 60ºF
Energy content
Higher heating value per base volume unit on a
“dry” basis
Joule
K-factor assigned to a flowmeter
Upstream tap location for orifice flowmeter
Downstream tap location for orifice flowmeter
Chordal path length for an ultrasonic flowmeter
Lower heating value
Maximum allowable operating pressure
A term in the RG discharge coefficient equation
A term in the RG discharge coefficient equation
Meter factor
Manual sampler
Molecular weight
Molecular weight of air
Molecular weight of gas
Number of chordal paths for ultrasonic flowmeter
Number of parallel flowmeter assembly(s) for
uncertainty
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Symbols
N
N1
N2
N3
N4
NKF
NHV
P
Pb
Pc
Pf
Pf
1
Pf
2
PDROP
PT
qH
qm
qav
qvb
QH
Qm
Qvb
R
RD
RDid
ReD
SCd
Sd
SD
SdP
SMF
SP
SRD
ST
SY
SZ
Sρtp
xxiii
Number of flowmeter pulses
Unit conversion factor (orifice flowrate equation)
Unit conversion factor (Reynolds number equation)
Unit conversion factor (expansion factor equation)
Unit conversion factor (for RG tap term)
Nominal K-factor assigned to a flowmeter
Net heating value
Pressure
Base pressure
Critical pressure
Pressure at flowing conditions
Absolute static pressure at upstream orifice sensing tap
Absolute static pressure at downstream orifice
sensing tap
Permanent pressure loss
Pressure transmitter
Energy flow rate at base conditions
Mass flow rate
Actual volumetric flow rate
Volume flow rate at base conditions
Energy quantity at base conditions
Mass quantity
Volume quantity at base conditions
Universal gas constant
Real relative density
Ideal relative density
Pipe Reynolds number
Sensitivity coefficient for Cd
Sensitivity coefficient for d
Sensitivity coefficient for D
Sensitivity coefficient for dP
Sensitivity coefficient for MF
Sensitivity coefficient for Pf
Sensitivity coefficient for RDid
Sensitivity coefficient for Tf
Sensitivity coefficient for Y
Sensitivity coefficient for Ztp
Sensitivity coefficient for ρtp
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SOS
SOSb
SOSi
SOStp
tu
td
T
Tb
Tc
Tf
Tm
Tr
TT
TW
U
Ur
Ub
U 95 or U95
V
Vavg
Vi
Wi
Ws
x
xj
Y
Z
Zb
Zb of air
Ztp
α
αplate
αpipe
β
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Page xxiv
Symbols
Speed of sound
Speed of sound of fluid at base conditions
Speed of sound of fluid along chordal path
Speed of sound of fluid at flowing conditions
Upstream transit time of the chordal path
Downstream transit time of the chordal path
Temperature
Base temperature
Critical temperature
Temperature of fluid at flowing conditions
Temperature of diameter measurements (Dm)
Reference temperature (68ºF or 20ºC) for diameters
(Dr)
Temperature transmitter
Thermowell
Uncertainty
Random uncertainty
Systematic (or bias) uncertainty
Uncertainty at 95% confidence interval
Velocity
Average or mean velocity of the flowmeter or pipe
Mean velocity measured by the chordal path
Weighting factor for individual ultrasonic chord
Wobbe index of a given composition
Ratio of differential pressure to absolute static
pressure
Mole fraction of component j
Expansion factor
Compressibility
Compressibility of gas at Pb and Tb
Compressibility of air at Pb and Tb
Compressibility of gas at Pf and Tf
Linear coefficient of thermal expansion
Linear coefficient of thermal expansion of orifice plate
Linear coefficient of thermal expansion of pipe or
flowmeter
Orifice diameter ratio (d/D) at Tf
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Symbols
βr
κ
κid
κr
ρ
ρb
ρtp
τ
θ
μ
Orifice diameter ratio (dr/Dr ) at Tr
Isentropic exponent
Ideal isentropic exponent
Real isentropic exponent
Mass density of fluid
Mass density of fluid at Pb and Tb
Mass density of fluid at Pf and Tf
Time period
Angle of the ultrasonic transducer or orifice plate
bevel angle
Absolute viscosity of flowing fluid
Units of Measure
USC
SI
ft
in.
m
mm
ºF
ºC
ºR
ºK
H2O @60
psi
bar
mbar
Pa
kPa
MPa
fps
mps
lbm
kgm
SCF
MSCF
United States Customary units
International System of units
Foot or feet
Inch
Meter
Millemeter
Degrees Fahrenheit
Degrees Celsius
Degrees Rankine
Degrees Kelvin
Inches of water at 60ºF
Pound per square inch
Bar
Millibar
Pascal
Kilopascal
Megapascal
Feet per second
Meters per second
Mass in pounds
Mass in kilograms
Standard cubic foot
Thousand standard cubic feet
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Symbols
MM SCF
Nm3
Btu
Dth
MM Btu
J
MJ
Million standard cubic feet
Normalized (standard) cubic meter
British thermal units
Dekatherm, equivalent to MM Btu
Million Btu, equivalent to a Dth
Joule
Megajoule
Subscripts
a
b
d
g
i
j
r
1
2
Atmospheric or absolute
Base conditions
Differential
Gauge
Chordal path i of ultrasonic flowmeter
Component j of a gas mixture
Reference conditions
Upstream
Downstream
Powers
Factor
1012
109
106
103
102
101
10–1
10–2
10–3
10–6
10–9
10–12
Prefix
tera
giga
mega
kilo
hecto
deka
deci
centi
milli
micro
nano
pico
Symbol
T
G
M
k
h
da
d
c
m
μ
n
p
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Unit Conversions
The following unit conversions have been found useful for measurement engineers, technicians, and operating personnel.
Length
m = ft × 0.3048
mm = in. × 25.4
mm = m × 1E –03
Flowing Temperature (Tf )
ºC = (ºF – 32) × (5/9)
ºF = [(9/5) × ºC] + 32
ºK = ºC + 273.15
ºR = ºF + 459.67
Flowing Pressure (Pf )
MPa = psi ×× 6.894 757E –03
KPa = psi × 6.894 757E +00
bar = psi × 6.894 757E –02
mbar = bar × 1E –03
KPa = Pa × 1E +03
MPa = Pa × 1E +06
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xxviii
Unit Conversions
Absolute Pressure (Pf )
psia = psig + Patm
bara = barg + Patm
kPaa = kPag + Patm
MPaa = psig + Patm
Differential Pressure (dP)
psid = in H2O at 60ºF/27.707 271
psid = in H2O at 68ºF/27.729 760
mbard = in H2O at 60ºF × 2.488 429
kPad = in H2O at 60ºF × 0.248 842 9
Pad = in H2O at 60ºF × 248.842 9
Mass (m)
kgm = lbm × 4.535 924E –01
grain= 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 +03
Calorie = BtuIT/3.968 3E –03
Calorie = Joule/4.1869E +00