-
~ ~
A P I MPMS*L4-3.3 92 W 0732290 053b085 556
Date of Issue: March 1994 Affected Publication: API Chapter 14
Natural Gas Fluids Measurement, Section 3, Concentric, Square-Edged
Orifice Meters, Part 3, Natural Gas Applications of the Manual of
Petroleum Measurement Standards, Third Edition, August 1992
ERRATA
On page 25, Equation 3-A-IO should read as follows:
g, = 0.0328096[978.01855 - 0.0028247L + 0.0020299L2 -
0.000015085L3 - 0.000094Hl (3-A-10)
On page 33, Equation 3-B-9 should read as follows: O 7
cl = 0.000511 + [O.O2i + 0.0049( 19, OOO 7* ]p4 ( - 1,000,000 I
J35 (3-B-9)
ReD Re,
On page 56, the second equation under 34.3. I . 7 should read as
follows:
Q,( 14.73)(0.570) ( (0.00OO069)(S.0085)(5 19.67)(0.999590) ReD =
(0.0114541) = 3.324464
On page 57, Equation 3-6b should read as follows:
= 7709.6 1 (0.60)( 1 .O3 1 60)( 0.9983 83)( 3 .99%9)2
(O. 5 70) (O. 9 5 1 308) (5 24.67) = 614,033 cubic feet per hour
at standard conditions
On page 57, the second equation in 3-6b should read as
follows:
Re, = 3.32446Q,. = 3.32446(614,033) = 2,041,328 (initial
estimate of Reynolds number)
(3-6b)
-
~ ~~
API MPMS+lY.3-3 92 0732290 0536086 492
On page 57, Equation 3-20 should read as follows:
19, OOO A = ( r ) 0 8
- - [ 19, 000(0.495597)]0 * 2,041,328
= 0.0135262
On page 57, Equation 3-21 should read as follows:
2,041,328 = 0.778988
(3-20)
(3-21)
On page 58, Equation 3-15 should read as follows:
Upstrm = C0.0433 + 0.0712e-85L1 - 0.1145e-60L'](1 - 0.23A)B
(3-15) = C0.0433 + 0.0712es~"'*' - 0.1145e6~u708s] x [i -
0.23(0.0135262)](0.0642005)
= 0.000876388
On page 58, Equation 3-16 should read as follows:
Dnstrm = -0.0116[M2 - 0.52M~3]'1(l - 0.14A)
= - 0.01 16[0.491284 - 0.52(0.491284)'3](0.495597)' ' (3-16)
x [i - 0.14(0.0135262)] = - 0.00152379
On page 58, Equation 3-14 should read as follows: Tap Term =
Upstrm + Dnstrm
= 0.000876388 + (-0.00152379) (3-14) = - 0.000647402
On page 58, Equation 3-12 should read as follows:
C,(F) = C,.(CT) + Tap Tem = 0.602414 - 0.000647402 =
0.601767
(3-12)
On page 58, Equation 3-11 should read as follows:
C,(FT) = C,(FT) + 0.000511 + (0.0210 + 0.0049A)P4C
= 0.601767 + 0.000511 [ 1O6(O.495597)]u7 2,041,328
(3-11)
+ [0.0210 + 0.0049(0.0135262)](0.495597)4(0.778988) = 0.602947
(second estimate of the coefficient of discharge)
2
-
On page 58, the third to the last equation should read as
follows: Qv = 617,048 cubic feet per hour at standard
conditions
[based on C, (F) = 0.6029471
On page 58, the second to the last equation should read as
follows: Re, = 3.32446Q,, = 3.32446(617,048)
= 2,05 1,35 1 (second estimate of Reynolds number)
On page 59, the second equation should read as follows: Re, =
3.32446Qv = 3.32446(617,046)
= 2,05 1,345 (third estimate of Reynolds number)
On page 59, Equation 3-7 should read as follows:
= 6 17,046(-)( 14.73 -)( 509.67 0.997839\, 14.65 519.67
0.997971)
(3- 7)
= 608,396 cubic feet per hour at base conditions
On page 60, Equation 3-B-9 should read as follows:
1,000, ooop ( 'i e, = 0.000511 o 3 5 (3-8-9)
1,000,000
On page 62, the$rst equation should read as follows:
= 0.5961 + 0.0291p2 - 0.2290px
+ (0.0433 + 0.0712en% - 0.1 1456') [ 1 - 0.23 ( -'- i9:;p)..] -
p;'
= 0.5961 + 0.0291(0.495597)2 - 0.2290(0.495597)* + [ 0.0433 +
0.0712e"07"~ - 0.1 145e6'07"')[l - 0.23(0.0137493)](0.0642005) -
0.01 16[0.491284 - 0.52(0.49128413)](0.495597)'.1[1 -
0.14(0.0137493)]
= 0.601767
3
-
A P I M P M S * 1 4 - 3 . 3 92 0732290 0536088 265
On page 62, Equation 3-B-9 should read as follows:
4 = 0.000511 (1 ,00 ;~00~)" '
0.0210 + 0.0049 ( 1 9 , 0 0 0 ~ ~ )"*]].(i, ooo,ooo 1 35 Re,
Re,
= 0.000511( 1,000,000(0.495597) 2,000,000
(3-8-9)
+ [0.02 1 O + 0.0049(0.0 137493)](0.495597)'(0.784584) =
0.00118960
On page 65, thefirst equation should read as follows:
Re, = 0.0114588 - (",or) = 3.32446Q" = 3.32446(617,057) = 2,05
1,400 (second iteration)
On page SO, Equation 3-0-9 should read as follows (that is,
Kpipe, should be inserted in the equation and the second line of
the equation should be deleted}:
Re, = 2 2 0 , 8 5 8 d l $ m x (Kpipe) (3-0-9)
On page 80, the nomenclature should read as follows (that is,
Kpipe, should be inserted in the list):
Where:
G = specific gravity. Kpipe = values from Table 3-D-4.
Red = orifice bore Reynolds number. T, = absolute flowing
temperature, in degrees Rankine. p = specific weight of a gas at
14.7 pounds force per squareinch absolute and 32F
On page 97, Equations 3-F-4 and 3-F-5 should read as
follows:
Hid = 4,(ff:d), + 4 2 W i d ) 2 + ... + 4wwid)w (3-F-4)
On page 102, the second line of Equation 3-4a should read as
follows:
(3-F-5)
ZbRT G, (28.9625)(144)hw eG,(28.9625)(144)
Qb = 359.072C,(FT)Evqd2
4
-
A P I M P M S * L 4 . 3 * 3 92 0732290 0503843 988
Manual of Petroleum Measurement Standards Chapter 14-Natural Gas
Fluids
Measurement Section 3-Concentric, Square-Edged
Orif ice Meters Part 3-Natural Gas Applications THIRD EDITION,
AUGUST 1992
I ACA American Gas Association Report No. 3, Part 3 I I i;pp Gas
Processors Association GPA 81 85, Part 3 1 American National
Standards Institute ANSVAPI 2530-1 991, Part 3 I
American Petroleum Institute 1220 L Street. Northwest
11 Washington, D.C. 20005
-
A P I M P M S * 1 4 - 3 a 3 92 0732290 0503844 814
Manual of Petroleum Measurement Standards Chapter 14-Natural Gas
Fluids Measurement Section 3-Concentric, Square-Edged
Orif ice Meters Part 3-Natural Gas Applications
Measurement Coordination Department
THIRD EDITION, AUGUST 1992
American Petroleum Institute
-
~ ~ ~~~
API M P M S * L 4 - 3 . 3 92 m 0732290 0503845 750 m
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 REVEWED.
2. API IS NOT UNDERTAKING TO MEET THE DUTIES OF EMPLOYERS, MANU-
FACTURERS, OR SUPPLIERS TO WARN AND PROPERLY TRAIN AND EQUIP THEIR
EMPLOYEES, AND OTHERS EXPOSED, CONCERNING HEALTH AND SAFETY RISKS
AND PRECAUTIONS, NOR UNDERTAKING THEIR OBLIGATIONS UNDER LOCAL,
STATE, OR FEDERAL LAWS.
3. INFORMATION CONCERNING SAFETY AND HEALTH RISKS AND PROPER
TIONS 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 CONSTRUED
AS
PRECAUTIONS WITH RESPECT TO PARTICULAR MATERIALS AND CONDI-
GRANTING ANY RIGHT, BY IMPLICATION OR OTHERWISE, FOR THE MANU-
FACTURE, SALE, OR USE OF ANY METHOD, APPARATUS, OR PRODUCT COV-
ERED BY LETTERS PATENT. NEITHER SHOULD ANYTHING CONTAINED IN
ITY FOR INFRINGEMENT OF LETI'ERS PATENT. THE PUBLICATION BE
CONSTRUED AS INSURING ANYONE AGAINST LIABIL-
5. GENERALLY, API STANDARDS ARE REVIEWED AND REVISED, REAF-
FIRMED, OR WITHDRAWN AT LEAST EVERY FIVE YEARS. SOMETIMES A ONE-
TIME EXTENSION OF UP TO TWO YEARS WILL BE ADDED TO THIS REVIEW
TER ITS PUBLICATION DATE AS AN OPERATIVE API STANDARD OR, WHERE
AN EXTENSION HAS BEEN GRANTED, UPON REPUBLICATION. STATUS OF
THE
CYCLE. THIS PUBLICATION WILL NO LONGER BE IN EFFECT FIVE YEARS
AF-
PUBLICATION CAN BE ASCERTAINED FROM THE API AUTHORING DEPART-
MENT [TELEPHONE (202) 682-8000]. A CATALOG OF API PUBLICATIONS AND
MATERIALS IS PUBLISHED ANNUALLY AND UPDATED QUARTERLY BY API, 1220
L STREET, N. W., WASHINGTON, D.C. 20005.
Copyright O 1992 American Petroleum Institute
-
FOREWORD
This foreword is for information and is not part of this
standard. Chapter 14, Section 3, Part 3, of the Manual of Petroleum
Measurement Standards pro-
vides an application guide along with practical guidelines for
applying Chapter 14, Section 3, Parts 1 and 2, to the measurement
of natural gas. Mass flow rate and base (or standard) volumetric
flow rate methods are presented in conformance with North American
industry practices.
This standard has been developed through the cooperative efforts
of many individuals from industry under the sponsorship of the
American Petroleum Institute, the American Gas Association, and the
Gas Processors Association, with contributions from the Chemical
Manufacturers Association, the Canadian Gas Association, the
European Community, Nor- way, Japan, 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 pub- lication and hereby expressly disclaims any liability or
responsibility for loss or damage re- sulting 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 Measure- ment Coordination Department, American
Petroleum Institute, 1220 L Street, N.W., Wash- ington, D.C.
2000.5.
i i 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 individ- uals 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.
K. West, Mobil Research and Development Corporation E- UPP
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 pro- viding 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 Na- tional Institute of Standards and
Technology in Gaithersburg, Maryland. C. Britton, S. Cald- well,
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 re- sponsible 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 partic- ipated in the development of this document.
R. Adamski, Exxon Chemical Americas-BOP R. Bass M. Bayliss,
Occidental Petroleum (Caledonia) Ltd. R. Beaty, Amoco Production
Company D. Bell, NOVA Corporation B. Berry J. Bosio, Statoil
iv
-
-
API MPMS*L4-3-3 92 = 0732290 0503848 4bT =
J. Brennan, National Institute of Standards and Technology E.
Buxton S. Caldwell T. Coker, Phillips Petroleum Company H. Colvard,
Exxon Company, U.S.A. L. Datta-Bania, United Gas Pipeline Company
D. Embry, Phillips Petroleum Company
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 Technology B. 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 Van Orsdol, Chevron U.S.A. Inc. N. Watanabe, National Research
Laboratory of Metrology, Japan K. West, Mobil Research and
Development Corporation P. Wilcox, Total of France J. Williams,
Oryx Energy Company
w. Fling
E. UPP
V
-
M. Williams, Amoco Production Company E. Woomer, United Gas
Pipeline Company C. Worrell, OXY USA, Inc.
vi
-
~~ ~ . ._ -
A P I MPMS*1V-3.3 92 = 0732290 0503850 018 W
CONTENTS
Page
CHAPTER 14 -NATURAL GAS FLUIDS MEASUREMENT SECTION 3
.CONCENTRIC. SQUARE-EDGED
ORIFICE METERS 3.1 Introduction
.....................................................................................................
1
3.1.1 Application
...............................................................................................
1 3.1.2 Basis for Equations
...................................................................................
1 3.1.3 Organization of Part 3
..............................................................................
1
3.2 Symbols. Units. and Terminology
...................................................................
1 3.2.1 General
.....................................................................................................
1 3.2.2 Symbols and Units
...................................................................................
2 3.2.3 Terminology
.............................................................................................
4
3.3 Flow Measurement Equations
.........................................................................
5 3.3.1 General
.....................................................................................................
3.3.2 Equations for Mass Flow of Natural Gas
................................................. 3.3.3 Equations
for Volume Flow of Natural Gas
............................................. 3.3.4 Volume
Conversion From Standard to Base Conditions
..........................
Flow Equation Components Requiring Additional Computation
................... 3.4.1 General
.....................................................................................................
3.4.2 Diameter Ratio
.........................................................................................
3.4.3 Coefficient of Discharge for Flange-Tapped Orifice Meter
..................... 3.4.4 Velocity of Approach Factor
....................................................................
3.4.5 Reynolds Number
.....................................................................................
3.4.6 Expansion Factor
......................................................................................
3.4
3.5 Gas Properties
.................................................................................................
3.5.1 General
.....................................................................................................
3.5.2 Physical Properties
...................................................................................
3.5.3 Compressibility
........................................................................................
3.5.4 Relative Density (Specific Gravity)
.........................................................
Density of Fluid at Flowing Conditions
................................................... 3.5.5
5 5 6 7 7 7 8 8
10 10 11 13 13 13 14 15 17
APPENDIX 3-A-ADJUSTMENTS FOR INSTRUMENT CALIBRATION ....... 21
APPENDIX 3-B-FACTORS APPROACH
.......................................................... 29
APPENDIX 3-C-FLOW CALCULATION EXAMPLES
.................................... 53 APPENDIX 3-D-PIPE TAP
ORIFICE METERING ........................................... 67
APPENDIX 3-E-SI CONVERSIONS
..................................................................
91 APPENDIX 3-F-HEATING VALUE CALCULATION
...................................... 95 APPENDIX 3-G-DEVELOPMENT
OF CONSTANTS FOR
FLOW EQUATIONS
...............................................................
99
Figures 3-D-1-Maximum Percentage Allowable Meter Tube Tolerance
Versus
Beta Ratio
.................................................................................................
73 78 3-D-2-Allowable Variations in Pressure Tap Hole Location
..............................
Tables 3-1-Linear Coefficient of Thermal Expansion
.................................................. 8
24 3-A-2-Mercury Manometer Factors (Fhgm)
....................................................... 27
3-B-1-Assumed Reynolds Numbers for Various Meter Tube Sizes
................. 35 3-B-2-Numeric Conversion Factor (E)
............................................................ 36
3-B-3-Orifice Calculation Factor: F, From Equations in 3-B.5
........................ 39
3-A- 1-Water Density Based on Wegenbreth Equation
......................................
-
- - ._ -_ A P I NPflS*l14-3 .3 92 m 0732290 0503851 T 5 4 m
3-B-4-Orifice Slope Factor: F,, From Equations in 3-B.6
.................................. 3-B-5-Conversion of ReD/106 to
Q,/lOOO (Qv in Thousands of
Cubic Feet per Hour)
.............................................................................
3-B-6-Expansion Factors for Flange Taps (Y,): Static Pressure Taken
From
Upstream Taps ........ .......... ..... ..... .. ..... .. ..
..... ..... .. ....... .. .. ..... .. .. .. ..... .. .... .. .
3-B-7-F,b Factors Used to Change From a Pressure Base of 14.73
Pounds
Force per Square Inch to Other Pressure Bases
..................................... 3-B-8-&, Factors Used to
Change From a Temperature Base of 60F to Other
Temperature Bases ........... .. ..... .. ..... ....... .. .....
... .. ....... .. .... ..... .. .. ....... .. ......
3-B-9-I$Factors Used to Change From a Flowing Temperature of 60F
to
Actual Flowing Temperature
..................................................................
3-B-lO-F,,. Factors Used to Adjust for Real Gas Relative Density
(GJ: Base
Conditions of 60F and 14.73 Pounds Force per Square Inch
Absolute 3-B-11-Supercompressibility Factors for G,. = 0.6 Without
Nitrogen or
Carbon Dioxide ........... .............. ................... ..
.....,.......... ......... .. ..... ...... 3-D-1-Basic Orifice
Factors (Fb) for Pipe Taps
................................................. 3-D-2-Meter Tube
Pressure Tap Holes ............ .. ..... ......... .........
....... .. ......... .. .. .. 3-D-3-b Values for Determining
Reynolds Number Factor F, for Pipe Taps ... 3-D-4-Values of K to Be
Used in Determining Rd for Calculation of F, Factor..
3-D-5-Expansion Factors for Pipe Taps (YJ: Static Pressure Taken
From
Upstream Taps ... .. . . . . . . . . . . . , . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 3-D-6-Expansion
Factors for Pipe Taps (Y2): Static Pressure Taken From
Downstream Taps
...................................................................................
3-E- 1-Volume Reference Conditions for Custody Transfer
Operations:
Natural Gas Volume
...............................................................................
3-E-2-Energy Reference Conditions ..... . . , , . . . , , . , , . .
. . . . . . . . . , . . , . . . . , . . , . . . . , . . . . . . . .
, . . . . . . . . . . . 3-E-3 -Heating Value Reference Conditions .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 3-F-1-Physical Properties of
Gases at Exactly 14.73 Pounds Force per Square
Inch Absolute and 60F
..........................................................................
Page
42
44
47
49
49
50
51
52 74 78 80 84
85
87
93 93 93
96
viii
-
Chapter 14-Natural Gas Fluids Measurement
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS
PART 3-NATURAL GAS APPLICATION
3.1 Introduction 3.1 .I APPLICATION 3.1 .I .I General
This part of Chapter 14, Section 3, has been developed as an
application guide for the calculation of natural gas flow through a
flange-tapped, concentric orifice meter, using the inch-pound
system of units. For applications involving SI units, a conversion
factor may be applied to the results (Q,, Qv, or Qb) determined
from the equations in 3.3. Intermediate conversion of units will
not necesskly produce consistent results. As an alternative, the
more universal approach specified in Chapter 14, Section 3, Part 1,
should be used. The me- ter must be constructed and installed in
accordance with Chapter 14, Section 3, Part 2.
3.1 .I .2 Definition of Natural Gas As used in this part, the
term natural gas applies to fluids that for all practical
purposes
are considered to include both pipeline- and production-quality
gas with single-phase flow and mole percentage ranges of components
as given in American Gas Association (A.G.A.) Transmission
Measurement Committee Report No. 8, Compressibility and Supercom-
pressibility for Natural Gas and Other Hydrocarbon Gases. For other
hydrocarbon mix- tures, the more universal approach specified in
Part 1 may be more applicable. Diluents or mixtures other than
those stipulated in A.G.A. Transmission Measurement Committee Re-
port No.8 may increase the flow measurement uncertainty.
3.1.2 BASIS FOR EQUATIONS The computation methods used in this
part are consistent with those developed in Part 1
and include the Reader-Harris/Gallagher equation for
flange-tapped orifice meter discharge coefficient. The equation has
been modified to reflect the more common units of the inch- pound
system. Since the new coefficient of discharge equation does not
address pipe tap meters, the pipe tap methodology of the 1985
edition of ANSUAPI 2530 has been retained for reference in Appendix
3-D.
3.1.3 ORGANIZATION OF PART 3 Chapter 14, Section 3, Part 3, is
organized as follows: Symbols and units are defined in
3.2, the basic flow equation is presented in 3.3, the key
equation components are defined in 3.4, and the gas properties
applicable to orifice metering of natural gas are developed in 3.5.
All values are assumed to be absolute. Factors to compensate for
meter calibration and lo- cation are included in Appendix 3-A. The
factor approach to orifice measurement is in- cluded in Appendix
3-B. Appendix 3-C covers examples to assist the user in
interpreting this part. Appendix 3-D covers pipe tap meters.
Appendix 3-E covers SI conversions, Ap- pendix 3-F covers heating
value calculation, and Appendix 3-G covers derivation of con-
stants. The user is cautioned that the symbols as defined in 3.2
may be different from those used in previous orifice metering
standards.
3.2 Symbols, Units, and Terminology 3.2.1 GENERAL
The symbols and units used are specific to Chapter 14, Section
3, Part 3, and were devel- oped based on the customary inch-pound
system of units. Regular conversion factors can
1
-
~~
A P I MPMS*L4.3-3 92 E 0732290 0503853 827
2 CHAPTER 1 '&NATURAL GAS FLUIDS MEASUREMENT
be used where applicable; however, if SI units are used, the
more generic equations in Part 1 should be used for consistent
results.
3.2.2 SYMBOLS AND UNITS Description
Orifice plate coefficient of discharge Coefficient of discharge
at a specified pipe Reynolds number for Bange-tapped orifice meter
Coefficient of discharge at infinite pipe Reynolds number for
coiner-tapped orifice meter Coefficient of discharge at infinite
pipe Reynolds number for Bange-tapped orifice meter Specific heat
at constant pressure Specific heat at constant volume Orifice plate
bore diameter calculated at flowing temperature, T, 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,
Napierian constant Velocity of approach factor Temperature, in
degrees Fahrenheit Temperature, in degrees Rankine
Supercompressibility factor Gas relative density (specific gravity)
Ideal gas relative density (specific gravity) Real gas relative
density (specific gravity) Orifice differential pressure Isentropic
exponent (see 3.4.5) Ideal gas isentropic exponent Perfect gas
isentropic exponent Real gas isentropic exponent Mass Molar mass
(molecular weight) of air Molar mass (molecular weight) of gas
Molar mass (molecular weight) of componen1 Number of moles Unit
conversion factor (discharge coefficient) Pressure Base pressure
Base pressure of air Base pressure of gas 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
Units/Value -
-
Btu/(lbm-OF) B tu/(lbm-OF)
in
in
in
in 2.7 1828
-
459.67 + O F
inches of water column at 60F
-
lbm 28.9625 lbm/ib-mol lbmfib-mol lbmbb-mol
-
lbf/in2 (abs) lbf/in2 (abs) ibf/in* (abs) lbf/in2 (abs) lbf/in2
(abs)
lbf/in2 (abs)
lbf/in2 (abs)
-
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART
Q-NATURAL GAS APPLICATIONS 3
Standard pressure Volume flow rate at base conditions Mass flow
rate per second Mass flow rate per hour Volume flow rate per hour
at standard conditions Universal gas constant Pipe Reynolds number
Temperature Base temperature Base temperature of air Base
temperature of gas Temperature of fluid at flowing conditions
Reference temperature of the orifice plate bore diameter and/or
meter tube inside diameter Standard temperature Flowing velocity at
upstream tap Volume Volume at base conditions Flowing volume at
upstream tap Ratio of differential pressure to absolute static
pressure Ratio of differential pressure to absolute static pressure
at the upstream pressure tap Ratio of differential pressure to
absolute static pressure at the downstream pressure tap Acoustic
ratio Expansion factor Expansion factor based on upstream absolute
static pressure Expansion factor based on downstream absolute
static pressure Compressibility Compressibility at base conditions
Compressibility of air at 14.73 psia and 60F Compressibility of the
gas at base conditions
Compressibility at flowing conditions (6, TI) Compressibility at
upstream flowing conditions Compressibility at downstream flowing
conditions Compressibility at standard conditions (e9 T,) Linear
coefficient of thermal expansion Linear 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 (d /D) calculated at
flowing temperature, TI Absolute viscosity of flowing fluid
(Pb8 Tb)
14.73 ibf/in2 (abs) ft3/hr Ibm/sec Ibm/hr
ft3/hr 1 545.35 (lbf-ft)/(lb-mol-oR)
OR "R "R OR OR
-
68F 5 l9.67"R ftlsec f e ft3 ft3
- - - 0.999590
- idin-"F
in/in-"F
iIl/in-"F
- lbm/ft-sec
-
4 CHAPTER 1 '&NATURAL GAS FLUIDS MEASUREMENT
K Universal constant pb Density of a fluid at base conditions
(Pb, Tb)
pb,,ir Density of air at base conditions (Pb, Tb) Pbtm Density
of a gas at base conditions (& Tb)
ps Density of a fluid at standard conditions
p,@ Density of a fluid at flowing conditions
pfp, Density of a fluid at flowing conditions at upstream tap
position (QI, T f )
pf,pz Density of a fluid at flowing conditions at downstream tap
position (e2, T f )
(e9 T,)
(49 T f )
@i Mole fraction of component Note: Factors, ratios and
coefficients are dimensionless.
3.14159 lbm/ft3 lbm/ft3 Ibm/ft3
lbm/ft3
Ibm/ft3
lbm/f?
lbm/ft3 %/loo
3.2.3 TERMINOLOGY
3.2.3.1 Pressure
One pound force (lbf) per square inch pressure is defined as the
force a 1-pound mass (lbm) exerts when evenly distributed on an
area of 1 square inch and when acted on by the standard
acceleration of free fall, 32.1740 feet per second per second.
3.2.3.2 Subscripts
The subscript 1 on the expansion factor (YJ, the flowing density
(pf,pl), the fluid flowing static pressure (P,), and the fluid
flowing compressibility (Zh) indicates that these variables are to
be measured, calculated, or otherwise determined relative to the
fluid flowing at the conditions of the upstream differential tap.
Variables related to the downstream differential pressure tap are
identified by the subscript 2, including Y,, pf,p2, pf,, and Zf2,
and can be used in the equations with equal precision of the
calculated flow rates (except for yZ, which has a separate
equation).
The subscript 1 is arbitrarily used in the equations in this
part to emphasize the necessity of maintaining the relationship of
these four variables to the chosen static pressure reference
tap.
3.2.3.3 Temperature
The temperature of the flowing fluid (Tf) does not have a
numerical subscript. This tem- perature is usually measured
downstream of the orifice plate for minimum flow disturbance but
may be measured upstream within the locations prescribed in Part 2.
It is assumed that there is no difference between fluid
temperatures at the two differential pressure tap loca- tions and
the measurement point, so the subscript is unnecessary.
3.2.3.4 Standard Conditions
Standard conditions are defined as a designated set of base
conditions. In this part, stan- dard conditions are defined as the
absolute static pressure, P,, of 14.73 pounds force per square inch
absolute; the absolute temperature, T,, of 519.67'R (60'F); and the
fluid com- pressibility, Z,, for a stated relative density
(specific gravity), G.
3.2.3.5 Definitions
porated in the text. General definitions are covered in Parts 1
and 2. Definitions specific to Part 3 are incor-
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A P I MPMS*LY.3 -3 72 = 0732270 0503856 536 ~
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3 - N A
T U W GAS APPLICATIONS 5
3.3 Flow Measurement Equations 3.3.1 GENERAL
The following equations express flow in terms of mass and volume
per unit time and pro- duce equivalent results. Since this section
deals exclusively with the inch-pound system of units, the numeric
constants defined in Part 1 have been converted to reflect these
units.
The numeric constants for the basic flow equations, unit
conversion values, density of water, and density of air are given
in 3.5 and Appendix 3-G. The tables in this part that list
solutions to these equations incorporate these constants and
values. Other physical proper- ties are given in 3.5. Key equation
components are developed in 3.4.
3.3.2 The equations for the mass flow of natural gas, in pounds
mass per hour, can be devel-
oped from the density of the flowing fluid (see Appendix 3-G),
the ideal gas relative density (specific gravity), or the real gas
relative density (specific gravity), using the following
equations.
The mass flow developed from the density of the flowing fluid
(p,J is expressed as fol- lows:
EQUATIONS FOR MASS FLOW OF NATURAL GAS
Mass flow developed from the ideal gas relative density
(specific gravity), Gi, is ex- pressed as follows:
The mass flow equation developed from the real gas relative
density (specific gravity), G,, assumes a pressure of 14.73 pounds
force per square inch absolute and a temperature of 519.67"R (60F)
as the reference base conditions for the determination of real gas
rela- tive density (specific gravity). This assumption allows the
base compressibility of air at 14.73 pounds force per square inch
absolute and 519.67"R (60F) to be incorporated into the numeric
constant of the flow rate equation. If the assumption about the
base reference conditions is not valid, the results obtained from
this flow rate equation will have an added increment of
uncertainity. The mass flow equation developed from real gas
relative density (specific gravity), G,, is expressed as
follows:
Where:
cd(m) = coefficient of discharge for flange-tapped orifice
meter. d = orifice plate bore diameter, in inches, calculated at
flowing temperature (Tf).
E, = velocity of approach factor. Gi = ideal gas relative
density (specific gravity). G, = real gas relative density
(specific gravity). h, = orifice differential pressure, in inches
of water at 60F. Pr, = flowing pressure at upstream tap, in pounds
force per square inch absolute. Q, = mass flow rate, in pounds mass
per hour.
Tf = flowing temperature, in degrees Rankine. Y, = expansion
factor (upstream tap). 2, = compressibility at standard conditions
(e, T,). Z,, = compressibility at upstream flowing conditions (el,
Tf).
pip, = density of the fluid at upstream flowing conditions (el,
q, and Z,,), in pounds mass per cubic foot.
-
6 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT
3.3.3 EQUATIONS FOR VOLUME FLOW OF NATURAL GAS The volume flow
rate of natural gas, in cubic feet per hour at base conditions, can
be de-
veloped from the densities of the fluid at flowing and base
conditions and the ideal gas rel- ative density (specific gravity)
or real gas relative density (specific gravity) using the following
equations.
The volume flow rate at base conditions, Q6, developed from the
density of the fluid at flowing conditions (P,,~,) and base
conditions (pb) is expressed as follows:
359. 072Cd(FT) EvY,d2 Q6 =
P b
(3-4a)
The volume flow rate at base conditions, developed from ideal
gas relative density (specific gravity), Gi, is expressed as
follows:
(3-5a)
To correctly apply the real gas relative density (specific
gravity) to the flow calculation, the reference base conditions for
the determination of real gas relative density (specific gravity)
and the base conditions for the flow calculation must be the same.
Therefore, the volume flow rate at base conditions, developed from
real gas relative density (specific gravity), G,., is expressed as
follows:
Qb = 218.573Cd(FI')E,Y,d - fi z;{T (3-6a) If standard conditions
are substituted for base conditions in Equations 3-4a, 3-5a, and
3-
6a, then P b = 4
= 14.73 pounds force per square inch absolute
= 519.67"R (60F)
= 0.999590
T , = T ,
z6,,;r = zsoir
The volume flow rate at standard conditions, Qb, can then be
determined using the follow- ing equations.
The volume flow rate at standard conditions, developed from the
density of the fluid at flowing conditions (P,,~,) and standard
conditions (p,), is expressed as follows:
359.072Cd(FT)EvY,d21/P,,h,
Ps Qv = (3-4b)
The volume flow rate at standard conditions, developed from
ideal gas relative density (specific gravity), Gi, is expressed as
follows:
(3-5b)
The volume flow rate equation at standard conditions, Q,,
developed from the real gas rel- ative density (specific gravity),
requires standard conditions as the reference base conditions for
G, and incorporates at 14.73 pounds force per. square inch absolute
and 519.67"R (60F) in its numeric constant. Therefore, the volume
flow rate at standard conditions, de- veloped from real gas
relative density ,(specific gravity), G,., is expressed as
follows:
(3-6b) r ; l ~ s h w iG Q, = 7709.61Cd(FI')Ev~d2
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- - - - _ _ _ _ A P I MPMS*LLI.3.3 ~ 72 0732290 0503858 309
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART
3-NATURAL GAS APPLICATIONS 7
Where: C,(FT) = coefficient of discharge for flange-tapped
orifice meter.
d = orifice plate bore diameter calculated at flowing
temperature (Tf), in inches. E, = velocity of approach factor. Gi =
ideal gas relative density (specific gravity). G, = real gas
relative density (specific gravity). h, = orifice differential
pressure, in inches of water at 60F. P b = base pressure, in pounds
force per square inch absolute. 5, = flowing pressure (upstream
tap), in pounds force per square inch absolute. e =
standardpressure
Qb = volume flow rate per hour at base conditions, in cubic feet
per hour. Q, = volume flow rate per hour at standard conditions, in
cubic feet per hour. Tb = base temperature, in degrees Rankine. T f
= flowing temperature, in degrees Rankine. T, = standard
temperature
= 519.67"R (60F). yi = expansion factor (upstream tap). z b =
compressibility at base conditions (pbt Tb).
zbo, = compressibility of air at base conditions (Pb, Tb). Zfl =
compressibility at upstream flowing conditions (ei, Tf). 2, =
compressibility at standard conditions (e, z).
Z,, = compressibility of air at standard conditions (e, T,). pb
= density of the flowing fluid at base conditions (Pb, Tb), in
pounds mass per cu-
ps = density of the flowing fluid at standard conditions (e, K),
in pounds mass per p,pI = density of the fluid at upstream flowing
conditions (GI, Tf), in pounds mass per
= 14.73 pounds force per square inch absolute.
bic foot.
cubic foot.
ciibic foot.
3.3.4 For the purposes of Part 3, standard and base conditions
are assumed to be the same.
However, if base conditions are different from standard
conditions, the volume flow rate calculated at standard conditions
can be converted to the volume flow rate at base condi- tions
through the following relationship:
VOLUME CONVERSION FROM STANDARD TO BASE CONDITIONS
Where: P b = base pressure, in pounds force per square inch
absolute. P, = standard pressure, in pounds force per square inch
absolute.
Qb = base volume flow rate, in cubic feet per hour. Q, =
standard volume flow rate, in cubic feet per hour. Tb = base
temperature, in degrees Rankine. T, = standard temperature, in
degrees Rankine. Zb = compressibility at base conditions (Pb,
&). 2, = compressibility at standard conditions (E, T,).
3.4 Flow Equation Components Requiring Additional Computation
3.4.1 GENERAL
developed in this section. Some of the terms in Equations 3-1
through 3-6 require additional computation and are
-
A P I MPMS*L4*3-3 92 m 0732290 0503859 245 m
8 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT
3.4.2 DIAMETER RATIO (/3) The diameter ratio (), which is used
in determining (a) the orifice plate coefficient of dis-
charge (C,), (b) the velocity of approach factor (E"), and (c)
the expansion factor (Y) , is the ratio of the orifice bore
diameter (d) to the internal diameter of the meter tube (0). For
the most precise results, the actual dimensions should be used, as
determined in Parts 1 and 2.
= d I D (3-8) Where
d = d,[ l + a,(? - T,)] (3-9) And
D = D,[l + a,(? - q) ] (3-10) Where:
d = orifice plate bore diameter calculated at flowing
temperature, q. d, = reference orifice plate bore diameter
calculated at reference temperature, T,. D = meter tube internal
diameter calculated at flowing temperature, q. D, = reference meter
tube internal diameter calculated at reference temperature, T..
T, = reference temperature for the orifice plate bore diameter
and/or the meter tube in-
a, = linear coefficient of thermal expansion of the orifice
plate material (see Table 3-1). a, = linear coefficient of thermal
expansion of the meter tube material (see Table 3-1).
= temperature of the fluid at flowing conditions.
ternal diameter.
= diameterratio. Note: a, q, and T, must be in consistent units.
For the purpose of this standard, T, is assumed to be 68F.
T, are the diameters determined in accordance with Part 2. The
orifice plate bore diameter, d,, and the meter tube internal
diameter, Dr, calculated at
3.4.3 COEFFICIENT OF DISCHARGE FOR FLANGE-TAPPED ORIFICE METER,
Cd(FT)
The coefficient of discharge for a flange-tapped orifice meter
(C,) has been determined from test data. It has been correlated as
a function of diameter ratio (), tube diameter, and pipe Reynolds
number. In this part, the equation for the flange-tapped orifice
meter coefficient of discharge developed in Part 1 has been adapted
to the inch-pound system of units.
The equation for the concentric, square-edged flange-tapped
orifice meter coefficient of discharge, C,(FT), developed by
Reader-Harris and Gallagher, is structured into distinct
Table 3-1-Linear Coefficient of Thermal Expansion
Material
Linear Coefficient of Thermal Expansion (a),
in/in-OF
o p e 304 and 316 stainless steel" Monela Carbon steelb
0.00000925 0.00000795 0.00000620
Note: For flowing temperature conditions other than those stated
in Foot- notes a and b and for other materials, refer to the
American Society for Met- als Metals Handbook (Desk Edition, 1985).
aFor flowing conditions between -100F and +30O0F, refer to the
American Society of Mechanical Engineers data in PTC 19.5,
Application, Part II of Fluid Meters: Supplement on Instruments and
Apparatus. ?or flowing conditions between-7'F and +154'F, refer to
Chapter 12, Sec- tion 2.
-
A P I MPMS*L4-3*3 92 m 0732290 0503Bb0 Tb7 m
SECTION 3--CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART
3-NATURAL GAS APPLICATIONS 9
linkage terms and is considered to best represent the current
regression data base. The equa- tion is applicable to nominal pipe
sizes of 2 inches and larger; diameter ratios () of 0.1-0.75,
provided the orifice plate bore diameter, d,, is greater than 0.45
inches; and pipe Reynolds numbers (ReD) greater than or equal to
4000. For orifice diameters, diameter ra- tios, and pipe Reynolds
numbers outside the stated limits, the uncertainty statement in-
creases. For guidance, refer to Part 1, 1.12.4.1,
The Reader-HanisIGallagher equation is defined as follows:
Cd(FT) = Ci(FT) + 0.000511 (lo:!)"' - + (0.0210 + 0.0049A)4C
Ci(FT) = Ci(CT) + Tap Term Ci(CT) = 0.5961 + 0.02912 - 0.22908 +
0.003(1 - ) M ,
Tap Term = Upstrm + Dnstrm Upstrm = [0.0433 + 0.0712e-8.5L1 -
0.1145e-"oL1](1 - 0.23A)B Dnstrm = -0.0116[M2 - 0.52M2'.3]'.1(1 -
0.14A)
Also,
B E - - - - 4 1 - 4
0.8 19,ooo
= (Re,)
(3-11)
(3-12)
(3-13)
(3-14)
(3-15)
(3-16)
(3-17)
(3-18)
(3-19)
(3-20)
(3-21)
Where:
cd(l?) = coefficient of discharge at a specified pipe Reynolds
number for a flange-
Ci(CT) = coefficient of discharge at an infinite pipe Reynolds
number for a corner-
Ci(FT) = coefficient of discharge at an infinite pipe Reynolds
number for a flange-
tapped orifice meter.
tapped orifice meter.
tapped orifice meter. d = orifice plate bore diameter calculated
at T, in inches.
D = meter tube internal diameter calculated at T, in inches. e =
Napierianconstant
= 2.71828.
= dimensionless correction for tap location = N4/D for flange
taps.
N4 = 1 .O when D is in inches.
L, = L,
Re, = pipe Reynolds number. = diameterratio
= d lD. Note: The equation for the coefficient of discharge for
a flange-tapped orifice meter, C,(FT), is different from those
included in prior editions of this standard.
-
A P I M P M S * 1 4 . 3 . 3 92 0732290 0503863 9T3 m-
10 CHAPTER I4-NATURAL GAS FLUIDS MEASUREMENT
3.4.4 VELOCITY OF APPROACH FACTOR (E,)
The velocity of approach factor (E,) is a mathematical
expression that relates the velocity of the flowing fluid in the
orifice meter approach section (upstream meter tube) to the fluid
velocity in the orifice plate bore.
The velocity of approach factor, E,, is calculated as
follows:
Where:
(3-22)
E, = velocity of approach factor. p = diameterratio
= d f D .
3.4.5 REYNOLDS NUMBER (Re,,)
The pipe Reynolds number (ReD) is used as a correlation
parameter to represent the change in the orifice plate coefficient
of discharge with reference to the meter tube diameter, the fluid
flow rate, the fluid density, and the fluid viscosity. The use of
the pipe Reynolds number is an additional change from prior
editions of this standard. The Reynolds number is a dimensionless
ratio when consistent units are used and is expressed as
follows:
Or
(3-23)
(3-24)
Note: The constant, 12, in the denominator of Equation 3-23 is
required by the use of D in inches.
The fluid velocity can be obtained in terms of the volumetric
flow rate at base conditions from the following relationship:
Substituting Equation 3-25 into Equation 3-23 results in the
following relationship:
(3-25)
(3-26)
The Reynolds number for natural gas can be approximated by
substituting the following relationship for pb (see 3.5.5.3 for
equation development) into Equation 3-26:
(3-27)
(3-28)
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__ A P I MPMS*14.3.3 92 0732290 0503862-83T ~ W
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART
Q-NATURAL GAS APPLICATIONS 11
By using an average value of 0.0000069 pounds mass per
foot-second for ,u and substituting the standard conditions of
519.67"R, 14.73 pounds force per square inch, and 0.999590 for
&, Pb, and zboir, Equation 3-28 reduces to the following:
Re, = 47.0723- (3-29) QvGr D
Where:
D = meter tube internal diameter calculated at the flowing
temperature ( T f ) , in inches. G, = real gas relative density
(specific gravity). Pb = base pressure. Qb = volume flow rate at
base conditions, in cubic feet per hour. qm = mass flow rate, in
pounds mass per second. Q, = volume flow rate at standard
conditions, in cubic feet per hour.
Tb = base temperature, in degrees Rankine. U, = velocity of the
flowing fluid at the upstream tap location, in feet per second.
Re, = pipe Reynolds number.
= compressibility of air at 14.73 pounds force per square inch
absolute and 60F. = compressibility of the gas at base conditions
(Pbi Tb).
,u = absolute (dynamic) viscosity, in pounds mass per
foot-second. ~t = 3.14159.
P b = density of the flowing fluid at base conditions (pb, Tb),
in pounds mass per cubic foot.
= density of the fluid at upstream flowing conditions (el, T f )
, in pounds mass per cubic foot.
If the fluid being metered has a viscosity, temperature, or real
gas relative density (specific gravity) quite different from those
shown above, the assumptions are not applic- able. For variations
in viscosity from 0.0000059 to 0.0000079 pounds mass per foot-sec-
ond, variations in temperature from 30F to 9OoF, or variations in
real gas relative density (specific gravity) from 0.55 to 0.75, the
variation should not be significant in terms of its ef- fect on the
orifice plate coefficient of discharge at higher Reynolds
numbers.
When the flow rate is not known, the Reynolds number can be
developed through itera- tion, assuming an initial value of 0.60
for the coefficient of discharge for a flange-tapped orifice meter,
C,(FT), and using the volume computed to estimate the Reynolds
number.
3.4.6 EXPANSION FACTOR (Y) 3.4.6.1 General
When a gas flows through an orifice, the change in fluid
velocity and static pressure is ac- companied by a change in the
density, and a factor must be applied to the coefficient to ad-
just for this change. The factor is known as the expansion factor (
Y ) and can be calculated from the following equations taken from
the report to the A.G.A. Committee by the Na- tional Bureau of
Standards datedMay 26,1934, and prepared by Howard S . Bean. The
ex- pansion factor ( Y ) is a function of diameter ratio @), the
ratio of differential pressure to static pressure at the designated
tap, and the isentropic exponent (k).
The real compressible fluid isentropic exponent, k,, is a
function of the fluid and the pres- sure and temperature. For an
ideal gas, the isentropic exponent, ki, is equal to the ratio of
the specific heats (c,/cv) of the gas at constant pressure (c,) and
constant volume (c,,) and is independent of pressure. A perfect gas
is an ideal gas that has constant specific heats. The perfect gas
isentropic exponent, k,, is equal to ki evaluated at base
conditions.
It has been found that for many applications, the value of k, is
nearly identical to the value of ki, which is nearly identical to
kp. From a practical standpoint, the flow equation is
-
A P I MPMS*L4*3-3 92 0732290 0503863 776 =
12 CHAPTER 1 &-NATURAL GAS FLUIDS MEASUREMENT
not particularly sensitive to small variations in the isentropic
exponent. Therefore, the per- fect gas isentropic exponent, kp, is
often used in the flow equation. Accepted practice for natural gas
applications is to use k, = k = 1.3. This greatly simplifies the
calculations and is used in the tables. This approach was adopted
by Buckingham in his correlation for the expansion factor.
The application of the expansion factor is valid as long as the
following dimensionless criterion for pressure ratio is
followed:
O < I 0.20 hW 27.707 4
Or
P 0.8 I < 1.0
G
(3-30)
(3-31)
Where:
h, = flange tap differential pressure across the orifice plate,
in inches of water at 60F. pf = flowing pressure, in pounds force
per square inch absolute.
p f l = absolute static pressure at the upstream pressure tap,
in pounds force per square
P, = absolute static pressure at the downstream pressure tap, in
pounds force per square
The expansion factor equation for flange taps may be used for a
range of diameter ratios from 0.10 to 0.75. For diameter ratios ()
outside the stated limits, increased uncertainty will occur.
inch absolute.
inch absolute.
3.4.6.2 Expansion Factor Referenced to Upstream Pressure
of the expansion factor, Y,, can be calculated using the
following equation: If the absolute static pressure is taken at the
upstream differential pressure tap, the value
= 1 - (0.41 + 0.354) i (3-32) When the upstream static pressure
is measured,
X I = G - 4 2 = hw G 27.707 4,
When the downstream static pressure is measured,
- hW X I = G - I;, - G2 + (G - G2) 27.707G2 + h,
Where:
(3-33)
(3-34)
h, = differential pressure, in inches of water at 60F.
Pr, = absolute static pressure at the upstream tap, in pounds
force per square inch ab-
e2 = absolute static pressure at the downstream tap, in pounds
force per square inch ab- x, = ratio of differential pressure to
absolute static pressure at the upstream tap. Y, = expansion factor
based on the absolute static pressure measured at the upstream
= diameter ratio (d/D).
k = isentropic exponent (see 3.4.6.1).
solute.
solute.
tap.
The quantity x , / k is known as the acoustic ratio.
-
SECTDN 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL
GAS APPLICATIONS 13
3.4.6.3 Expansion Factor Referenced to Downstream Pressure
expansion factor, yZ, can be calculated using the following
equation: If the absolute static pressure is taken at the
downstream differential tap, the value of the
And
Or
And
x, = G - % = h w $2 27.707 Gl
(3-35)
(3-36)
(3-37)
(3-38)
Where: h, = differential pressure, in inches of water at
60F.
4, = absolute static pressure at the upstream tap, in pounds
force per square inch ab-
Pr, = absolute static pressure at the downstream tap, in pounds
force per square inch ab-
x, = ratio of differential pressure to absolute static pressure
at the upstream tap. x2 = ratio of differential pressure to
absolute static pressure at the downstream tap. yi = expansion
factor based on the absolute static pressure measured at the
upstream tap. y2 = expansion factor based on the absolute static
pressure measured at the downstream
Zh = Compressibility at upstream flowing conditions (e,, T f ) .
Z,, = compressibility at downstream flowing conditions ( p f , ,
q).
k = isentropic exponent (see 3.4.5.1).
solute.
solute.
tap.
= diameter ratio (d/D). Note: xz equals the ratio of the
differentid pressure to the static pressure at the downstream tap
(p/,, .
3.5 Gas Properties 3.5.1 GENERAL
The measurement of gaseous flow rate in volume units under other
than standard or base conditions requires conversion for pressure,
temperature, and the deviation of the measured volume from the
ideal gas laws (compressibility). Energy measurement also requires
adjust- ment for heat content. The standard conditions used in Part
3 are a base pressure of 14.73 pounds force per square inch
absolute and a base temperature of 5 19.67"R (60F).
As a mixture of compounds, natural gas complicates the
calculation of some of these conversion factors. The factors that
cannot be determined by simple calculations can be de- rived from
gas composition and/or other measurements. Certain factors can be
measured in the field, using instruments calibrated against
standard gas samples. Either approach will produce equivalent
results when rigorous methods are applied.
3.5.2 PHYSICAL PROPERTIES Table 3-F-1 in Appendix 3-F lists
physical properties taken from GPA 2145-91. The data
for ideal density and ideal heating value per cubic foot from
GPA 2145-91 have, where nec-
-
14 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT
essary, been corrected in Table 3-F-1 for the base pressure of
14.73 pounds force per square inch absolute through the following
relationship:
Table 3-F-lvalue = - 14*73 x GPA 2145-91 table value (3-39)
14.696
Table 3-F-1 provides the best currently available data on
physical properties. These data are subject to modification yearly
as additional research is accomplished. Future revisions to GPA
2145 may include updated values. The values from the most recent
edition of GPA 2145 should be used, and the values for density and
British thermal units per cubic foot should be corrected through
the use of Equation 3-39.
In addition, GPA Publication 2172 and Publication 18 1 are
incorporated in this standard as the method of calculating heating
values of natural gas mixtures from compositional analysis. An
abbreviated form of that methodology is included in Appendix 3-F as
a refer- ence.
In this edition, the compressibility of air at standard
conditions (Zsoir) has been updated to the value of 0.999590.
3.5.3 COMPRESSIBILITY
3.5.3.1 Ideal and Real Gas
The terms ideal gas and real gas are used to dene calculation or
interpretation methods. An ideal gas is one that conforms to the
thermodynamic laws of Boyle and Charles (ideal gas laws), such that
the following is true:
144PV = nRT (3-40)
If Subscript 1 represents a gas volume measured at one set of
temperature-pressure con- ditions and Subscript 2 represents the
same volume measured at a second set of tempera- ture-pressure
conditions, then
(3-41)
The numerical constant in Equation 3-40 is required to convert
P, in pounds force per square inch absolute, to units that are
consistent with the value of R given in Part 2.
All gases deviate from the ideal gas laws to some extent. This
deviation is known as compressibility and is denoted by the symbol
Z . Additional discussion of compressibility and the method for
determining the value of 2 for natural gas are developed in detail
in A.G.A. Transmission Measurement Committee Report No. 8. The
method used in that re- port is included as a part of this
standard.
The application of Z changes the ideal relationship in Equation
3-40 to the following real relationship:
4% = eV, I; T,
144PV = nZRT (3-42)
As modified by Z , Equation 3-41 allows the volume at the
upstream flowing conditions to be converted to the volume at base
conditions by use of the following equation:
(3-43)
Where:
ri = number of pound-moles of a gas. P = absolute static
pressure of a gas, in pounds force per square inch absolute. Pb =
absolute static pressure of a gas at base conditions, in pounds
force per square inch
absolute.
-
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART
3-NATURAL GAS APPLICATIONS 15
el = absolute static pressure of a gas at the upstream tap, in
pounds force per square R = universal gas constant
T = absolute temperature of a gas, in degrees Rankine. Tb =
absolute temperature of a gas at base conditions, in degrees
Rankine. $ = absolute temperature of a flowing gas, in degrees
Rankine. V = volume of a gas, in cubic feet. V, = volume of a gas
at base conditions (pb, &)i in cubic feet. 5, = volume of a gas
at flowing conditions (e,, Tf), in cubic feet. Z = compressibility
of a gas at P and T.
z b = compressibility of a gas at base conditions (& Ti).
Zfl = compressibility of a gas at flowing conditions (el, Tf).
inch absolute.
= 1545.35 (lbf-ft)/(lbmol-OR).
3.5.3.2 Compressibility at Base Conditions
in A.G.A. Transmission Measurement Committee Report No. 8. The
value of Z at base conditions ( z b ) is required and is calculated
from the procedures
3.5.3.3 Supercompressibility
In orifice measurement, z b and 2, appear as a ratio to the 0.5
power. This relationship is termed the sicpercompressibility factor
and may be calculated from the following equation:
Or
Where:
(3-44)
(3-45)
F,, = supercompressibility Luctor. z b = compressibility of the
gas at base conditions (Pb, Tb). Z,, = compressibility of the gas
at flowing conditions (el, Tf).
3.5.4 RELATIVE DENSITY (SPECIFIC GRAVITY)
3.5.4.1 General
Relative density (specific gravity), G, is a component in
several of the flow equations. The relative density (specific
gravity) is defined as a dimensionless number that expresses the
ratio of the density of the flowing fluid to the density of a
reference gas at the same ref- erence conditions of temperature and
pressure. The gas industry has historically referred to the
relative density (specific gravity) as either ideal or real and has
designated the reference gas as air and the standard reference
conditions as a pressure of 14.73 pounds force per square inch
absolute and a temperature of 519.67"R (60F). The value for
relative density (specific gravity) may be determined by
measurement or by calculation from the gas com- position.
3.5.4.2 Ideal Gas Relative Density (Specific Gravity)
The ideal gas relative density (specific gravity), Gi, is
defined as the ratio of the ideal den- sity of the gas to the ideal
density of dry air at the same reference conditions of pressure and
temperature. Since the ideal densities are defined at the same
reference conditions of pres- sure and temperature, the ratio
reduces to a ratio of molar masses (molecular weights).
-
A P I MPMS*L4.3.3 92 I 0732290 0503867 311
16 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT
Therefore, the ideal gas relative density (specific gravity) is
set forth in the following equa- tion:
(3-46)
Where:
Gi = ideal gas relative density (specific gravity).
= 28.9625 pounds mass per pound-mole. Mrair = molar mass
(molecular weight) of air
Mr,,, = molar mass (molecular weight) of a flowing gas, in
pounds mass per pound- mole.
3.5.4.3 Real Gas Relative Density (Real Specific Gravity)
Real gas relative density (specific gravity), Gr, is defined as
the ratio of the real density of the gas to the real density of dry
air at the same reference conditions of pressure and tem- perature.
To correctly apply the real gas relative density (specific gravity)
to the flow cal- culation, the reference conditions for the
determination of the real gas relative density (specific gravity)
must be the same as the base conditions for the flow calculation.
At ref- erence (base) conditions (P', Tb), real gas relative
density (specific gravity) is expressed as fol10 ws :
G, =
Since the pressures and temperatures are defined to be at the
same designated base con- ditions,
Pbgar = pboir
And the real gas relative density (specific gravity) is
expressed as follows:
(3-47)
The use of real gas relative density (specific gravity) in the
flow calculations has a his- toric basis but may add an increment
of uncertainty to the calculation as a result of the lim- itations
of field gravitometer devices. When real gas relative densities
(specific gravities) are directly determined by relative density
measurement equipment, the observed values must be adjusted so that
both air and gas measurements reflect the same pressure and tem-
perature. The fact that the temperature and/or pressure are not
always at base conditions re- sults in small variations in
determinations of relative density (specific gravity). Another
source of variation is the use of atmospheric air. The composition
of atmospheric air-and its molecular weight and density-varies with
time and geographical location.
When recording gravitometers are used and calibration is
performed with reference gases, either ideal or real gas relative
density (specific gravity) can be obtained as a recorded relative
density (specific gravity) by proper certification of the reference
gas. The relationship between ideal gas relative density (specific
gravity) and real gas relative den- sity (specific gravity) is
expressed as follows:
Gr = Gi - Zhou (3-48) ' b g m
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A P I M P M S * l 4 - 3 - 3 92 0732290 0503868 258 W
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART
3-NATURAL GAS APPLICATIONS 17
W
= &biMC
Where: Gi = ideal gas relative density (specific gravity). Gr =
real gas relative density (specific gravity).
= 28.9625 pounds mass per pound-mole. Mr,, = molar mass
(molecular weight) of air
Mrgos = molar mass (molecular weight) of the flowing gas, in
pounds mass per pound-
Pb = absolute static pressure of a gas at base conditions, in
pounds force per square mole.
inch absolute. = base pressure of air, in pounds force per
square inch absolute.
Pbgor = base pressure of a gas, in pounds force per square inch
absolute. R = universal gas constant
& = absolute temperature of a gas at base conditions, in
degrees Rankine. = 1545.35 (Ibf-ft)/(lbmol-OR).
Tbdi, = base temperature of air, in degrees Rankine. Tbga, =
base temperature of a gas, in degrees Rankine.
= compressibility of air at base conditions (Pbi Tb). =
compressibility of a gas at base conditions (Pi,, Tb).
3.5.5
3.5.5.1 General
The flowing density (p,,) is a key component of certain flow
equations. It is defined as the mass per unit volume at flowing
pressure and temperature and is measured at the se- lected static
pressure tap location. The value for flowing density can be
calculated from equations of state or from the relative density
(specific gravity) at the selected static pres- sure tap. The fluid
density at flowing conditions can also be measured using commercial
densitometers. Most densitometers, because of their physical
installation requirements and design, cannot accurately measure the
density at the selected pressure tap location. There- fore, the
fluid density difference between the density measured and that
existing at the defined pressure tap location must be checked to
determine whether changes in pressure or temperature have an impact
on the flow measurement uncertainty.
An approximation for field calculation is the direct application
of tables from the equa- tion of state. Such density tables have
considerable bulk if they cover a wide range of con- ditions in
small increments. Tables have a further deficiency in that they do
not readily lend themselves to interpolation or extrapolation with
fluctuating temperature and/or pressure.
At the time of publication, it was anticipated that a computer
program for IBM and com- patible personal computers that generates
density and/or compressibility tables for user- defined gas and
pressure-temperature ranges would be available through A.G.A. This
program uses the equations in A.G.A. Transmission Measurement
Committee Report N0.8.
DENSITY OF FLUID AT FLOWING CONDITIONS
3.5.5.2 Density Based on Gas Composition
When the composition of a gas mixture is known, the gas
densities p,, and pb may be cal- culated from the gas law
equations. The molecular weight of the gas may be determined from
composition data, using mole fractions of the components and their
respective mole- cular weights.
M ~ ~ ( L F = $,Mq + $2Mr2 + ... + $&rW (3-49)
i=l
In the following, the gas law equation, Equation 3-42, is
rearranged to obtain density val- ues:
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A P I M P M S * L 4 - 3 . 3 92 = 0732290 0503869 194
18 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT
Therefore:
And
Or
144PV = nZRT
144PV = ( g ] Z R T (3-51)
(3-52)
(3-53)
Where: Gi = ideal gas relative density (specific gravity). m =
mass of a fluid, in pounds mass.
Mroir = molar mass (molecular weight) of air
Mrgns = molar mass (molecular weight) of the flowing gas, in
pounds mass per pound-
Mr, = molar mass (molecular weight) of a component, in pounds
mass per pound-
= 28.9625 pounds mass per pound-mole.
mole.
mole. n = numberof moles. P = absolute static pressure of a gas,
in pounds force per square inch absolute. Pb = absolute static
pressure of a gas at base conditions, in pounds force per
square
GI = absolute static pressure of a gas at the upstream tap, in
pounds force per square
R = universal gas constant
T = absolute temperature of a gas, in degrees Rankine. Tb =
absolute temperature of a gas at base conditions, in degrees
Rankine. Tf = absolute temperature of a flowing gas, in degrees
Rankine. V = volume of a gas, in cubic feet. Z = Compressibility of
a gas at 8 T.
z b = compressibility of a gas at base conditions (Pb, Tb). Z,,
= compressibility of a gas at flowing conditions (el, Tf). p b =
density of a gas at base conditions (Pb, &), in pounds mass per
cubic foot.
inch absolute.
inch absolute.
= 1545.35 (lbf-ft)/(lbmol-OR).
ptPi = density of a gas at upstream flowing conditions (e,, Tf),
in pounds mass per cu- bic foot.
@i = mole fraction of a component.
3.5.5.3 Density Based on Ideal Gas Relative Density (Specific
Gravity) The gas densities P,,~, and p b may be calculated from the
ideal gas relative density
(specific gravity), as defined in 3.5.5.2. The following
equations are applicable when a gas analysis is available:
(3-46)
-
A P I M P M S * 1 4 . 3 - 3 92 W 0732290 0503870 706 -~
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART
3-NATURAL GAS APPLICATIONS 19
Note: Themolecular weight of dry air, from GPA 2145-91, is given
as 28.9625 pounds mass per pound-mole (ex- actly).
MG^^ = G.Mcir = G.(28.9625) (3-54) Substituting for Mrgos in
Equations 3-52 and 3-53, p,pi and pb are determined as follows:
$GI: (28.9625)(144) - ZART
P,,P, -
And
eG.(28.9625)(144)
' b R T P b =
eci = 2.69881- ' b Tb
Where:
(3-55)
(3-56)
Gi = ideal gas relative density (specific gravity).
= 28.9625 pounds mass per pound-mole. Mr,, = molar mass
(molecular weight) of air
Mrnos = molar mass (molecular weight) of a flowing gas, in
pounds mass per pound-
Pb = absolute static pressure of the gas at base conditions, in
pounds force per square
el = absolute static pressure of a gas at the upstream tap, in
pounds force per square R = universal gas constant
5 = absolute temperature of a gas at base conditions, in degrees
Rankine. T f = absolute temperature of a flowing gas, in degrees
Rankine.
z b = compressibility of a gas at base conditions (pb, Tb). Zfl
= compressibility of a gas at flowing conditions (e,, T f ) . pb =
density of a gas at base conditions (Pbi Tb, and zb), in pounds
mass per cubic
plei = density of a gas at upstream flowing conditions (el, j,
and ZfJ, in pounds mass
mole.
inch absolute.
inch absolute.
= 1545.35 (lbf-ft)/(lbmol-oR).
foot.
per cubic foot.
3.5.5.4 Density Based on Real Gas Relative Density (Specific
Gravity)
(specific gravity) is given by the following equation: The
relationship of real gas relative density (specific gravity) to
ideal gas relative density
G, = Gi - zb,, (3-48) -%
Or
G. = G, -% zh,,
Note: The real gas relative density (specific gravity) of dry
air at base conditions is defined as exactly 1.00000.
Substituting for Gi in Equations 3-55 and 3-56 results in the
following:
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API MPMS*14.3.3 92 W 0732290 0 5 0 3 8 7 1 842 W
20 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT
2.6988 14 G,. n. = P b Tb 'b,,
(3-57)
(3-58)
To correctly apply the density equations, Equations 3-57 and
3-58, which were devel- oped from the real gas relative density
(specific gravity), to the flow calculation, the refer- ence base
conditions for the determination of real gas relative density
(specific gravity) and the base conditions for the flow calculation
must be the same. When standard conditions are substituted for base
conditions,
P b = = 14.73 pounds force per square inch absolute
= 519.67"R (60'F)
= 0.999590
Tb = T,
-Goir = z,,
The gas density based on real gas relative density (specific
gravity) is given by the follow- ing equations:
- 2 . 6 9 a a i 5 ~ , z , ~ ~ O. 999590 Zh A,,, -
And
(2.69881)(14.73)Gr (O. 999590)(5 19.67) ps =
= O. 0765289 G,
(3-59)
(3-60)
Where: Gi = ideal gas relative density. G, = real gas relative
density. Pb = absolute static pressure of a gas at base conditions,
in pounds force per square
4, = absolute static pressure of a gas at the upstream tap, in
pounds force per square
T6 = absolute temperature of a gas at base conditions, in
degrees Rankine. Tf = absolute temperature of a flowing gas, in
degrees Rankine.
inch absolute.
inch absolute.
ZbOir = compressibility of air at base conditions (Pb, Tb). =
compressibility of a gas at base conditions (Pb, Tb).
Z, = compressibility of a gas at flowing conditions (e,, Tf).
Z,, = compressibility of air at standard conditions (4, T,). Zsgns
= compressibility of a gas at standard conditions (4, T,).
p b = density of a gas at base conditions (Pb, Tb, and zb), in
pounds mass per cubic foot. ps = density of a gas at standard
conditions (4, T,, and Z,), in pounds mass per cubic foot.
p,,,, = density of a gas at upstream flowing conditions (e,, Tf,
and Zf,), in pounds mass The density equations for standard
conditions based on the real gas relative density (specific
gravity) developed above require standard conditions as the
designated reference base con- ditions for G, and incorporate
&,,, at 14.73 pounds force per square inch absolute and
519.67"R in their numeric constants.
per cubic foot.
-
APPENDIX 3-A-ADJUSTMENTS FOR INSTRUMENT CALIBRATION
3-A.l Scope This appendix provides equations and procedures for
adjusting and correcting field mea-
surement calibrations of secondary instruments.
3-A.2 General Field practices for secondary instrument
calibrations and calibration standard applica-
tions contribute to the overall uncertainty of flow measurement.
Calibration standards for differential pressure and static pressure
instruments are often
used in the field without local gravitational force adjustment
or correction of the values in- dicated by the calibrating
standards. For example, it is common to use water column manometers
to calibrate differential pressure instruments without making field
corrections to the manometer readings for changes in water density.
The manometer readings are af- fected by local gravitational
effects, water temperatures, and the use of other than distilled
water.
Pressure devices that employ weights are also used to calibrate
differential pressure in- struments without correction for the
local gravitational force. Similarly, deadweight testers are used
to calibrate static pressure measuring equipment without correction
for the local gravitational force. It is usually more convenient
and accurate to incorporate these adjust- ments in the flow
computation than for the person calibrating the instrument to apply
these small corrections during the calibration process. Therefore,
additional factors are added to the flow equation for the purpose
of including the appropriate calibration standard correc- tions in
the flow computation either by the flow calculation procedure in
the office or by the meter technician in the field.
Six factors are provided that may be used individually or in
combination, depending on the calibration device and the
calibration procedure used:
Correction for air over the water in the water manometer during
the differential in- strument calibration. Local gravitational
correction for the water column calibration standard. Water density
correction (temperature or composition) for the water column
calibra- tion standard. Local gravitational correction for the
deadweight tester static pressure standard. Manometer factor
(correction for the gas column in mercury manometers). Mercury
manometer temperature factor (span correction for instrument
temperature change after calibration).
F,,
FW, FtiI
FhRni FhRI
These factors expand the base volume flow equation to the
following:
Q, = Qv e m 4.t 4.t
-
22
A P I MPMS*L4.3-3 92 = O732290 0503873 bL5
CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT
applicable; however, if SI units are used, the more generic
equations in Part 1 should be used for consistent results.
3-A.3.2 SYMBOLS AND UNITS Description
Temperature, in degrees Fahrenheit Temperature, in degrees
Rankine Correction for air over the water in the water manometer
Manometer factor Mercury manometer temperature factor Local
gravitational correction for deadweight tester Local gravitational
correction for water column Water density correction Local
acceleration due to gravity Acceleration of gravity used to
calibrate weights or deadweight calibrator Ideal gas relative
density (specific gravity) Real gas relative density (specific
gravity) Differential pressure above atmospheric Elevation above
sea level Latitude on earth's surface Molar mass of gas Molar mass
of air Absolute gas pressure Local atmospheric pressure Base
pressure Absolute pressure of flowing gas Volume flow rate at
standard conditions modified for instrument calibration adj us
tments Universal gas constant Absolute gas temperature Base
temperature Absolute temperature of a flowing gas Mercury ambient
temperature Gas ambient temperature Compressibility of a gas at T
and P Compressibility of a gas at standard conditions (Gr, PbJ and
Tb) Compressibility of air at 5 19.67"R Compressibility of air at
P,,, and 519.67"R Compressibility of air at 14.73 psia and 519.67"R
Compressibility of gas at flowing conditions (Gr, 4, and Tf )
Density of air at pressure above atmospheric Density of atmospheric
air Density of gas or vapor in the differential pressure instrument
Density of mercury in the differential pressure instrument
+ h, and
Units/Value - -
ft/sec2 - -
inches of water column at 60F ft degrees lbm/ib-mol 28.9625
lbm/ib-mol lbf/inz (abs) lbf/in2 (abs) lbf/in2 (abs) lbf/in2
(abs)
ft3/hr 1545.35 (Ibf-ft)/(lb-mol-OR) OR OR
OR O R
OR -
0.999590
-
lbm/ft3 lbm/ft3
1bm/ft3
lbm/ft3
-
A P I MPMS*L4.3.3 92 M 0732290 0503874 5 5 1 M
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART
3-NATURAL GAS APPLICATIONS 23
phgc
phgo
Density of mercury in the differential pressure instrument at
the time of its calibration Density of mercury in the differential
pressure instrument at the mercury gauge operating conditions
lbm/ft3 Density of water in the manometer at other than 60F
lbm/ft3
lbm/ft3
pw
3-A.4 Water Manometer Gas Leg Correction Factor (Ern) The factor
F,, corrects for the gas leg over water when a water manometer is
used to cal-
ibrate a differential pressure instrument:
4 = dpwi. pa (3-A-2) When atmospheric air is used as the medium
to pressure both the differential pressure in- strument and the
water U-tube manometer during calibration, the density of air at
atmos- pheric pressure and 60F must be calculated using the
following equation:
Mr c;. P p = - RZT
(3-A-3)
Substituting local atmospheric pressure (e,) for absolute
pressure (P), 519.67"R (60F) for the absolute temperature (T),
28.9625 for Mra,, 1.0 for the ideal relative density (specific
gravity) of air (GJ, and 1545.35 for the universal gas constant (R)
provides the following relationship:
(28.9625)(1. O)em
1545*35 Z (519.67) 144 a-
Pottn =
(3-A-4)
The local atmospheric pressure may be calculated using an
equation published in the Smith- sonian Meteorological Tables:
1 55096 - (Elevation, ft - 361) 55096 + (Elevation, ft - 361)
t,,,, = 14.54 (3-A-5) The density of air at any given differential
pressure (h,) above atmospheric pressure can then be represented by
the following:
(3-A-6)
The density of water can be obtained from Table 3-A-1 or
calculated from the following Wegenbreth density equation:
p, = 0.0624280[999.8395639 + 0.06798299989q. - 0.009106025564~2
+ 0.0001005272999T~ - 0.000001 126713526Tw + 0 . ~ 6 5 9 1 7 9 5 6
0 6 T ~ I
Where:
(3-A-7)
Gi = ideal gas relative density (specific gravity). h, =
differential pressure above atmospheric, in inches of water at 60F.
Mr = molar mass of a gas, in pounds mass per pound-mole.
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A P I MPMS*14-3.3 92 W 0732290 0503875 498 W
24 CHAPTER 1 &-NATURAL GAS FLUIDS MEASUREMENT
Table 3-A-i-Water Density Based on Wegenbreth Equation
Temperature Density ("F) (ibm/ft3)
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
62.42 12 62.4193 62.4172 62.4148 62.4 12 1 62.4092 62.4060
62.4026 62.3980 62.3949 62.3908 62.3863 62.3817 62.3768 62.3711
62.3663 62.3608 62.3550
Temperature Density (OF) (ibm/ft3)
63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
62.3490 62.3427 62.3363 62.3297 62.3228 62.3157 62.3085 62.3010
62.2934 62.2855 62.2775 62.2692 62.2608 62.2522 62.2434 62.2344
62.2252 62.2159
P = absolute gas pressure, in pounds force per square inch
absolute.
R = universal gas constant
T = absolute gas temperature, in degrees Rankine. T, =
temperature of water, in degrees Celsius. 2 = compressibility of a
gas at P and T. 2, = compressibility of air at
p = density of a gas, in pounds mass per cubic foot. pa =
density of air at pressure above atmospheric, in pounds mass per
cubic foot.
pIY = density of water in a manometer at a temperature other
than 6OoF, in pounds
etnt = local atmospheric pressure, in pounds force per square
inch absolute. = 1545.35 (lbf-ft)/(lbmol-OR).
+ h,, and 519.67"R. = compressibility of air at e,ff1 and
519.67"R.
palm, = density of atmospheric air, in pounds mass per cubic
foot.
mass per cubic foot.
3-A.5 Water Manometer Temperature Correction Factor (FJ The
factor F,, corrects for variations in the density of water used in
the manometer when
the water is at a temperature other than 60F. The F,, correction
factor should be included in the flow measurement computation when
a differential instrument is calibrated with a water manometer.
P," = 62.3663 (3-A-8)
Where:
pw = density of water in a manometer at a temperature other than
60"F, in pounds mass per cubic foot.
3-A.6 Local Gravitational Correction Factor for Water Manometers
(Fw,)
The factor fiv, corrects the weight of the manometer fluid for
the local gravitational force. The effect on the quantity is the
square root of the ratio of the local gravitational force to
-
A P I M P M S * L 4 - 3 - 3 7 2 U O732270 0503876 324 W ~~
SECTION 3-CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART
3-NATURAL GAS APPLICATIONS 25
the standard gravitational force used in the equation
derivations. This relationship is ex- pressed as follows:
(3-A-9)
Where:
g, = local acceleration due to gravity, in feet per second per
second.
The local value of gravity at any location may be obtained from
a U.S. Coast and Geo- detic Survey reference to aeronautical data
or from the Smithsonian Meteorological Tables. Using Equation E l l
from the 1985 edition of ANSUAPI 2530 and the 45"-latitude-at-sea-
level reference value, approximate values of g, may be obtained
from the following curve- fit equation covering latitudes from O"
to 90":
gl = 0.0328095[978.01855 - 0.0028247L + 0.0020299L2 -
0.00001505SL3 - 0.000094HI (3-A- 10)
Where:
L = latitude, in degrees. H = elevation, in feet above sea
level.
3-A.7 Local Gravitational Correction Factor for Deadweight
Calibrators Used to Calibrate Differential and Static Pressure
Instruments (bW,)
The factor $KI is used to correct for the effect of local
gravity on the weights of a dead- weight calibrator. The calibrator
weights are usually sized for use at a standard gravitational force
or at some specified gravitational force. A correction factor must
then be applied to correct the calibrations to the local
gravitational force:
(3-A- 1 1)
Where:
g, = acceleration due to local gravitational force, in feet per
second per second. go = acceleration of gravity used to calibrate
the weights of a deadweight calibrator, in
When a deadweight calibrator is used for the differential
pressure and the static pressure, both must be corrected for local
gravity. This involves using
feet per second per second.
twice.
3-A.8 Correction for Gas Column in Mercury Manometer Instruments
(hgm)
The factor FhRm corrects for the gas or vapor leg of fluid at
static pressure and the temper- ature of the manometer or other
instrument. Mercury U-tube manometers and mercury- manometer-type
differential pressure instruments are sometimes used to measure h,.
The manometer factor Fhgm is added to the flow equation to correct
for the effect of the gas col- umn above the mercury during flow
measurements:
(3-A-12)
Where:
phg = density of mercury in the differential pressure
instrument, in pounds mass per cu- bic foot. The effect of
atmospheric air (usually defined as the weight in vacuo of
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API MPMS*14.3m3 92 0732290 0503877 260
26 CHAPTER 14-NATURAL GAS FLUIDS MEASUREMENT
the mercury sample at the base pressure and temperature defined
for the flow mea- surement) is excluded.
pg = density of the gas or vapor in the differential pressure
instrument, in pounds mass per cubic foot. The effect of
atmospheric air (usually defined as weight in vacuo of the fluid
sample at the flowing pressure existing at the orifice meter during
the flow measurement and at the temperature existing at the
differential pressure in- strument during the flow measurement) is
excluded.
The density of mercury at ambient temperature Zjga, in degrees
Rankine, may be calcu- lated from the following equation:
phg = 846.324C1.0 - O.OOOlOl(l;,, - 519.67)] (3-A-13)
The density of a gas at ambient temperature may be calculated
using the following equa- tion:
' b Gr 5 'bOirR ' f T a s .
Pg =
For standard conditions of
= 14.73 lbf /in2 (abs) q = r
= 519.67"R (60F)
= 0.999590
Then
(3-A-14)
(3-A- 15)
Where:
G, = real gas relative density (specific gravity).
= 28.9625 pounds mass per pound-mole. Mrai, = molar mass of
air
6 = absolute pressure of a flowing gas, in pounds force per
square inch absolute. R = univeral gas constant
T, = absolute temperature of a flowing gas, in degrees Rankine.
= 1545.3 5 (lbf-ft)/(lbmol-OR) .
Tgaso = gas ambient temperature, in degrees Rankine. = mercury
ambient temperature, in degrees Rankine.
zb = compressibility of a gas at G,, Tb, and Pb. Zbajr =
compressibility of air at 519.67"R and 14.73 pounds force per
square inch ab-
solute = 0.999590.
Zf = compressibility of a gas at flowing conditions (G,., T,,
and e). Zs = compressibility of a gas at 519.67"R and 14.73 pounds
force per square inch ab-
solute.
Tabular data for &,m are given in Table 3-A-2. Correction
for a liquid leg over the mercury can also be made if the liquid
density is sub-
stituted for pg in Equation 3-A-12. If the mercury differential
pressure instrument is cali- brated using a water column or a
weight calibrator, the Fw,, and F,, factors are also needed.
-
~-
A P I M P M S * l Y . 3 . 3 92 H 0732290 0503878 l T 7
SECTION CONCENTRIC, SQUARE-EDGED ORIFICE METERS, PART 3-NATURAL
GAS APPLICATIONS 27
Table 3-AP-Mercury Manometer Factors (ihg,) ~ ~~
Real Gas Ambient Relative Temperature Density (OW O 500 loo0
1500 2000 2500 3000
Static Pressure (pounds force per square inch gauge)
0.550 O 0.600 O 0.650 O 0.700 O 0.750 O 0.550 20 0.600 20 0.650
20 0.700 20 0.750 20 0.550 40 0.600 40 0.650 40 0.700 40 0.750 40
0.550 60 0.600 60 0.650 60 0.700 60 0.750 60 0.550 80 0.600 80
0.650 80 0.700 80 0.750 80 0.550 100 0.600 100 0.650 100 0.700 100
0.750 100 0.550 120 0.600 120 0.650 120 0.700 120 0.750 120
1.0030 1.0030 1.0030 1.0030 1.0030 1.0020 1 .o020 1 .o020 1
.o020 1.0020 1.0010 1.0010 1.0010 1.0010 1.0010 1 .oooo 1 .m 1.Oooo
1 .oooo 1 .oooo 0.9990 0.9990 0.9990 0.9990 0.9990 0.9980 0.9980
0.9980 0.9980 0.9980 0.9970 0.9970 0.9970 0.9970 0.9970
1.0019 1.0018 1.0017 1.0015 1.0014 1.0010 1.0009 1 .O008 1 .O007
1.0005 1 .oooo 0.9999 0.9998 0.9997 0.9996 0.9991 0.9990 0.9989
0.9988 0.9987 0.9981 0.9980 0.9979 0.9978 0.9977 0.9972 0.9971
0.9970 0.9969 0.9968 0.9962 0.9961 0.9960 0.9959 0.9958
1 .o006 1.0002 0.9997 0.9991 0.9984 0.9997 0.9994 0.9990 0.9985
0.9980 0.9989 0.9986 0.9983 0.9980 0.9975 0.9980 0.9978 0.9975
0.9972 0.9968 0.9971 0.9969 0.9967 0.9964 0.9961 0.9962 0.9960
0.9958 0.