~                                          ~                           A P I MPMS*L4-3.3 9 2 W 0732290 053b085 556        ...
~                                                                    ~~                      API MPMS+lY.3-3 92           ...
On page 58, the third to the last equation should read as follows:                                     Qv = 617,048 cubic ...
A P I MPMS*14-3.3                 92              0732290 0536088 265                      On page 62, Equation 3-B-9 shou...
API MPMS*L4.3*3         92       0732290 0503843 988                   Manual of Petroleum                   Measurement S...
A P I M P M S * 1 4 - 3 a 3 92   0732290 0503844 814                    Manual of Petroleum                    Measurement...
~    ~~~                                                  ~                          API M P M S * L 4 - 3 . 3       92   ...
FOREWORD                            This foreword is for information and is not part of this standard.                    ...
ACKNOWLEDGMENTS                        From the initial data-collection phase through the final publication of this revisi...
-                         API MPMS*L4-3-3 92             = 0732290 0503848 4bT =                                    J. Bre...
M. Williams, Amoco Production Company                                E. Woomer, United Gas Pipeline Company               ...
.. _-                                                                                   = 0732290 0503850 018 W           ...
-                                                                 - ._                                           -_       ...
Chapter 14-Natural                Gas Fluids Measurement                        SECTION 3-CONCENTRIC,                     ...
~~                                A P I MPMS*L4.3-3 92 E 0732290 0503853 827       2                                     C...
S C I N 3-CONCENTRIC,                              E TO                   SQUARE-EDGED METERS, PART Q-NATURAL             ...
4                                           CHAPTER 1&NATURAL        GASFLUIDS                                            ...
A P I MPMS*LY.3-3              72    = 0732270 0503856 536         ~                              SECTION 3-CONCENTRIC,   ...
6                                          CHAPTER 14-NATURAL   GASFLUIDS                                                 ...
-     ---____                                    A P I MPMS*LLI.3.3        ~   72       0 7 3 2 2 9 0 0503858 3 0 9       ...
A P I M P M S * L 4 * 3 - 3 92                m 0732290 0503859                      245       m       8                  ...
A P I MPMS*L4-3*3 92                         m 0732290                 0 5 0 3 B b 0 Tb7           m                      ...
A P I MPMS*14.3.3                  92            0732290 0503863 9T3                      m-       10                     ...
__                             A P I MPMS*14.3.3              92          0732290 0 5 0 3 8 6 2 - 8 3 T W                 ...
A P I MPMS*L4*3-3 92                             0732290 0503863 776           =       12                                 ...
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  1. 1. ~ ~ A P I MPMS*L4-3.3 9 2 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: O7 cl = 0.000511 + [O.O2iû + 0.0049( 19, OOOß 7 * ] p 4 (1,000,000J35 - I (3-B-9) ReD Re, On page 56, the second equation under 3 4 . 3 . I . 7 should read as follows: Q,( 14.73)(0.570) ReD = (0.0114541) ( (0.00OO069)(S.0î085)(519.67)(0.999590) = 3.324464 On page 57, Equation 3-6b should read as follows: (3-6b) = 7709.61(0.60)( .O3160)(0.998383)(3.99%9)2 1 (O. 570)(O. 95 1308)(524.67) = 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)COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  2. 2. ~ ~~ API MPMS+lY.3-3 92 0732290 0536086 492 On page 57, Equation 3-20 should read as follows: 19,OOOß A = ( r ) 0 8 [ - 19,000(0.495597)]0* - 2,041,328 (3-20) = 0.0135262 On page 57, Equation 3-21 should read as follows: (3-21) 2,041,328 = 0.778988 On page 58, Equation 3-15 should read as follows: Upstrm = C0.0433 + 0.0712e-85L1 0.1145e-60L](1 0.23A)B - - = C0.0433 + 0.0712es~"* 0.1145e6~u708s] - (3-15) 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]ß1(l 0.14A) - = - 0.0116[0.491284 - 0.52(0.491284)3](0.495597) (3-16) x [1 - 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,(Fï) = C,.(CT) + Tap Tm e = 0.602414 - 0.000647402 (3-12) = 0.601767 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) 2COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  3. 3. 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 (Fï) = 0.6029471 , On page 58, the second to the last equation should read as follows: Re, = 3.32446Q,, = 3.32446(617,048) = 2,05 1,351 (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, (3-7) 14.65 519.67 0.997971) = 608,396 cubic feet per hour at base conditions On page 60, Equation 3-B-9 should read as follows: e, = 0.000511 ( 1,000,ooop i 1,000,000 o35 (3-8-9) On page 62, the$rst equation should read as follows: = 0.5961 + 0.0291p2- 0.2290px + (0.0433 + 0.0712en%- 0.1145ë6) [ ( 1 - 0.23 -: ) i; . -p 9] - p; = 0.5961 + 0.0291(0.495597)2- 0.2290(0.495597)* + [ 0.0433 + 0.0712e"07"~- 0.1 145e607")[l - 0.23(0.0137493)](0.0642005) - 0.01 16[0.491284 - 0.52(0.49128413)](0.495597).1[10.14(0.0137493)] - = 0.601767 3COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  4. 4. A P I MPMS*14-3.3 92 0732290 0536088 265 On page 62, Equation 3-B-9 should read as follows: 4 = 0.000511( 1 , 0 0 ; ~ 0 0 ~ ) " 0.0210 + )"*]].(i, ooo,ooo 0.0049 ( 1 9 , 0 0 0 ~ ~ Re, Re, 1 35 (3-8-9) = 0.000511( 1,000,000(0.495597) 2,000,000 + [0.021O + 0.0049(0.0 137493)](0.495597)(0.784584) = 0.00118960 On page 65, thefirst equation should read as follows: Re, = 0.0114588 - = 3.32446Q" (",or) = 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 32°F On page 97, Equations 3-F-4 and 3-F-5should read asfollows: Hid = 4,(ff:d),4 2 W i d ) 2 + + ... + 4wwid)w (3-F-4) (3-F-5) On page 102, the second line of Equation 3-4a should read as follows: G, (28.9625)(144)hw ZbRT Qb = 359.072C,(FT)Evqd2 eG,(28.9625)(144) 4COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  5. 5. API MPMS*L4.3*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 8 85, Part 3 1 1 American National Standards Institute ANSVAPI 2530-1991, Part 3 I American Petroleum Institute 1220 L Street. Northwest Washington, D.C. 20005 1’ 1COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  6. 6. 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 InstituteCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  7. 7. ~ ~~~ ~ 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 PRECAUTIONS WITH RESPECT TO PARTICULAR MATERIALS AND CONDI- 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 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 THE PUBLICATION BE CONSTRUED AS INSURING ANYONE AGAINST LIABIL- ITY FOR INFRINGEMENT OF LETIERS PATENT. 5. GENERALLY, API STANDARDS ARE REVIEWED AND REVISED, REAF- FIRMED, OR WITHDRAWN AT LEAST EVERY FIVEYEARS. SOMETIMES A ONE- TIME EXTENSION OF UP TO TWO YEARS WILL BE ADDED TO THIS REVIEW CYCLE. THIS PUBLICATIONWILL NO LONGER BE IN EFFECT FIVE YEARS AF- TER ITS PUBLICATION DATE AS AN OPERATIVE API STANDARD OR, WHERE AN EXTENSION HAS BEEN GRANTED, UPON REPUBLICATION. STATUS OF THE 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 InstituteCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  8. 8. FOREWORD This foreword is for information and is not part of this standard. Chapter 14, Section 3, Part 3, of the Manual o Petroleum Measurement Standards pro- f 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, 1220L Street, N.W., Wash- ington, D.C. 2000.5. iiiCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  9. 9. 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. E- UPP K. West, Mobil Research and Development Corporation During much of the corresponding time period, a similar effort occurred in Europe. The following individuals provided valuable liaison between the two efforts: D. Gould, Commission of the European Communities F, Kinghorn, National Engineering Laboratory M. Reader-Harris, National Engineering Laboratory J. Sattary, National Engineering Laboratory E. Spencer, Consultant J. Stolz, Consultant P. van der Kam, Gasunie The American Petroleum Institute provided most of the funding for the research project. Additional support was provided by the Gas Processors Association and the American Gas Association. Special thanks is given to the Gas Research Institute and K. Kothari for pro- viding funding and manpower for the natural gas calculationsused 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 ivCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  10. 10. - 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 w. Fling J. Gallagher, Shell Pipe Line Corporation V. Gebben, Kerr-McGee Corporation B. George, Amoco Production Company G. Givens, CNG Transmission Corporation T. Glazebrook, Tenneco Gas Transportation Company D. Goedde, Texas Gas Transmission Corporation D. Gould, Commission of the European Communities K. Gray, Phillips Petroleum Company R. Hankinson, Phillips 66 Natural Gas Company R. Haworth E. Hickl, Union Carbide Corporation L. Hillburn P. Hoglund, Washington Natural Gas Company J. Hord, National Institute of Standards and Technology E. Jones, Jr., Chevron Oil Field Research Company M. Keady K. Kothari, Gas Research Institute P. LaNasa G. Less G. Lynn, Oklahoma Natural Gas Company R. Maddox G. Mattingly, National Institute of Standards and 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. UPP 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 VCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  11. 11. M. Williams, Amoco Production Company E. Woomer, United Gas Pipeline Company C. Worrell, OXY USA, Inc. viCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  12. 12. .. _- = 0732290 0503850 018 W ~~ ~ A P I MPMS*1V-3.3 9 2 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 ..................................................................................................... 5 3.3.2 Equations for Mass Flow of Natural Gas ................................................. 5 3.3.3 Equations for Volume Flow of Natural Gas ............................................. 6 3.3.4 Volume Conversion From Standard to Base Conditions .......................... 7 3.4 Flow Equation Components Requiring AdditionalComputation ................... 7 3.4.1 General ..................................................................................................... 7 3.4.2 Diameter Ratio ......................................................................................... 8 3.4.3 Coefficient of Discharge for Flange-Tapped Orifice Meter ..................... 8 3.4.4 Velocity of Approach Factor .................................................................... 10 3.4.5 Reynolds Number ..................................................................................... 10 3.4.6 Expansion Factor ...................................................................................... 11 3.5 Gas Properties ................................................................................................. 13 3.5.1 General ..................................................................................................... 13 3.5.2 Physical Properties ................................................................................... 13 3.5.3 Compressibility ........................................................................................ 14 3.5.4 Relative Density (Specific Gravity) ......................................................... 15 3.5.5 Density of Fluid at Flowing Conditions ................................................... 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 3-D-2-Allowable Variations in Pressure Tap Hole Location.............................. 78 Tables 3-1-Linear Coefficient of Thermal Expansion .................................................. 8 3-A- 1-Water Density Based on Wegenbreth Equation ...................................... 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 ........................ 39COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  13. 13. - - ._ -_ A P I NPflS*l14-3.3 92 m 0732290 0503851 T 5 4 m Page 3-B-4-Orifice Slope Factor: F,, From Equations in 3-B.6 .................................. 42 3-B-5-Conversion of ReD/106 Q,/lOOO (Qv in Thousands of to Cubic Feet per Hour) ............................................................................. 44 3-B-6-Expansion Factors for Flange Taps (Y,): Static Pressure Taken From Upstream Taps ..................................... .................................................. 47 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 ..................................... 49 3-B-8-&, Factors Used to Change From a Temperature Base of 60°F to Other Temperature Bases ................................................... ............................ .. 49 3-B-9-I$Factors Used to Change From a Flowing Temperature of 60°F to Actual Flowing Temperature .................................................................. 50 3-B-lO-F,,. Factors Used to Adjust for Real Gas Relative Density (GJ: Base Conditions of 60°F and 14.73 Pounds Force per Square Inch Absolute 51 3-B-11-Supercompressibility Factors for G,. = 0.6 Without Nitrogen or Carbon Dioxide ............................................ .....,.......... .. ...................... 52 3-D-1-Basic Orifice Factors (Fb) for Pipe Taps ................................................. 74 .. 3-D-2-Meter Tube Pressure Tap Holes ............ ....................... ........................ 78 3-D-3-b Values for Determining Reynolds Number Factor F, for Pipe Taps ... 80 3-D-4-Values of K to Be Used in Determining Rd for Calculation of F, Factor.. 84 3-D-5-Expansion Factors for Pipe Taps (YJ: Static Pressure Taken From .. .. . .. . ... .... .... . ...... .. . ... .. .. .. . .. Upstream Taps ......... . . , . . . . . . . . . .. . .. ..... .. ......... ... . 85 3-D-6-Expansion Factors for Pipe Taps (Y2):Static Pressure Taken From Downstream Taps ................................................................................... 87 3-E- 1-Volume Reference Conditions for Custody Transfer Operations: Natural Gas Volume ............................................................................... 93 3-E-2-Energy Reference Conditions ....... . . . . . . . .. . .. ,, . ,,.,,. ..... ...,.., .. ,..,....,.... ... . ..... , 93 . . . . .. . . . 3-E-3-Heating Value Reference Conditions ................... .. .... . . . ........ .. ...... 93 3-F-1-Physical Properties of Gases at Exactly 14.73 Pounds Force per Square Inch Absolute and 60°F .......................................................................... 96 viiiCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  14. 14. 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. TransmissionMeasurement 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/Gallagherequation 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 1COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  15. 15. ~~ A P I MPMS*L4.3-3 92 E 0732290 0503853 827 2 CHAPTER&NATURAL 1 MEASUREMENT GASFLUIDS 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 Units/Value 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 Btu/(lbm-OF) Specific heat at constant volume Btu/(lbm-OF) Orifice plate bore diameter calculated at flowing temperature, T, in Meter tube internal diameter calculated at flowing temperature, $ in Orifice plate bore diameter calculated at reference temperature, T, in Meter tube internal diameter calculated at reference temperature, T, in Napierian constant 2.7 1828 Velocity of approach factor Temperature, in degrees Fahrenheit - Temperature, in degrees Rankine 459.67 + OF Supercompressibilityfactor Gas relative density (specific gravity) Ideal gas relative density (specific gravity) Real gas relative density (specific gravity) Orifice differential pressure inches of water column at 60°F Isentropic exponent (see 3.4.5) Ideal gas isentropic exponent Perfect gas isentropic exponent Real gas isentropic exponent - Mass lbm Molar mass (molecular weight) of air 28.9625 lbm/ib-mol Molar mass (molecular weight) of gas lbmfib-mol Molar mass (molecular weight) of componen1 lbmbb-mol Number of moles Unit conversion factor (discharge coefficient) - Pressure lbf/in2(abs) Base pressure lbf/in2(abs) Base pressure of air ibf/in* (abs) Base pressure of gas lbf/in2(abs) Static pressure of fluid at the pressure tap lbf/in2(abs) Absolute static pressure at the orifice upstream differential pressure tap lbf/in2 (abs) Absolute static pressure at the orifice downstream differential pressure tap lbf/in2(abs)COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  16. 16. S C I N 3-CONCENTRIC, E TO SQUARE-EDGED METERS, PART Q-NATURAL ORIFICE GASAPPLICATIONS 3 Standard pressure 14.73 ibf/in2 (abs) Volume flow rate at base conditions ft3/hr Mass flow rate per second Ibm/sec Mass flow rate per hour Ibm/hr Volume flow rate per hour at standard conditions ft3/hr Universal gas constant 1545.35 (lbf-ft)/(lb-mol-oR) Pipe Reynolds number - Temperature OR Base temperature "R Base temperature of air "R Base temperature of gas OR Temperature of fluid at flowing conditions OR Reference temperature of the orifice plate bore diameter and/or meter tube inside diameter 68°F Standard temperature 5l9.67"R Flowing velocity at upstream tap ftlsec Volume fe Volume at base conditions ft3 Flowing volume at upstream tap ft3 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 60°F 0.999590 Compressibility of the gas at base conditions (Pb8 T b ) TI) Compressibility at flowing conditions (6, Compressibility at upstream flowing conditions Compressibility at downstream flowing conditions Compressibility at standard conditions ( 9 e T,) - Linear coefficient of thermal expansion idin-"F Linear coefficient of thermal expansion of the orifice plate material in/in-"F Linear coefficient of thermal expansion of the meter tube material iIl/in-"F Ratio of orifice plate bore diameter to meter tube internal diameter ( d / D ) calculated at flowing temperature, TI - Absolute viscosity of flowing fluid lbm/ft-secCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  17. 17. 4 CHAPTER 1&NATURAL GASFLUIDS MEASUREMENT K Universal constant 3.14159 pb Density of a fluid at base conditions (Pb, Tb) lbm/ft3 pb,,ir Density of air at base conditions (Pb, Tb) lbm/ft3 Pbtm Density of a gas at base conditions (& Tb) Ibm/ft3 ps Density of a fluid at standard conditions ( 9 e T,) lbm/ft3 p,@ Density of a fluid at flowing conditions ( 9Tf) 4 Ibm/ft3 pfp, Density of a fluid at flowing conditions at upstream tap position (QI,Tf) lbm/f? pf,pz Density of a fluid at flowing conditions at downstream tap position Tf)(e2, lbm/ft3 @i Mole fraction of component %/loo Note: Factors, ratios and coefficients are dimensionless. 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), fluid flowing the static pressure (P,), the fluid flowing compressibility(Zh)indicates that these variables and 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 pf,, pressure tap are identified by the subscript 2, including Y,, pf,p2, 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 1is 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 519.67R (60F); and the fluid com- pressibility, Z,, for a stated relative density (specific gravity), G. 3.2.3.5 Definitions General definitions are covered in Parts 1 and 2. Definitions specific to Part 3 are incor- porated in the text.COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  18. 18. 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 GASAPPLICATIONS 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 P r 1have been converted to reflect these units. at 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 EQUATIONS FOR MASS FLOW OF NATURAL GAS .. 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: Mass flow developed from the ideal gas relative density (specific gravity), Gi, ex- is 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 (60°F) 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 (60°F) 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-tappedorifice 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 60°F. 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.COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  19. 19. 6 CHAPTER 14-NATURAL GASFLUIDS 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,,~,) base conditions ( p b ) is expressed as follows: and 359.072Cd(FT)EvY,d2 Q6 = (3-4a) Pb The volume flow rate at base conditions, developed from ideal gas relative density (specific gravity), Gi, expressed as follows: is (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 - z;{T fi (3-6a) If standard conditions are substituted for base conditions in Equations 3-4a, 3-5a, and 3- 6a, then Pb =4 = 14.73 pounds force per square inch absolute T,=T, = 519.67"R (60°F) z6,,;r = zsoir = 0.999590 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,,~,) standard conditions (p,), is expressed as follows: and 359.072Cd(FT)EvY,d21/P,,h, Qv = (3-4b) Ps The volume flow rate at standard conditions, developed from ideal gas relative density (specific gravity), Gi, expressed as follows: is (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 (60°F) in its numeric constant. Therefore, the volume flow rate at standard conditions, de- veloped from real gas relative density ,(specificgravity), G,.,is expressed as follows: iG Q, = 7709.61Cd(FI)Ev~d2 r ; l ~ s h w (3-6b)COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  20. 20. - ---____ A P I MPMS*LLI.3.3 ~ 72 0 7 3 2 2 9 0 0503858 3 0 9 SECTION 3-CONCENTRIC, SQUARE-EDGED METERS, PART 3-NATURAL ORIFICE GASAPPLICATIONS 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 60°F. 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 = 14.73 pounds force per square inch absolute. 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 (60°F). 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). (e, Z,, = compressibility of air at standard conditions T,). p = density of the flowing fluid at base conditions (Pb, Tb),in pounds mass per cu- b bic foot. (e, ps = density of the flowing fluid at standard conditions K), pounds mass per in cubic foot. p,pI = density of the fluid at upstream flowing conditions (GI, Tf), in pounds mass per ciibic foot. 3.3.4 VOLUME CONVERSION FROM STANDARD TO BASE CONDITIONS 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: Where: Pb = base pressure, i pounds force per square inch absolute. n 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 Some of the terms in Equations 3-1 through 3-6 require additional computation and are developed in this section.COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  21. 21. A P I M P M S * L 4 * 3 - 3 92 m 0732290 0503859 245 m 8 CHAPTER 14-NATURAL GASFLUIDS MEASUREMENT 3.4.2 DIAMETER RATIO (/3) The diameter ratio (ß), 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) the internal diameter of the meter tube (0). the to For most precise results, the actual dimensions should be used, as determined in Parts 1 and 2. ß = dID (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.. = temperature of the fluid at flowing conditions. T, = reference temperature for the orifice plate bore diameter and/or the meter tube in- ternal diameter. 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). ß = diameterratio. q, Note: a, and T, must be in consistent units. For the purpose of this standard, T,is assumed to be 68°F. The orifice plate bore diameter, d,, and the meter tube internal diameter, Dr, calculated at T, are the diameters determined in accordance with Part 2. 3.4.3 COEFFICIENT OF DISCHARGE FOR FLANGE-TAPPED ORIFICE METER, Cd(FT) The coefficient of discharge for a flange-tapped orifice meter ( , has been determined C ) from test data. It has been correlated as a function of diameter ratio (ß), 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 Linear Coefficient of Thermal Expansion (a), Material in/in-OF o p e 304 and 316 stainless steel" 0.00000925 Monela 0.00000795 Carbon steelb 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). aForflowing conditions between -100°F 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-7F and +154F, refer to Chapter 12, Sec- tion 2.COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  22. 22. A P I MPMS*L4-3*3 92 m 0732290 0 5 0 3 B b 0 Tb7 m SECTION 3--CONCENTRIC, ORIFICE METERS, SQUARE-EDGED PART 3-NATURAL GASAPPLICATIONS 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 (ß) 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 P r 1, 1.12.4.1, at The Reader-HanisIGallagher equation is defined as follows: Cd(FT) = Ci(FT) + 0.000511 - ")!:ol( + (0.0210 + 0.0049A)ß4C (3-11) Ci(FT) = Ci(CT) + Tap Term (3-12) Ci(CT) = 0.5961 + 0.0291ß2 - 0.2290ß8 + 0.003(1 - ß ) M , (3-13) Tap Term = Upstrm + Dnstrm (3-14) Upstrm = [0.0433 + 0.0712e-8.5L1 0.1145e-"oL1](1 0.23A)B - - (3-15) Dnstrm = -0.0116[M2 - 0.52M2.3]ß.1(1- 0.14A) (3-16) Also, B E - - - - ß4 (3-17) 1 - ß4 (3-18) (3-19) 0.8 19,oooß (3-20) = (Re,) (3-21) Where: cd(l?ï)= coefficient of discharge at a specified pipe Reynolds number for a flange- tapped orifice meter. Ci(CT) = coefficient of discharge at an infinite pipe Reynolds number for a corner- tapped orifice meter. Ci(FT) = coefficient of discharge at an infinite pipe Reynolds number for a flange- 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. L, = L, = dimensionless correction for tap location = N4/D for flange taps. N4 = 1.O when D is in inches. Re, = pipe Reynolds number. ß = diameterratio = dlD. 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.COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  23. 23. A P I MPMS*14.3.3 92 0732290 0503863 9T3 m- 10 CHAPTER I4-NATURAL GASFLUIDS 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: (3-22) Where: E, = velocity of approach factor. p = diameterratio = dfD. 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: (3-23) Or (3-24) Note: The constant, 12, in the denominator of Equation 3-23 is required by the use of D i inches. n The fluid velocity can be obtained in terms of the volumetric flow rate at base conditions from the following relationship: (3-25) Substituting Equation 3-25 into Equation 3-23 results in the following relationship: (3-26) The Reynolds number for natural gas can be approximated by substituting the following relationship for p (see 3.5.5.3 for equation development) into Equation 3-26: b (3-27) (3-28)COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  24. 24. __ A P I MPMS*14.3.3 92 0732290 0 5 0 3 8 6 2 - 8 3 T W ~ SECTION 3-CONCENTRIC, ORIFICE METERS, SQUARE-EDGED PART Q-NATURAL GASAPPLICATIONS 11 By using an average value of 0.0000069 pounds mass per foot-second for , and substituting u 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- QvGr (3-29) 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. Re, = pipe Reynolds number. Tb = base temperature, in degrees Rankine. U ,= velocity of the flowing fluid at the upstream tap location, in feet per second. = compressibility of air at 14.73 pounds force per square inch absolute and 60°F. = compressibility of the gas at base conditions (Pbi Tb). , = absolute (dynamic) viscosity, in pounds mass per foot-second. u = ~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 30°F 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 compressiblefluid isentropic exponent, k,, is a function of the fluid and the pres- sure and temperature. For an ideal gas, the isentropic exponent, ki, equal to the ratio of is 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 kievaluated 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 isCOPYRIGHT American Petroleum InstituteLicensed by Information Handling Services
  25. 25. A P I MPMS*L4*3-3 92 0732290 0503863 776 = 12 CHAPTER 1&-NATURAL GASFLUIDS 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 < hW I0.20 (3-30) 27.707 4 Or P 0.8 I < 1.0 (3-31) G Where: h, = flange tap differential pressure across the orifice plate, in inches of water at 60°F. pf = flowing pressure, in pounds force per square inch absolute. pfl = absolute static pressure at the upstream pressure tap, in pounds force per square inch absolute. P, = absolute static pressure at the downstream pressure tap, in pounds force per square inch absolute. 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 (ß) outside the stated limits, increased uncertainty will occur. 3.4.6.2 Expansion Factor Referenced to Upstream Pressure If the absolute static pressure is taken at the upstream differential pressure tap, the value of the expansion factor, Y,, can be calculated using the following equation: = 1 - (0.41 + 0.35ß4) i (3-32) When the upstream static pressure is measured, XI = G-42 = h w (3-33) G 27.707 4, When the downstream static pressure is measured, XI = G - I;, - - W h (3-34) G2 + (G - G2) 27.707G2 + h, Where: h, = differential pressure, in inches of water at 60°F. k = isentropic exponent (see 3.4.6.1). Pr, = absolute static pressure at the upstream tap, in pounds force per square inch ab- solute. e2 = absolute static pressure at the downstream tap, in pounds force per square inch ab- solute. 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 tap. ß = diameter ratio (d/D). The quantity x , / k is known as the acoustic ratio.COPYRIGHT American Petroleum InstituteLicensed by Information Handling Services

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