Aga 8 Part 1

 

 

 AGA Report No. 8 Part 1

Thermodynamic Properties of Natural Gas and Related Gases DETAIL and GROSS Equations of State

Third Editio Edition n April 2017 A revision of AGA Report No. 8, 2nd edition, 1994)

Prepared by Transmission Measurement Committee

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AGA Report No 8 Part 1

Thermodynamic Properties of Natural Gas and Related Gases DETAIL and GROSS Equations of State  Prepared by  by  Transmis sion Measur ement Committ ee  

Third Edition April 2017 (A revision of AGA Report No. 8, 2nd  edition,1994) Copyright © 2017 American Gas Association All Rights Reserved

Catalog No. XQ1704-1

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DISCLAIMER AND COPYRIGHT The American Gas Association’s (AGA) Operations and Engineering Section provides a forum for industry experts to bring their collective knowledge together to improve the state of the art in the areas of operating, engineering and technological aspects of producing, gathering, transporting, storing, distributing, measuring and utilizing natural gas. Through its publications, of which this is one, AGA provides for the exchange of information within the natural gas industry and scientific, trade and governmental organizations. Many AGA publications are prepared or sponsored by an AGA Operations and Engineering Section technical committee. While AGA may administer the  process, neither neither AGA nor the technical committee committee independently independently tests, evaluates evaluates or verifies the accuracy of any information or the soundness of any judgments contained therein. AGA disclaims liability for any personal injury, property or other damages of any nature whatsoever, whether special, indirect, consequential or compensatory, directly or indirectly resulting from the publication, use of or reliance on AGA publications. AGA makes no guaranty or warranty as to the accuracy and completeness of any information published therein. The information contained therein is provided on an “as is” basis and AGA makes no representations or warranties including any expressed or implied warranty of merchantability or fitness for a  particular purpose. Nothing contained in th this is doc document ument should be be viewed viewed as an an end endorsement orsement or disapproval disapproval of any any  particular manufacturer manufacturer or product. product. In issuing and making this document available, AGA is not undertaking to render professional or other services for or on behalf of any person or entity. Nor is AGA undertaking to perform any duty owed by any person or entity to someone else. Anyone using this document should rely on his or her own independent judgment or, as appropriate, seek the advice of a competent professional in determining the exercise of reasonable care in any given circumstances. AGA has no power, nor does it undertake, to police or enforce compliance with the contents of this document.  Nor does AGA list, certify, test or inspect products, designs or installations for compliance compliance with this document. Any certification or other statement of compliance is solely the responsibility of the certifier or maker of the statement. AGA does not take any position with respect to the validity of any patent rights asserted in connection with any items that are mentioned in or are the subject of AGA publications, and AGA disclaims liability for the infringement of any patent resulting from the use of or reliance on its publications. Users of these publications are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, is entirely their own responsibility. Users of this publication should consult applicable federal, state and local laws and regulations. AGA does not, through its publications, intend to urge action that is not in compliance with applicable laws, and its publications may not be construed as doing so. Information concerning safety risks, proper installation or use, performance or fitness or suitability for any purpose with respect to particular products or materials should be obtained from the manufacturer or supplier of the material used. Changes to this document may become necessary from time to time. If changes are believed appropriate by any  person or entity, such such suggested ch changes anges should be communicated communicated to AGA in writing and sent to: to: Operations &  th  Engineering Section, American Gas Association, 400 North Capitol Street, NW, 4  Floor, Washington, DC  20001, U.S.A. or E-mail to: [email protected]. [email protected]. Suggested changes must include: contact information, including name, address and any corporate affiliation; full name of the document; suggested revisions to the  text of the document; the rationale for the suggested revisions; and permission to use the suggested revisions in an amended publication of the document. Copyright © 2017, American Gas Association, All Rights Reserved.

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FOREWORD AGA Report No. 8, Part 1, is designated as the third edition of the revised 1994 second edition of AGA Report No. 8. As in the second edition, the third edition provides the technical information necessary to compute thermodynamic properties including compressibility factors and densities of natural gas and related gases for states in the gas phase only. Additionally, equations for calculating speeds of sound and other thermodynamic  properties are given. Historical Historical information on this document is given in S Section ection 1.2, Background. Analy Analyses ses of the calculation of uncertainties are provided for various gas temperatures, pressures, and compositions. It is based on research managed and sponsored by the then Gas Research Institute (GRI) in cooperation with AGA and the Groupe Europeen de Recherches Gazieres  (GERG). Because the equations of state contained within International Standards Organization documents ISO 12213:  Natural Gas  –   Calculation of Compression Factor , Part 2: Calculation Using Molar-Composition Analysis, 2006 edition, and ISO 20765:  Natural Gas  –   Calculation of Thermodynamic Properties, Part 1: Gas Phase Properties for Transmission and Distribution Applications, 2005 edition, are based on the same equations in this revision, calculated properties should have the same values. This revised edition, now designated as AGA Report No. 8, Part 1, uses the same DETAIL and GROSS equations of state as in the 1994 edition of AGA Report No. 8. However, the temperature, pressure, and gas composition limits have been modified in this edition; and therefore, it will be necessary to ensure that the temperature, pressure, and gas composition fall within the new limits for the desired uncertainty. The users are advised to verify the applicability/acceptability of the program for the new limits based on the 1994 edition of AGA 8. The documentation of programs for calculating properties from the methods described in this document is available as supplementary material in Appendix C. Examples are available in Fortran, VB, and C++ code. The supplementary material also contains a Microsoft Excel spreadsheet for property calculations. This can be used to determine if, for a particular temperature, pressure, and composition, the property values calculated from the equations in Part 1 are within the desired uncertainty (by comparing with those in Part 2) even though one or more of these inputs may be outside the ranges given in Part 1. A file containing calculated points at different compositions (not necessarily related to typical natural gas) is included, which can be used to verify that programs or equipment have been implemented or upgraded correctly to produce values that are in agreement with the equations in this document. The user is encouraged to compare property values obtained through the use of the software rom the user’s existing software and determine if the provided in this edition with those obtained f rom differences are within the uncertainty limits of of their respective calculation methods. The Excel spreadsheet provided in the supplementary material can be used to determine if property values are within the acceptable uncertainty limits even though the state point may be outside the ranges given in this revision. If the property values are not within the uncertainty limits, the user should consider implementing AGA Report No. 8, Part 2, noted below.

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AGA Report No. 8, Part 2, published separately, is based on the GERG-2008 equation of state, and is applicable for temperature, pressure, and composition ranges outside those in Part 1, with uncertainties in density, compressibility factor, and speed of sound still within 0.1 %. Part 2 can also be used for operating conditions and compositions that are applicable for Part 1, with differences in the calculated values within the uncertainty limits of each equation, where uncertainties are given with a 95 % level of confidence ( k =2). =2). While adoption of the equations in Part 2 is encouraged, e ncouraged, the decisions to upgrade existing installations to use AGA Report No. 8, Part 2, are left to the discretion of the parties involved.  Some material described in Part 1 also applies to Part 2, and vice versa, and is not repeated in both parts. For example, Part 1 describes an algorithm for obtaining densities through an iterative procedure that can also be used with the equations Part 2 (and which is applied for this purposeSimilarly, to the GROSS, DETAIL, GERG2008 equations of state ininthe programs in the supplementary material). Part 2 outlines theand method for reporting calculated results and uncertainties from the equations in both parts, and also describes the experimental

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database available for natural gas mixtures (both binary and multicomponent systems), much of which was used in the development of the equations in Part 1. Some information, however, is repeated in both parts, such as the material in Sections 2 and 3. The combination of Parts 1 & 2 gives a wider overview of the equations of state and their appropriate application to natural n atural gas. The publication AGA Report No. 10: Speed of Sound in Natural Gas and Other Related Hydrocarbon Gases has been discontinued with the release of this AGA Report No. 8, Part 1. The calculation of the speed of sound no longer requires integration of the compressibility factor equation, as was done in AGA Report No. 10,  but is implemented implemented through differentiation of the fundam fundamental ental Helmholtz energy equa equation tion of state. This results in faster calculations through direct computation of the required derivatives.

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ACKNOWLEDGEMENTS AGA Report No. 8, Thermodynamic Properties of Natural Gas and Related Gases, Part 1, DETAIL and GROSS Equations of State, was revised by a Task Group of the American Gas Association’s Transmission Measurement Committee under the chairmanship of Dr. Eric W. Lemmon with the National Institute of Standards and Technology (NIST). AGA thanks NIST for the extensive amount of time allocated to Dr. Lemmon for the preparation of this report. Andrew Laughton from DNV GL (Oil & Gas), UK, has been of great help reviewing the documents and programs. Individuals who made substantive contributions are:

Ian Bell, NIST, USA Ilia Bluvshtein, Union Gas Ltd., Canada David Bromley, BP Pipelines, USA Greg Dunn, Eagle Research Corporation, USA Juan Escobar, ARAMCO, Saudi Arabia Volker Heinemann, Honeywell, Germany Randy Herman, Flow-Cal Measurement Applications, USA Gurwinder Kamboz, Krohne Oil & Gas, The Netherlands Jason Lu, Thermo Fisher Scientific, USA Ian McDavid, Flow-Cal Measurement Applications, USA Warren Peterson, Alliance Pipeline, Canada Ken Starling, Starling Associates, USA Jim Witte, Southwest Research Institute, USA In addition, comments from the following individuals were of great help:

Dale Embry, ConocoPhillips, USA David Escobar, SPL Inc., USA Graham Forbes, Emerson Automation Solutions, Canada Keith Fry, Formerly with Quorum Business Solutions, USA Darin George, Southwest Research Institute, USA Ken Hall, Formerly with Texas A&M University Daniel Harris, Columbia Pipeline Group – TransCanada TransCanada Corp., USA Masahiro Ishibashi, Research Institute for Engineering Measurement, Japan James McAdams, Interlink Systems, USA Gary McCargar, Oneok, USA Roy Meyer, ExxonMobil, USA Sam Patel, Consumers Energy Co., USA King Poon, Thermo Fisher Scientific, USA Danny Rekers, Kiwa Technology, The Netherlands Don Sextro, Targa Resources, USA Tushar Shah, Eagle Research Corporation, USA David Solis, Williams, USA Rick Spann, QPC Services Company, USA Scott Tanner, Flow-Cal Measurement Applications, USA Tim Tucker, ABB Inc., USA Armand Lloret Vallès, Premegas, Spain AGA acknowledges the contributions of the above individuals and thanks them for f or their time and effort in reviewing the document or suggesting changes to the programs in the supplementary material.

Christina Sames Vice President, Operations & Engineering Engineerin g

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Ali Quraishi Director, Operations & Engineering Services

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TABLE OF CONTENTS DISCLAIMER AND COPYRIGHT ................................................................................................................. iii  FOREWORD ..................................................................................................................................................... v  ACKNOWLEDGEMENTS ............................................................................................................................. vii  1 INTRODUCTION ................................. ................ ................................... ................................... ................................... ................................... ................................... ................................... ................. 1  1.1 Scope ........................................................................................................................................................ 1 

 

1.2 Background............................................................................................................................................... 1  1.3 Overview of Properties from Equations of State ...................................................................................... 2 1.3.1 DETAIL Equation of State ................................................................................................................................ 2  1.3.2 GROSS Equation of State ................................................................................................................................. 6  

1.4 Uncertainty ............................................................................................................................................... 7  1.4.1 DETAIL Equation of State Uncertainty ............................................................................................................ 7   1.4.2 GROSS GROSS Equation of State Uncertainty Uncertainty .................... ......... ..................... ..................... ..................... ..................... ..................... ..................... ..................... .................... ................. ....... 7 

1.5 Recommendations .................................................................................................................................... 7  2 DEFINITIONS AND GENERAL EQUATIONS ................. ................................... ................................... ................................... .................................... .................... .. 8  2.1 Definitions of Phase Regions ............................................................................................................................... 8  2.2 Nome Nomenclatu nclature re ........................... ......................................... ............................ ............................ ............................ ............................. ............................. ............................ ............................ ......................... ........... 9  2.3 General Equations ...............................................................................................................................................10 

3 UNITS, CONVERSIONS, PRECISION, AND ACCURACY ................................... ................. .................................... ................................. ............... 11  4 THEMODYNAMIC PROPERTIES FROM THE DETAIL EQUATION OF STATE .............................. .................. ............ 12  4.1 Nome Nomenclatu nclature re ........................... ......................................... ............................ ............................ ............................ ............................. ............................. ............................ ............................ ........................12 ..........12  4.2 DETAIL Equation of State for Thermodynamic Properties Including Compressibility Factor and Pressure .....13   4.3 Equation Equation of State for the Helmholtz En Energy ergy .................... .......... ..................... ..................... .................... ..................... ..................... ..................... ..................... ..................... ...........15 15  4.4 Speed of Sound Sound and Other Thermodynamic Properties .......... ..................... ..................... .................... ..................... ..................... .................... ..................... ...............16 ....16 

5 THERMODYNAMIC PROPERTIES FROM THE GROSS EQUATION OF STATE ............................. ................. ............ 23  5.1 Nome Nomenclatu nclature re ........................... ......................................... ............................ ............................ ............................ ............................. ............................. ............................ ............................ ........................23 ..........23  5.2 Equation of State for Compressibility Factor ......................................................................................................23  5.3 Interaction Virial Coefficient Terms for Nitrogen and Carbon Dioxide .............................................................26   5.4 Interaction Virial Coefficient Terms for the Equivalent Hydrocarbon .................... .......... ..................... ..................... ..................... ..................... ............26 ..26 

6 COMPUTATION OF DENSITIES AND COMPRESSIBILITY COMPRESSIBILIT Y FACTORS ................................... .................. ........................... .......... 28  6.1 Iterative Procedure to Determine Density from Temperature and Pressure ........................................................28   6.2 Computer Computer Programs for the Calculation of Properties .......... ..................... ..................... ..................... ..................... ..................... ..................... .................... ................29 ......29  

7 ASSIGNMENT OF TRACE COMPONENTS ................................. ............... ................................... ................................... .................................... ........................ ...... 30  8 REFERENCES ................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................... 32  APPENDIX A –  A –  GROSS   GROSS EQUATION OF STATE ........................................................................................ 33  A.1 Nomenclature ................................. ................ ................................... ................................... ................................... ................................... ................................... ................................. ............... 33  A.2 Reference Conditions ................................... .................. .................................. ................................... ................................... ................................... .................................... .................. 33  A.3 GROSS Equation of of State Computation Procedures .................................. ................. ................................... ................................... ........................ ....... 34 

A.3.1 Method 1. Volumetric Gross Heating Value, Relative Density, and Mole Fraction of CO2 .........................3 .........................36 6  A.3.2 Method 2. Relative Density and Mole Fractions of N 2 and CO2 ............ .......................... ............................ ............................ ...........................3 .............36 6  A.3.3 Method 3. Molar Mass and Mole Fractions of N2 and CO2 ............. ........................... ............................ ............................ ............................. ....................37 .....37  

APPENDIX B –  B –  EXAMPLES  EXAMPLES AND COMPARISON TO MEASUREMENTS ............................................. 38   B.1 Nomenclature ................................. ................ ................................... ................................... ................................... ................................... ................................... ................................. ............... 38  B.2 Calculation Examples ................................... .................. .................................. ................................... ................................... ................................... .................................... .................. 38  B.3 Comparisons of Calculated Properties with Measurements ................................... ................. .................................... .............................. ............ 43  APPENDIX C –  C –  DESCRIPTION  DESCRIPTION OF THE SUPPLEMENTARY FILES ....................................................... 46   FORM TO PROPOSE CHANGES .................................................................................................................. 49 

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1 INTRODUCTION 1.1 Scope Part 1 presents information for the computation of thermodynamic properties ( e.g., compressibility factor, density, and speed of sound) of natural gas and related gases with the DETAIL and GROSS equations of state. Uncertainty estimations for different compositions, pressures, and temperatures are given. The computations are valid for single-phase gaseous states only. For mixed or liquid phases, refer to Part Part 2.

1.2 Background Research in 1928 and 1929 under the th e direction of Mr. Howard S. Bean of the National Bureau of Standards Stan dards  provided the natural gas industry with its initial compressibility factor data covering pressures up to 600 psia (4 MPa). However, it was not until 1954 that extensive tables of natural gas supercompressibility factors were  published, based on tests supervised by Professor Samuel Samuel R. Beitler of Ohio State University. The natural gas supercompressibility factor tables were extended and an equation of state was developed in 1956-1962 under the direction of Mr. R. H. Zimmerman of Ohio State University. The results of this project, designated PAR Project  NX-19, appear in in AGA’s Manual for Determination of Supercompressibility Supercompressibility Factors for Natural Gas , published in 1962. The research leading to the 1985 and 1992 reports was initiated in 1981 under the sponsorship of GRI in close liaison with the AGA Transmission Measurement Committee. This research, carried out under the direction of Professor Kenneth E. Starlingfactors of the beyond University Oklahoma,pressure, was aimed extending capabilities for accurate computation of compressibility the of temperature, andatcomposition ranges of PAR Project  NX-19. The results results for for pipeline-quality pipeline-quality natural gas, which were complete completed d in 1984, provided the basis basis for the 1985 1985 report. The initial 1981-1984 research used data ranging in pressures up to approximately 900 psia (6 MPa) obtained from the literature and provided by GERG. However, the GERG data bank was extended considerably over the period 1985-1990. The new data showed that the original equation of state, developed in the period 19811984, needed to be improved. In addition, speed of sound data obtained under GRI sponsorship during 1985-1989 showed calculations calculations for rich gases were not sufficiently sufficiently accurate for critical flow applications. `  `  `    ,   , `  `  `  `    ,   ,   , `    , `  `    ,   , `  `    , `    ,   , `    ,   , `  `    ,   , `    ,   , `    , `    ,   , `  -

Although the 1992 and 1994 AGA 8 publications of the equation of state are explicit in the compressibility factor Z , the formulation was originally developed with an equation of state explicit in the Helmholtz energy a with independent variables of molar density d  and  and temperature T . The Helmholtz energy equation was not given in the 1992 and 1994 AGA 8 documents, where only equations explicit in pressure and compressibility factor were reported. The Helmholtz energy is a fundamental thermodynamic thermodyna mic property from which all other thermodynamic  properties can be calculated calculated as derivatives derivatives with respect to density or temperature. temperature. For example, example, the expression for calculating pressure is

 a   .  d  T 

  2 P  d   

(1-1)

When starting from the pressure explicit equation, the calculation of other properties, including the speed of sound, requires not only derivatives of the compressibility factor with respect to density and temperature, but also integration of  Z  over   over density, which can be quite complicated. Equations are presented in this revision that start with the Helmholtz energy form, and allow access to other thermodynamic properties such as heat capacities, enthalpies, and entropies by differentiation different iation of this fundamental property. Formulations explicit in the Helmholtz energy haveofbeen used heavily overthermodynamic the last two decades to represent the properties of pure fluids and mixtures due to the ease calculating all other properties. 1  Copyright American Gas Association Provided by IHS Markit No reproduction or networking permitted without license from I HS Markit

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Work began in the 1990’s at the t he Ruhr University in Bochum, Germany, under the direction of Wolfgang Wagner to develop even more sophisticated models to represent not only the gas phase, as in the case of AGA 8,  but also the liquid phase and retrograde region. The first version was released in 2004 for f or 18 fluids, and then updated in 2008 with three additional fluids. These 21 fluids are identical to the fluids available in this document. Because the calculation of dew points requires knowledge of the liquid phase as well as the gas phase, the DETAIL equation of state presented in Part 1 is not able to determine the state where liquids will condense from a natural gas stream. With the addition of accurate liquid calculations in the GERG-2008 equati equation, on, dew points, as well as bubble points and saturation states in the retrograde region can now be evaluated for any temperature or  pressure input input state. The equations equations required to do so are are covered covered in Part 2.

1.3 Overview of Properties from Equations of State This report provides recommended equations of state to compute accurate compressibility factors, densities, and other thermodynamic properties for natural gas. The information in this report can be used for calculations of compressibility factors and densities for pure methane, ethane, nitrogen, carbon dioxide, hydrogen, and hydrogen sulfide, and for gas mixtures of up to twenty-one components. Compressibility factors, supercompressibility factors, and density values can be applied directly in calculations of gas volume and gas flow rate. These computations can also be used in other instances where the relationship between the temperature,  pressure, and and volume of a gas is is important. Other thermodynamic properties that can be calculated with the information in this report include the heat capacity, enthalpy, entropy, sonic velocity, critical flow factor (see Appendix E of ASME/ANSI MFC-7M-1987), and component chemical potentials. Applications that use these properties include calculations for sonic nozzles, compressors, heat exchangers, gas mixture reaction equilibrium, and gas mixture component fugacities (for use in vapor-liquid equilibrium calculations). Two equations of state are provided in Part 1. All information needed to efficiently implement the appropriate equation of state as a function of the natural gas composition ( i.e., a gas analysis) is contained in this report, except the molar heating values, which can be obtained from AGA Report No. 5,  Natural Gas Energy  Measurement . The two equations differ by their complexity and the range over which calculations can be made. The equation of state with a wider range of conditions is referred to as the "DETAIL Equation of State." See References [1] and [2]. The equation of state with a limited range of conditions, herein referred to as the "GROSS Equation of State," uses second and third virial coefficients to compute the compressibility factor. See References [3] and [3] and [4]. [4]. Although gas properties are best calculated through the use of the natural gas composition, they can also be obtained with an aggregate or gross knowledge of the gas (given by heating value and/or relative density, and diluent gas content information).

1.3.1 DETAIL Equation of State The DETAIL equation of state was developed to accurately describe the gas-phase pressure-temperaturedensity behavior of natural gas mixtures. This equation of state reduces the uncertainties of compressibility factor and density calculations for natural gas, which can contain mole percentages of hexanes plus heavier hydrocarbons greater than 1 %. Equations of the density behavior of pure hydrogen sulfide and binary mixtures of hydrogen sulfide with methane, ethane, nitrogen, and carbon dioxide were developed to reduce the calculation uncertainty for natural gas containing hydrogen sulfide (sour gas). Second virial equations were developed for water and binary mixtures of water with methane, ethane, nitrogen, and carbon dioxide to reduce the calculation uncertainty for natural gas containing water vapor. Section 4 presents complete information for the DETAIL equation of state.

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Part 1 is only valid for the gas phase. For the liquid phase, mixed phase, and saturation properties (including dew points), see Part 2. The DETAIL equation of state can be applied, as shown in Figure 1, for temperatures above –  above – 200 200 °F ( –   – 130 130 °C) and at pressures up to 40,000 psia (280 MPa). The upper temperature limit is the onset of decomposition of the components in the gas [which is generally above 350 °F (180 °C)]. For applications outside these ranges of temperature and pressure, refer to Part 2 or experimental verifi verification. cation. Use of the DETAIL equation of state is not recommended within the vicinity of the critical point or liquid-like states.

Temperatur e, °C °C 40,000  –130

 –60

 –4

280

Regio Re gio n 4  –  1.0 % 10,000

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70

Regio Re gio n 3  –  0.5 %

Pressure, psia   psia

2,500

Pressure, MPa   MPa

17.2

Regio Re gio n 2  –  0.3 % 1,500

10.3

Regio Re gio n 1  –  0.1 % See Table 1 Range A for composition ranges.  0

 –200

0 

 –80

25

Temperatur e, °F °F

Figure 1. Overview of uncertainties for natural gas compressibility factors with the DETAIL equation of state (not to scale). The upper temperature limit is the onset o off decomposition of the components in the gas. Note: This figure is not intended for contractual c ontractual use. Table 1 should be consulted for specific uncertainty information. 

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A database for mixtures with water, heavy hydrocarbons, or hydrogen sulfide in natural gas is not presently available for the determination of uncertainties of calculated gas properties. Therefore, as a practical matter, the only limitation is that the calculation is for the gas phase. Thus, the limits are the water dew point for mole percent water and the hydrocarbon dew point for mole percent heavy hydrocarbons. Figure 1 gives a simple overview of typical uncertainties for the DETAIL equation of state, but should not  be used used as a basis basis to estimate the uncertaint uncertainties ies in calculated calculated properties. properties. Rather, Table 1 lists lists comprehensive comprehensive ranges for which the uncertainties are less than 0.1 % (details are given in Reference [5]). [5]). Three different sets of ranges are defined below, each having its own range of validity for temperature, pressure, and component fractions. Range A in Table 1 shows the limits of the mole percent of components in a natural gas mixture in which the uncertainties in compressibility factors are less than 0.1 % for temperatures above 25 °F ( –  ( – 4 °C), pressures less than 1500 psia (10.3 MPa), heating values from 630 to 1200 Btu/scf, and relative densities from 0.554 to 0.91. However, a mixture with compositions near the upper limits of every component in this range, except methane and nitrogen, will have an uncertainty higher than 0.1 %. Most typical natural gases do not fall under such a condition. This was verified through the use of the 200 gas compositions available in the supplementary material. Deviations  between the the DETAIL and GERG GERG equations of state were compared for each gas composition composition –   –  those  those that met the 0.1 % uncertainty limit fell within the ranges listed in Range A of Table 1, or were slightly outside this range at the lower temperature limit with pressures slightly below the upper pressure limit. Several of the limits listed in this range have been modified from those given in Reference [5] to [5] to give better better results. The regions in Figure 1 with uncertainty uncertaint y limits of 0.3 %, 0.5 %, and 1.0 % are also based on the Range A compositions. However, it is important to make use of a phase diagram to ensure that states are not in the 2-phase or in the critical region. The DETAIL equation of state should not be used for states at pressures exceeding exceeding the dew or bubble point (including 2-phase states). This applies for Ranges B and C as well. Range B  in Table 1 shows the maximum allowable mole percent composition for temperatures above 25 °F ( –   – 4 °C), but with pressures less than 300 psia (2 MPa), heating values from 680 to 1500 Btu/scf, and relative densities from 0.47 to 0.91. Range B allows higher upper range values of the compositions for operations below 300 psia. Range C  in Table 1 has a composition range that is much smaller than the other ranges, but allows temperatures down to 17 °F ( –   – 8 °C) and pressures up to 3000 psia (21 MPa).

In this AGA 8, Part 1, document the upper pressure limit for 0.1 % uncertainty has been changed from 1750 psia to 1500 psia (12 MPa to 10.3 MPa), and the lower temperature limit has been changed from 17 °F ( –   – 8 °C) to 25 °F ( – 4 °C) based on work presented in Reference [5]. [5]. However, uncertainties in the DETAIL equation of state are often below 0.1 % far outside the ranges listed in Table 1, especially at temperatures above 40 °F. For continued use of the DETAIL equation of state outside the ranges listed in Table 1, comparisons can be made  between this and the GERG-2008 GERG-2008 equation equation of state. When the difference difference is less than than 0.1 %, %, the DETAIL equation of state can be used with a stated uncertainty of 0.1 %. The Excel application given in the supplementary material will calculate the difference between the DETAIL and GERG-2008 equations for any gaseous state. Other tools can also be used (e.g., Reference [6]) to ascertain the differences in the calculations between the two equations. When exceeding the limits of Table 1 but claiming the 0.1 % uncertainty, users should specify the method or software used to arrive at this claim.

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Table 1 –  1 –  Ranges  Ranges for Temperature, Pressure, Heating Value, and Relative Density with Uncertainties Less than 0.1 % in Compressibility Factors of  Natural Gas Gas Calculated Calculated with the the DETAIL Equation of State Lower temperature limit Upper pressure limit

Range A

Range B

Range C

25 °F  – 4 °C 1500 psia 10.3 MPa

25 °F  – 4 °C 300 psia 2.1 MPa

17 °F  °F   – 8 °C 3000 psia 21 MPa

630 to 1200 23.5 to 44.7 0.554 to 0.91

680 to 1500 25.3 to 56 0.47 to 0.91

960 to 1090 35.8 to 40.6 0.554 to 0.64

†

Gross heating value   Btu/scf MJ/m3  Relative density† 

Upper composition limits (mole percent)

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

Methane  Nitrogen Carbon dioxide Ethane Propane Isobutane n-Butane Isopentane n-Pentane

100.0 50.0 30.0‡  10.0 4.0 0.4 0.6 0.3 0.3

100.0 50.0 80.0 25.0 6.0 1.5 6.0 2.0 2.0

100.0 3.0 3.0 4.0 2.0 0.1 0.4 0.1 0.1

Total pentanes n-Hexane n-Heptane n-Octane  Nonane n- Nonane n-Decane Total hexanes plus Total heptanes plus Hydrogen Oxygen Carbon monoxide Water Hydrogen sulfide Helium Argon

0.3 0.12 0.04 0.03 0.03 0.03 0.15 0.04

2.0 0.2 0.2 0.2 0.2 0.2

0.03 0.01 0.003 0.003 0.003

5.0 0.2 1.0 0.05 0.1 0.4 0.2

100.0 1.0 10.0 1.4 4.0 5.0 3.0

1.0 0.2 1.0 0.005 0.1 0.4 0.2

Note: The above table provides component mole percent limits under the specified ranges of pressure, temperature, Btu value, and relative density for states with an uncertainty in density generally less than 0.1 %. The composition limits for different pressures, temperatures, Btu values, and relative densities outside of these ranges can be determined from the Excel spreadsheet provided in the supplementary material.  material.  †

Values are based on a methane lower limit composition of 60 mole percent. Reference conditions in U.S. customary units are (60 °F, 14.73 psia; density at 60 °F, 14.73 psia) and in SI units are (15 °C, 0.101325 MPa; density at 0 °C, 0.101325 MPa).

‡

The upper limit for the mole percent of CO 2 is reduced under the following conditio conditions: ns:  xCO2,max = 5 % when xC3 > 2 %  xCO2,max = 20 % when xN2 > 7 %  xCO2,max = 10 % when xN2 > 15 %

 xCO2,max = 10 % when xiC4 > 0.1 %

 xCO2,max = 7 % when xC3 > 1 %

 xCO2,max = 10 % when xnC4 > 0.3 %

See the discussion in Section 1.3.1 for further information.

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1.3.2 GROSS Equation of State The GROSS equation of state was developed for dry, sweet natural gas to calculate compressibility factors. The limits for this method are listed in Table 2. For some gases at the upper limits of the allowed compositions, compositions , with temperatures below 80 °F (27 °C) or at pressures above 800 psia (5.5 MPa), the uncertainty of the GROSS equation of state can exceed 0.1 %. The maximum composition limits were therefore significantly significantl y reduced from the 1994 edition of AGA 8 so as to meet the 0.1 % uncertainty level. When exceeding the bounds listed in Table 2, the procedure given at the end of Section 1.3.1 for validating the uncertainty of a particular state should  be followed. followed. Section 5 and Appendix A present information for this equation of state. Optimally, natural natur al gas property calculations from the GROSS equation require the gas composition, i.e., the mole fractions of the components in the mixture. When this information is not available, methods given in Appendix A can be used as a substitute to obtain the molar ideal gross heating value  H CH CH of the mixture of hydrocarbon components present in the natural gas along with the compositions of nitrogen and carbon dioxide in the mixture. Table 2 –  2 –  Ranges  Ranges for Temperature, Pressure, Heating Value, and Relative Density with Uncertainties Less than 0.1 % in Compressibility Factors of Natural Gas Calculated with the GROSS Equation of State Quantity

Range 1 

Range 2

Temperature Maximum pressure Relative density Gross heating value† 

25 °F to 143 °F (  –  – 4 °C to 62 °C) 1500 psia (10.3 MPa) 0.554 to 0.63  930 to 1040 Btu/scf   34.7 to 38.7 MJ/m3 

17 °F to 143 °F ( –   – 8 °C to 62 °C) 600 psia (4.1 MPa) 0.554 to 0.89  665 to 1100 Btu/scf   24.8 to 41 MJ/m3 

7  3  2  0.5  0.3  0.2  0.04  0.2 0.2 0.4 0.03

20 25 8 4 0.5 0.3 0.08 2 0.5 1 0.2

0.08 0.05 0.1

0.2 0.3 0.2

Upper composition limits (mole percent)  Nitrogen Carbon dioxide Ethane Propane Total butanes Total pentanes Hexanes plus Hydrogen‡  Oxygen‡  Carbon monoxide‡  Water ‡  ‡

Hydrogen sulfide   Helium‡  Argon‡  †

Values are based on a methane lower composition limit of 60 mole percent. Reference conditions in U.S. customary units are (60 °F, 14.73 psia; density at 60 °F, 14.73 psia) and in SI units u nits are (15 °C, 0.101325 MPa; density at 0 °C, 0.101325 MPa). ‡

The nonhydrocarbon species listed in this table (except nitrogen and CO 2) are considered here as impurities for use in the GROSS equation of state, and should be added to the equivalent equivalent hydrocarbon mole fraction as explained in Section 5.2. The SGERG-88 equation contains additional parameters parameters for hydrogen and carbon monoxide, and Reference [3], ISO 12213:3, or GERG TM 5 (1991) should shou ld be consulted when the mixture contains these fluids.

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1.4 Uncertainty The uncertainties of compressibility factors or densities (relative deviations calculated in terms of  Z  or  or in terms of d  are   are nearly identical but with an opposite sign) calculated with either the DETAIL equation of state or the GROSS equation of state depend upon the natural gas composition and the operating temperature and pressure conditions. Evaluations of the uncertainties of calculated compressibility factors for natural gas were made by comparing to the GRI and GERG compressibility factor reference databases. The reference databases have similar natural gas physical characteristics as those listed in Table 1. Comparisons were also made with data for pure fluids and binary mixtures. Lastly, comparisons were made with experimental speed-of-sound data to access derived thermodynamic property capabilities of the DETAIL equation of state. Uncertainty analyses are available in Appendix B.

1.4.1 DETAIL Equation of State Uncertainty The GRI and GERG compressibility factor reference databases and comparisons with the GERG-2008 equation of state have verified the expected uncertainties uncert ainties given in Table 1 and within Region 1 and parts of Regions 2, 3, and 4 of Figure 1. The boundaries in Table 1 can often be exceeded at lower temperatures or higher pressures than those given. The last paragraph of Section 1.3.1 explains the procedure that can be used to determine if a  particular gas or operating operating condition condition still resides wi within thin the 0.1 0.1 % uncertainty uncertainty limit. limit.

1.4.2 GROSS Equation of State Uncertainty In general, the expected uncertainty inidentified density ofinthe GROSS equation of GERG state is compressibility 0.1 % for natural gas having compositions and operating conditions Table 2. The GRI and factor reference databases and comparisons with the GERG-2008 equation of state have verified the expected uncertainties given in Table 2. The equation was not designed for and should not be used outside of these limits, unless comparisons as described in the last paragraph of Section 1.3.1 have been made.  made.  

1.5 Recommendations Two different equations for the compressibility factor, the DETAIL equation of state and the GROSS equation of state, are provided in Part 1. The choice of a particular equation of state depends on the natural gas composition and operating conditions, and the uncertainty expectation. See Part 2 for liquid phase and vaporliquid equilibrium phases, or for applications outside the uncertainty ranges given in Figure 1 and Tables 1 and 2. The GERG-2008 equation of state given in Part 2 is the most accurate in the calculation of compressibility factors and densities, alsoGROSS has the equation most complex form. equation of state is moreisaccurate the GROSS equation.butThe of state is The only DETAIL recommended when simplicity needed than for calculations of natural gas compressibility factors and densities, provided the natural gas compositions and operating conditions are within the ranges given in Table 2. Use of the GERG-2008 equation of state may be considered due to its higher accuracy and for maintaining consistency for operating conditions that may lie either within or outside the ranges in Table 1. Switching between the GERG-2008 and DETAIL equations based on the operating state will lead to discontinuities in calculated values at the point of overlap. For conditions that never exceed the ranges in Table 1, the DETAIL equation of state may be the most practical for certain applications based applications based on the the operator’s operator’s needs.  needs. 

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2 DEFINITIONS AND GENERAL EQUATIONS 2.1 Definitions of Phase Regions This AGA 8, Part 1, puts forth a new approach to define the gas phase, dense phase, and liquid phase of a mixture. Figure 2 shows the phase boundary of a natural gas mixture with about 83 % methane. The heaviest hydrocarbons are heptane with a mole percent composition of 0.027 %, octane with 0.017 %, and nonane with 0.0009 %, where these three components play the largest role in the upper temperature and pressure limits of the saturation boundaries. Although a fluid transitions smoothly from vapor to liquid without discontinuities discontinuities when the path is such that it does not cross the phase boundary, defined regions are useful to give a general indication of the fluid’s state. Most definitions of the phase regions use pressure and temperature parameters for bounding the gas, liquid, and dense regions, resulting in different parsing techniques with varying degrees of complexity depending on a group’s  point of view. view. Most of these bounding bounding techniques techniques result result in some inappropriately labeled areas, e.g., more gas-like than dense-like or vice-versa, due to the extent to which a certain bounding box extends into a temperature or  pressure space. space. As shown in Figure 2, the three phase regions are now defined in terms of the critical density only. (The critical point is the state where the co-existing liquid and vapor phases have the same density and composition.) The gas phase is the region with densities less than 50 % of the critical density. Liquids are defined as states with densities greater than 125 % of the critical density. The dense phase of a fluid is any single-phase single-phas e state between these two areas, i.e., a state with a density greater than 50 % and less than 125 % of the critical density. Other  points or curves are also shown in Figure 2, including the cricondentherm (maximum (maximum 2-phase temperature), temperature), the cricondenbar (maximum 2-phase pressure), the bubble point curve, the dew point curve, and the retrograde curve. In the dense phase region near the critical point for any pure fluid or mixture, the properties change rapidly as the state approaches the critical point. For example, for a pure fluid the isobaric heat capacity increases to infinity and the speed of sound approaches zero. For temperatures near the critical point, the area between 50 % and 125 % of the critical density represents states where property changes become more significant. There are various approaches that can be used to determine the critical density of a mixture, such as the tools available in Reference [6] that use the GERG-2008 equation of state (given in Part 2) to locate the critical  point. The use of cubic equations of state (PR, SRK, etc.), though not as accurate as the GERG-2008, will determine a state point that is in the general vicinity of the true critical point of the mixture when volume translation transla tion is applied. The simplest but least accurate approach is to use a mole fraction average of the critical volumes of the  pure fluids (the critical critical density density would then be the reciproc reciprocal al of the critical critical volume). volume). The approach taken taken depends depends on the needs of a particular application.

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Figure 2. Example of gas, liquid, and dense phase regions of a natural gas mixture.

2.2 Nomenclature The symbols used in this publication are generally specific to thermodynamics, although those specific to flow measurement have been used as a convenience to the reader. General symbols that do not refer to a specific equation of state are given below. Symbols that are specific in the equations of state are given in Sections 4 and 5. d  Dc  F  pv   M  M i  n  N P  R T V  xi   Z (T , P)  Z  b(T  b, P b)    

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Molar density (mol/dm3) Critical density (mol/dm3) Supercompressibility factor Molar mass (molecular weight) (g/mol) Molar mass of the component i in the mixture (g/mol)  Number of moles moles of a gas (mol)  Number of components components in the mixture mixture Absolute pressure (MPa) Gas constant [J/(mol∙K)] [J/(mol∙K)]   Absolute temperature (K) Gas volume (dm3) Mole fraction of component i in the mixture Compressibility Compressibili ty factor at T  and  and P  Base compressibility compressibili ty factor at T  b and P b (generally 60 °F and 14.73 psia in the U.S.) Mass density (mass per unit volume) (kg/m3)

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2.3 General Equations This section contains general equations involving the compressibility factor, molar density, and mass density of natural gas and other hydrocarbon gases. The compressibility factor Z  is  is defined by the equation

PV 

 Z    

,

(2-1)

nRT  where T  is  is the absolute temperature of the gas , P is the absolute static pressure of the gas, V  is  is the gas volume, n is the number of moles, and  R is the molar gas constant. Both the DETAIL and GROSS equations of state express the compressibility factor Z  in  in terms of the molar density d  (in  (in moles per unit volume),

d    

n V 

.

(2-2)

The gas mixture molar mass (molecular weight) M   is is calculated from the gas composition with the relation

 M  

 N 

 x M  , i

(2-3)

i

i 1

where M i is the molar mass of component i, N is the number of components in the gas mixture, and  xi is the mole fraction of component i  in the gas mixture. The summation in this equation is over all components in the gas mixture. The mass density   density    (mass  (mass per unit volume) is related to the molar density d  by  by the relation      Md  .

(2-4)

Combining Equations (2-2) Equations (2-2) and  (2-4)  (2-4) in Equation (2-1) Equation (2-1) results in the following equations for the molar density d   and the mass density   density    in  in terms of the compressibility factor:

d    

P  ZRT 

 

(2-5)

    M  P    ZRT 

(2-6)

Tabulations of the supercompressibility factor F  pv are defined by

F  pv2 

 Z  b T   b , P  b   Z T , P 

,

(2-7)

where F  pv is the supercompressibility factor expressed as the square root of the ratio of a base compressibility factor to the operating compressibility factor. The operating compressibility compressibil ity factor Z (T , P) is calculated at the measured operating pressure and temperature. The base compressibility factor Z  b is defined by the base conditions specified in the custody transfer agreement. Base conditions may be specified by regulation, contract, local conditions, or organizational organization al needs. In the United States, for inter-state custody transfer of natural gas, they are considered to be 60 °F and 14.73 psia. 10  --```,,````,,,`,``,,``,`,,`,,-`-`,,`,,`,`,,`---

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3 UNITS, CONVERSIONS, CONVERSIONS, PRECISION, AND ACCU ACCURACY RACY The computer program subroutines provided in the supplementary material to this document use SI units. The subroutines use the following units for the principal dimensional quantities: absolute temperature in kelvins (K), pressure in kilopascals (kPa), molar density in moles per cubic decimeter (mol/dm 3), real gas volumetric heating value in megajoules per cubic meter (MJ/m 3), and molar ideal gross heating value in kilojoules  per mole (kJ/mol). Conversion Conversion factors are required for conversions to and from other units. Some common conversion factors are given in Table 3. Because the DETAIL and GROSS equations were developed prior to 1990, temperatures are not based on the ITS-90 temperature scale, but on the older IPTS-68 temperature scale. Except for the mass and mole conversions (where exact conversions are given), the values given in Table 3 are identical to those in API Chapter 15, Guidelines for Use of the International System of Units (SI) in the Petroleum and Allied Industries, and ASTM-SI10,  American National Standard for Metric Practice  (which rounded the conversion factors to seven significant digits). Most calculations in this report are not accurate to more than seven significant digits; thus, the accuracy of computed compressibility factors is not improved by the use of more significant digits. For example, a calculation precision of five significant digits is approximately 1 part in 100,000 (or 10 ppm) for the compressibility factor. Appendix B presents information showing that the expected uncertainties of computed natural gas compressibility factors are 0.048 % (one standard deviation) for both the DETAIL equation of state and the GROSS equation of state. The uncertainty of 0.048 % corresponds to 48 parts in 100,000 (or 480 ppm), so the calculation precision precision of 1 part in 100,000 is an order of magnitude better better than the uncertainty in the computed compressibility factor. The computed compressibility factors in the region of validity for each equation of state generally agree with the best available compressibility factor data for natural gas with differences approaching approachin g the experimental uncertainty of 0.1 %. Thus, for compressibility factors less than one, calculated values are at best accurate to about one part in 10,000 (or 100 ppm), or to about four significant digits. When more than four significant digits are quoted in this document, the purpose is generally for computer program verification only. Table 3 –  3 –  Unit   Unit Conversions Quantity

Unit conversion 

Length Mass Moles Temperature Temperature Temperature Pressure

1.0 in = 0.0254 m (exact)  1.0 lbm = 0.453 592 37 kg (exact)   1.0 lbmol = 0.453 592 37 kmol (exact)  Temperature (in °R) = Temperature (in °F) + 459.67 (exact)  Temperature (in K) = Temperature (in °C) + 273.15 (exact)  1.8 °R = 1.0 K (exact)  1.0 psia = 0.006 894 757 MPa 

Pressure Gas constant Gas constant Energy

1.0 bar = 0.1 MPa (exact)  10.73164 psia psia∙∙ft3/(lbmol /(lbmol∙∙R) = 8.31451 J/(mol∙ J/(mol∙K)†  1.985886 Btu/(lbmol Btu/(lbmol∙∙R) = 8.31451 J/(mol∙ J/(mol ∙K)†  ‡ 1.0 Btu = 1.055056 kJ  

†

For the gas constant, the values given do not represent the most current scientific values, but are used here to conform with the 1994 edition of AGA 8 so that calculated property values match those from the original equations. ‡ Corresponds to the IT value of 1 cal = 4.1868 J.

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4 THEMODYNAMIC PROPERTIES FROM THE DETAIL EQUATION OF STATE 4.1 Nomenclature Constants and coefficients coefficients (Tables 4 and 7) an, bn, cn, f n, gn, k n, qn, un, sn, wn  Coefficients and parameters in the equation of state n, ϑ  Coefficients of the ideal-gas heat capacity equation Component parameters (Table 5)  E i  Characteristic energy parameters F i  High temperature parameters Gi  Orientation parameters K i  Size parameters Qi  Quadrupole parameters S i  Dipole parameters W i  Association parameters Mixture parameters parameters (Table 6 for ij parameters) *  B nij  Binary characterization parameters * C  n  Parameters that are functions of composition  E iijj  Second virial coefficient energy binary interaction parameters F Mixture high temperature parameters G Gij  K K iijj  Q U U iijj 

Orientation parameters Binary interaction parameters for orientation Size parameters Binary interaction parameters for size Quadrupole parameters Mixture energy parameters Binary interaction parameters for conformal energy

Properties a  a0 ar  B c p0  c p  cv  d  D g  h      N P  R s  T u  w 

Molar Helmholtz energy (J/mol)   Molar ideal-gas Helmholtz energy (J/mol)  Molar residual Helmholtz energy (J/mol)  Second virial density coefficient (dm3/mol) Molar ideal-gas isobaric heat capacity [J/(mol∙K)] [J/(mol∙K)]   Molar isobaric heat capacity [J/(mol∙K)] [J/(mol∙K)]   Molar isochoric heat capacity [J/(mol∙K)] [J/(mol∙K)]   3 Molar density (mol/dm ) Reduced density of gas Molar Gibbs energy (J/mol) Molar enthalpy (J/mol) Isentropic exponent  Number of components components in the mixture mixture Absolute pressure (MPa) Gas constant [J/(mol∙K )] )] Molar entropy [J/(mol∙K)] [J/(mol∙K)]   Absolute temperature (K) Molar energy (J/mol) Speed of sound (m/s)

 xi   Z

Mole fraction of factor component i in the mixture (mol) Compressibility 12 

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4.2 DETAIL Equation of State for Thermodynamic Properties Including Compressibility Factor and Pressure In the DETAIL equation of state, a natural gas is characterized by its composition, that is, the mole fractions or mole percentages of the components in the natural gas. The equations, constants, and parameters needed to calculate thermodynamic properties for natural gas mixtures with the DETAIL equation of state are given here. Procedures to apply the DETAIL equation of state and the available programs are provided in the supplementary supplementar y material material accompanying this document. An uncertainty discussion is given in Appendix B. The equation of state used in this method is a hybrid formulation based on the work of Starling et al., Reference [1]. [1]. It combines features of the virial equation of state (a power series in density) for low-density conditions and exponential functions for applications at high-density conditions (extended Benedict-Webb-Rubin equation of state). This formulation provides high accuracy, a broad temperature-pressure-composition application range, and derived thermodynamic property capabilities. A detailed description of the performance of the equation is available in Reference [2]. [2]. The equation of state for the compressibility factor Z  for  for the DETAIL method is given by the equation 18

58

 C T 

 Z   1  Bd  D

* n

k    C n*T u bn  cn k n D k   Db ex exp p  cn D  ,

un

n

n 13

n

n

(4-1)

n

n13

where d  is  is the molar density of the gas, B is the second virial coefficient, D is the reduced density, C n* are parameters that are functions of composition, and un, bn, cn, and k n are coefficients and parameters given in Table 4. The units for temperature and molar density are kelvins and moles per ccubic ubic decimeter. The reduced density D is related to the molar density d  by  by the equation

 D    K 3d ,

(4-2)

where K   is the mixture size parameter. Converting the expression for the compressibility factor of the gas to  pressure results results in the equation 18 58  k  b k   u * u exp p  cn D  . P  dRT 1  Bd   D  C nT    C n*T  bn  cn k n D  D ex  n13  n13 n

n

n

n

n

(4-3)

In the computation of Z   or P through the use of the DETAIL equation of state, the composition of the gas, the absolute temperature T , and the molar density d  are  are required. When the temperature, pressure, and composition of a gas are known, the only unknown quantity in this equation is the molar density d . The density can be determined with appropriate iterative procedures, as explained in Section 6. Before computations can be performed with the equations above, the values of  B, C n*, and K   must be calculated from the composition composition and temperature of the gas. The mixture size parameter K  for   for a mixture of  N   components is 2

 N 1  N     N     K     xi K i   2   xi x j K ij5  1K i K  j  , i 1  j  i 1  i 1  

5

5

2

 

5

2

(4-4)

where the K iijj are binary interaction parameters for size (Table 6), K i and K  j are size parameters for components i and j (Table 5), and xi and x j are mole fractions of components i and j in the gas mixture.

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The subscript i refers to component i in the gas mixture and the subscript  j refers to component  j in the mixture. In the single sum, i  ranges over the integer values from 1 to  N . For example, for a mixture of 12 components ( N =12), =12), there would be 12 terms in the single sum. In the double sum, i ranges from 1 to N   – 1 and each value of  j ranges from i+1 to  N . For example, for a mixture of 12 components, there would be 66 terms in the double sum when all values of K iijj differ from one. However, because many of the values of K ijij are one, the number of nonzero terms in the double sum is small for many natural gas mixtures. All values of K ijij are one except for the values listed in Table 6. The second virial coefficient B is given by the following equations:

 B 

18

 a T 

un

n

 B* , with

(4-5)

n 1

 B  *

 

 N 



un

2 i

 N 1  N 

3 i

* nii

 x  E i K  B

 2  

i 1

 xi x  j  E ij  E i E  j

 

    Q Q S S   1  s  W W   1  w  gn

i

sn

i

    K  K   1

2

un

3

i

 j

2

* Bnij  

(4-6)

i 1  j i 1

 Bnij  Gij Gi  G j / 2  1  g n *

 

  

 j

 j

 1  qn q F i F  j  1   f n  f  n

n

w   n

n

i

 j

 

(4-7)

n

Equations (4-1) and  (4-3)  (4-3) are The coefficients C n* (n=13 to 58) in Equations (4-1)

 

C n*  an G  1  g n   n  Q   2   1  qn g

   F  1   f   qn  

n

 f n

un   . U 

(4-8)

The parameters in these equations are defined in the nomenclature. The constants an,  f n, gn, qn, sn, un, and wn are given in Table 4. The mixture parameters F , G, Q, and U  are  are calculated with the following equations, where in the double sums i ranges from 1 to N  – 1, 1, and each value of j ranges from i+1 to N : 2

 N 1  N     N     5 U     xi E i   2   xi x j U ij  1 E i E  j  i 1  j i 1   i1   5

5

G

 N 

 



 xi Gi 

i 1

Q

 

2

 N 1  N 

  x x  G i

 j

ij

5

2

 1Gi  G j 

(4-9)

(4-10)

i 1  j i 1

 N 

 x Q   i

(4-11)

i

i 1

F  

 N 

 x  F    2 i

(4-12)

i

i 1

Values of  E i, F i, Gi, K i, Qi, S i, and W i are given in Table 5. The binary interaction parameters  E ijij, Gij, K ijij, and U ijij  are given in Table 6. All values of the binary interaction parameters  E ijij, Gij, K ijij, and U ijij are one except for the values in Table 6.

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4.3 Equation of State for the Helmholtz Energy The Helmholtz energy a of a mixture is the sum of two contributions contribution s (see References [7,8]), [7,8]), one accounting 0 r  for that of the ideal gas a  and the other for that of the real fluid a ,

a   a 0  a r  .

(4-13)

The equation for the ideal-gas Helmholtz energy is a

0

 RT 

ln x i   nio,1  n    io, 2 / T   nio,3  1ln  T    d     N     ln     x i o o o o       n T  n T      l n sinh / l n cosh /    i, k  i , k  i , k  i , k   d 0   i 1  k k  5, 7   4, 6 

(4-14)

The coefficients are given in Table 7, and the derivation of this equation is given further below. The value of the molar density d  is  is given in mol/dm3, and that of T   is is given in kelvins. kelvins. The real gas contribution contributio n is

a r   RT 

18

 Bd  D  C  T  * n

n 13

u n

58

exp p  cn D k  ,   C n*T u  D b ex n

n

n

(4-15)

n 13

where a is the molar Helmholtz energy and the superscript r indicates a residual property, or the contribution from the interaction of molecules in a non-ideal gas. All other symbols were defined under Equation Equation (4-1).  (4-1). This  This equation results from the integration of Equation  Equation  (1-1) with the pressure taken from Equation (4-3),  (4-3),  and is the original formulation used in the development of AGA 8. The equation for the ideal-gas Helmholtz energy [given in Equation (4-14)] Equation  (4-14)] was  was obtained through the use of thermodynamic relationships. The contribution to the ideal gas can be expressed as a summation involving the ideal-gas enthalpy h0 and entropy s0,

a 0  h 0   RT   Ts 0 .

(4-16)

When an expression for the ideal-gas heat capacity  c p0 is available, the ideal-gas enthalpy can be derived from the relation 0  p

c

 h0   ,     T   p

(4-17)

        `         -

resulting in  

h  h0  0

0

T 



T 0

0

c  p d    T ,

(4-18)

where the enthalpy at T 0  is h00. (The value of T 0  is not necessarily set to zero, but can be any arbitrary value, resulting in the integration constant h00.) Likewise, the ideal-gas entropy can be derived from a fundamental relationship (see Reference [7]), resulting in

s

0

T 

 s  T  0 0

0

  Td     N    R xi ln xi  , d T   R ln T  T  d    0 0  i1 0

c p

(4-19)

where d 0 is the ideal-gas density at T 0 and P0 (d 0 = P0/T 0 R), and T 0 and P0 are arbitrary reference conditions. The molar gas constant R is 8.31451 J/(mol∙K) (as given in the 1994 revision revision of AGA Report Report No. 8). The last part of 15  Copyright American Gas Association

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this term, summed over the number of components N  in   in the mixture, accounts for the ideal-gas entropy of mixing of the components components in the gas. Combining these equations results in the following expression for the Helmholtz energy of the ideal gas  N    Td      RT  xi lnxi  . a  h   c d T   RT   Ts  T  d T    RT ln T  T  T  T  d  i 1   0 0  

0

0 0

T 

0 0

0   p

0

0 T   p

c

(4-20)

0

The reference state of zero enthalpy and zero entropy is here adopted at T 0 = 298.15 K and P0 = 0.101325 MPa for the ideal unmixed gas [i.e. , no entropy of mixing (the and last Schley term in (see this equation equatio n is[9]), set),togiven zero)]. taken from Jaeschke Reference [9] as Expressions for the ideal-gas heat capacity c p0 were 2 2 o o         T    T  / / i , k  i , k  o o o   xi ni ,3   ni , k   .    ni ,k  o o  R i 1    T    T      sinh / cosh / k  4, 6 i , k  i , k      k  5,7       

c po

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

 N 

(4-21)

The coefficients and parameters are given in Table 7. The equation for the ideal-gas isobaric heat capacity is taken o from [9] and given as a function of the temperature T . The values of the parameters parameters k   (for k  =   = 4 to 7) are in o o o o o agreement with the original parameters  D , F , H ,  and  J   in reference [9], and the values of nk  (for   (for k  =  = 3 to 7) are o o o o o identical to the coefficients  B , C  , E  , G ,  and  I  . Integrating Integratin g Equation (4-21) Equation  (4-21) and combining the outcome with Equation (4-20) Equation  (4-20) results in the ideal-gas Helmholtz energy given in Equation Equation (4-14).  (4-14).  

4.4 Speed of Sound and Other Thermodynamic Properties The AGA Report No. 10, Speed of Sound in Natural Gas and Other Related Hydrocarbon Gases , on the calculation of speeds of sound from the DETAIL equation of state, obtained values through numerical integration of the compressibility factor equation. The equations presented here for the calculation of thermodynamic  properties are implemented implemented through differentiation differentiation of the fundamental fundamental Helm Helmholtz holtz energy energy equation. equation. This results results in faster calculations through direct computation of the required derivatives and is more precise since finite differences are not required. The equations used for calculating compressibility factor, pressure, and the derivatives of pressure with respect to density and temperature are given in the following equations:

 Z  

P dRT 

1

a P  d 2        d  T 

d   a r  



  

(4-22)

 RT   d  T 

r   a      dRT   d 2      d  T 

(4-23)

2 r   a r    P  2   a     d   2       RT   2d   d     d  T     T    d   T 

(4-24)

3 r    2 P   a r     2a r   2   a    2   2   4d  2   d   3      d  d     d   T     T     T    d   T 

(4-25)

2 r   P  2    a         dR d   d  T     T   d     

(4-26)

The equations for calculating entropy s, energy u, enthalpy h, Gibbs energy g, isochoric heat capacity cv, isobaric heat capacity c p, speed of sound w, Joule-Thomson coefficient  , and the isentropic exponent   are  are given 16  Copyright American Gas Association

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 below. Additional equations for other properties and alternativ alternativee methods for expressing Helmholtz energy equations are given in Lemmon et al. (see Reference [7]). [7]).

 a 0    a r    a         s        T    T   T   d      d      d 

(4-27)

u   a  Ts  

(4-28)

h   u 

P

g   a 

P

d 

d 

 

(4-29)

 

(4-30)

  2 a 0    2 a r      2 a  s   u      cv     T    T  2   T  2    2      T   d   T   d   T    d    T    d    T    d  

(4-31)

2

    2 a r      R  d  2 1 d T  c p  cv  T 2   P    T   P   cv  T      2 r    d      d   d  T   a r     a     d 2  2    RT  2d    d  T    d   T    1000 c p  P  1000 c p w      Mcv  d   T   Mcv 2

2 r     a r   2   a        RT  d  d  2     d    2      T    d   T   

1    1  T   P   P     1        c p d   d    T   d   d  T  

(4-32)

(4-33)

(4-34)

2 `  `  `    ,   , `  `  `  `    ,   ,   , `    , `  `    ,   , `  `    , `    ,   , `    ,   , `  `    ,   , `    ,   , `    , `    ,   , `  -

   w  M     ZRT 

(4-35)

The following nomenclature is used to simplify the appearance of the derivative equations:   *   u n  n  C    nT 

(4-36)

 n  C n *T un D  bn ex exp p   cn Dk n   

(4-37)

 n  c  n k n D n  

(4-38)

    bn    n     n 

(4-39)

 i,  k     io, k  / T  

(4-40)

k 

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The derivatives of the Helmholtz energy required in the equations for calculating thermodynamic properties are given below.

ln xi   nio,1  n  io,2 / T   nio,3  1ln  T     d   a     ln    xi o o     n n ln sinh ln cosh        RT   i,k  i , k  i , k  i , k    d 0   i 1  k k  5, 7   4,6 

(4-41)

   ln xi   n io,1  nio,3  11   lnT    0  N    d   1 a    ln    xi   nio, k ln sinh i , k     i, k  / tanh i , k      R T   d 0  i 1  k  4,6   no ln cosh      tanh    i , k  i , k  i , k  i , k    k   5, 7

(4-42)

2 2  o o o    1   / sinh        / cosh     x n n       n          i , k  i , k  i , k  i , k  i , k  i , k  i  i ,3  R T 2 k  k  i 1  4 , 6    5 , 7  

(4-43)

0

 N 

T   2 a 0

a r   RT 

 N 

18

58

 Bd  D  n   n   n 13

d  a r   RT  d 

 RT  d 2 d 3 3a r   3

1 a r   R T 

18

58

n 13

n 13

 Bd  D   n    n  n

2 2 r  d   a  

 RT  d 

n 13

 

 

(4-44)



 

(4-45)

58

        1  k       n

n

n

n

(4-46)

  n

n 13

58

    n  2  n   n  1   k n n   k  n n 1  k n  2  n  n  

(4-47)

n 13

 Bd  Td 

58  B   18  D  un  1 n    un  1 n T  n 13 n 13

 

(4-48)

18 58  2 B   B 2  2Td   T  d  2  D  un un  1   n   un un  1 n T  T   R T 2 n 13 n 13

T   a 2

r 

d   2 a r 

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

18 58  B     un  1bn   n  n  Bd  Td   D  un  1 n    R d T  T  n 13 n 13

 B 18 T     u n anT u  B*   T  n1 T 

 2 B 18   un un  1 anT     u 2 T  n 1

n

*

B  

(4-50)

(4-52)

18  Copyright American Gas Association

 

(4-49)

(4-51)

n

2

 

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Table 4 –  4 –   DETAIL DETAIL Equation of State Coefficients and Parameters

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

n 1 2 3 4 5 6 7 8

an  0.1538326 1.341953 −2.998583   −2.998583 −0.04831228   −0.04831228 0.3757965 −1.589575   −1.589575 −0.05358847   −0.05358847 0.88659463

bn  1 1 1 1 1 1 1 1

cn  0 0 0 0 0 0 0 0

k n  0 0 0 0 0 0 0 0

un  0.0 0.5 1.0 3.5 −0.5   −0.5 4.5 0.5 7.5

gn  0 0 0 0 1 1 0 0

qn  0 0 0 0 0 0 1 0

 f n  0 0 0 0 0 0 0 0

sn  0 0 0 0 0 0 0 1

wn  0 0 0 0 0 0 0 0

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

−0.71023704   −0.71023704 −1.471722  −1.471722  1.32185035 −0.78665925   −0.78665925 2.291290×10−9  0.1576724 −0.4363864   −0.4363864 −0.04408159   −0.04408159 −0.003433888   −0.003433888 0.03205905 0.02487355 0.07332279 −0.001600573   −0.001600573 0.6424706 −0.4162601   −0.4162601 −0.06689957   −0.06689957 0.2791795

1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2

0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1

0 0 0 0 3 2 2 2 4 4 0 0 2 2 2 4 4

9.5 6.0 12.0 12.5 −6.0   −6.0 2.0 3.0 2.0 2.0 11.0 −0.5   −0.5 0.5 0.0 4.0 6.0 21.0 23.0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

−0.6966051  −0.6966051  −0.002860589   −0.002860589 −0.008098836   −0.008098836 3.150547 0.007224479 −0.7057529   −0.7057529 0.5349792 −0.07931491   −0.07931491 −1.418465   −1.418465 −5.99905×10−17  0.1058402 0.03431729 −0.007022847   −0.007022847 0.02495587 0.04296818 0.7465453 −0.2919613   −0.2919613

2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4

1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1

4 4 0 1 1 2 2 3 3 4 4 4 0 0 2 2 2

22.0 −1.0  −1.0  −0.5   −0.5 7.0 −1.0   −1.0 6.0 4.0 1.0 9.0 −13.0   −13.0 21.0 8.0 −0.5   −0.5 0.0 2.0 7.0 9.0

0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0

1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1

0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

7.294616 −9.936757  −9.936757  −0.005399808   −0.005399808 −0.2432567   −0.2432567 0.04987016 0.003733797 1.874951 0.002168144 −0.6587164   −0.6587164 0.000205518 0.009776195 −0.02048708   −0.02048708 0.01557322 0.006862415 −0.001226752   −0.001226752 0.002850908

4 4 5 5 5 5 5 6 6 7 7 8 8 8 9 9

1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1

4 4 0 2 2 4 4 0 2 0 2 1 2 2 2 2

22.0 23.0 1.0 9.0 3.0 8.0 23.0 1.5 5.0 −0.5   −0.5 4.0 7.0 3.0 0.0 1.0 0.0

0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0

0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Table 5 –  5 –   DETAIL DETAIL Equation of State Characterization Parameters i

Compound

Molar mass†   M i  (g/mol)

Energy  parameter  E i  (K)‡ 

Size  parameter K i  (m3/kmol)1/3 

Orientation Quadrupole High temp. Dipole  parameter  parameter  parameter  param. Gi  Qi  F i  S i 

Association  parameter

W i 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Methane Nitrogen Carbon dioxide Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane n-Heptane n-Octane n- Nonane  Nonane n-Decane Hydrogen Oxygen Carbon monoxide Water

16.043 28.0135 44.01 30.07 44.097 58.123 58.123 72.15 72.15 86.177 100.204 114.231 128.258 142.285 2.0159 31.9988 28.01 18.0153

151.3183 99.73778 241.9606 244.1667 298.1183 324.0689 337.6389 365.5999 370.6823 402.636293 427.72263 450.325022 470.840891 489.558373 26.95794 122.7667 105.5348 514.0156

0.4619255 0.4479153 0.4557489 0.5279209 0.583749 0.6406937 0.6341423 0.6738577 0.6798307 0.7175118 0.7525189 0.784955 0.8152731 0.8437826 0.3514916 0.4186954 0.4533894 0.3825868

0. 0.027815 0.189065 0.0793 0.141239 0.256692 0.281835 0.332267 0.366911 0.289731 0.337542 0.383381 0.427354 0.469659 0.034369 0.021 0.038953 0.3325

0. 0. 0.69 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.06775

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.5822

0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.

19 20 21

Hydrogen sulfide Helium Argon

34.082 4.0026 39.948

296.355 2.610111 119.6299

0.4618263 0.3589888 0.4216551

0.0885 0. 0.

0.633276 0. 0.

0. 0. 0.

0.39 0. 0.

0. 0. 0.

†

These are not the current internationally accepted values of the molar masses, but are identical to those reported in the 1994 edition of AGA 8 to maintain consistency. For other properties not related to the DETAIL or GROSS equations of stat state, e, the molar masses in AGA 5 or GPA 2145 should be used. ‡ The nomenclature "(K)" in the energy parameter column refers to the kelvin temperature unit of the values in the column, not to the variable used for the size parameter.

Table 6 –  6 –   DETAIL DETAIL Equation of State Binary Interaction Parameter Values† 

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

i

j

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19

Component pair Methane

Nitrogen Carbon dioxide Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane n-Heptane n-Octane n- Nonane  Nonane n-Decane Hydrogen Carbon monoxide Water Hydrogen sulfide

 E ijij 

U ijij 

K ijij 

Gij 

0.97164 0.960644

0.886106 0.963827

1.00363 0.995933

0.807653

0.994635 1.01953 0.989844 1.00235 0.999268 1.107274 0.88088 0.880973 0.881067 0.881161 1.17052 0.990126 0.708218 0.931484

0.990877

1.007619

0.992291

0.997596

1.00367 1.302576 1.191904 1.205769 1.219634 1.233498 1.15639

1.002529 0.982962 0.983565 0.982707 0.981849 0.980991 1.02326

0.736833

1.00008

20  Copyright American Gas Association

1.95731

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Table 6 –  6 –  continued   continued Component pair

 E ijij 

U ijij 

K ijij 

Gij 

Carbon dioxide Ethane Propane i-Butane n-Butane i-Pentane n-Pentane Hydrogen Oxygen Carbon monoxide Water Hydrogen sulfide

1.02274 0.97012 0.945939 0.946914 0.973384 0.95934 0.94552 1.08632 1.021 1.00571 0.746954 0.902271

0.835058 0.816431 0.915502

0.982361 1.00796

0.982746

Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane n-Heptane n-Octane

0.925053 0.960237 0.906849 0.897362 0.726255 0.859764 0.855134 0.831229 0.80831

n- Nonane  Nonane n-Decane Hydrogen Carbon monoxide Water Hydrogen sulfide

0.786323 0.765171 1.28179 1.5 0.849408 0.955052

Propane i-Butane n-Butane i-Pentane n-Pentane Hydrogen Water Hydrogen sulfide

1.02256

1.00532 1.16446 0.693168 0.946871

Propane

n-Butane

1.0049

i-Butane n-Butane n-Hexane n-Heptane n-Octane  Nonane n- Nonane n-Decane Hydrogen

Hydrogen Hydrogen Hydrogen Hydrogen sulfide Hydrogen sulfide Hydrogen sulfide Hydrogen sulfide Hydrogen sulfide Carbon monoxide

1.034787 1.3 1.3 1.008692 1.010126 1.011501 1.012821 1.014089 1.1

i

j

2 2 2 2 2 2 2 2 2 2 2 2

3 4 5 6 7 8 9 15 16 17 18 19

Nitrogen

3 3 3 3 3 3 3 3 3

4 5 6 7 8 9 10 11 12

Carbon dioxide

3 3 3 3 3 3

13 14 15 17 18 19

4 4 4 4 4 4 4 4

5 6 7 8 9 15 18 19

Ethane

5

7

5 6 7 10 11 12 13 14 15

15 15 15 19 19 19 19 19 17

1.01306

†

0.993556

0.408838

1.03227

0.993476

0.942596

0.96987

1.00851

1.066638 1.077634 1.088178

0.910183 0.895362 0.881152

1.098291 1.108021

0.86752 0.854406

0.370296

0.9 1.67309 1.04529

1.00779

1.065173 1.25 1.25 1.25 1.25 1.61666

0.986893

1.02034

0.971926

0.999969

1.028973 1.033754 1.038338 1.042735 1.046966

0.96813 0.96287 0.957828 0.952441 0.948338

alll binary Values for the j,i pair are equal to the i j  ,j pair, that is, E  ji = E ijij, U  ji =U ijij, K  ji =K ijij, and G ji =Gij. Values of 1.0 should be used for al interaction parameters except for the entries in this table.

21  Copyright American Gas Association

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

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Table 7 –  7 –  Coefficients  Coefficients and Parameters of the Ideal-gas Heat Capacity Equations Compound Methane  Nitrogen Carbon dioxide Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane n-Heptane n-Octane n- Nonane  Nonane n-Decane Hydrogen Oxygen Carbon monoxide Water Hydrogen sulfide Helium Argon

o

n1 

29.83843397 17.56770785 20.65844696 36.73005938 44.70909619 34.30180349 36.53237783 43.17218626 42.67837089 46.99717188 52.07631631 57.25830934 62.09646901 65.93909154 13.07520288 16.8017173 17.45786899 21.57882705 21.5830944 10.04639507 10.04639507 o

 4  Methane  Nitrogen Carbon dioxide Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane n-Heptane n-Octane n- Nonane  Nonane n-Decane Hydrogen Oxygen Carbon monoxide Water Hydrogen sulfide Helium Argon

820.659 662.738 919.306 559.314 479.856 438.270 468.270 292.503 178.670 182.326 169.789 158.922 156.854 164.947 228.734 2235.71 1550.45 268.795 1833.63 0. 0.

o

n2 

15999.69151  – 15999.69151 2801.729072  – 2801.729072 4902.171516  – 4902.171516 23639.65301  – 23639.65301 31236.63551  – 31236.63551 38525.50276  – 38525.50276 38957.80933  – 38957.80933  – 51198.30946 51198.30946 45215.83  – 45215.83 52746.83318  – 52746.83318 57104.81056  – 57104.81056 60546.76385  – 60546.76385 66600.12837  – 66600.12837 74131.45483  – 74131.45483 5836.943696  – 5836.943696 2318.32269  – 2318.32269 2635.244116  – 2635.244116 7766.733078  – 7766.733078 6069.035869  – 6069.035869 745.37500  – 745.37500 745.37500  – 745.37500 o

 5  178.410 680.562 865.070 223.284 200.893 198.018 183.636 910.237 840.538 859.207 836.195 815.064 814.882 836.264 326.843 1116.69 704.525 1141.41 847.181 0. 0.

o

n3 

4.00088 3.50031 3.50002 4.00263 4.02939 4.06714 4.33944 4. 4. 4. 4. 4. 4. 4. 2.47906 3.50146 3.50055 4.00392 4. 2.5 2.5 o

 6  1062.82 1740.06 483.553 1031.38 955.312 1905.02 1914.10 1919.37 1774.25 1826.59 1760.46 1693.07 1693.79 1750.24 1651.71 0. 0. 2507.37 0. 0. 0.

22  --```,,````,,,`,``,,``,`,,`,,-`-`,,`,,`,`,,`---

Copyright American Gas Association

o

n4 

0.76315 0.13732 2.04452 4.33939 6.60569 8.97575 9.44893 11.7618 8.95043 11.6977 13.7266 15.6865 18.0241 21.0069 0.9580 0.95806 6 1.07558 1.02865 0.01059 3.11942 0 0 o

 7  1090.53 0. 341.109 1071.29 1027.29 893.765 903.185 0. 0. 0. 0. 0. 0. 0. 1671.69 0. 0. 0. 0. 0. 0.

o

n5 

0.00460 0.14660  – 0.14660 1.06044  – 1.06044 1.23722 3.19700 5.25156 6.89406 20.1101 21.8360 26.8142 30.4707 33.8029 38.1235 43.4931 0.45444 1.01334 0.00493 0.98763 1.00243 0. 0.

o

o

n6 

n7 

8.74432 0.90066 2.03366 13.1974 19.1921 25.1423 24.4618 33.1688 33.4032 38.6164 43.5561 48.1731 53.3415 58.3657 1.56039 0. 0. 3.06904 0. 0. 0.

4.46921  – 4.46921 0. 0.01393 6.01989  – 6.01989 8.37267  – 8.37267 16.1388 14.7824 0. 0. 0. 0. 0. 0. 0. 1.3756  – 1.3756 0. 0. 0. 0. 0. 0.

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5 THERMODYNAMIC PROPERTIES FROM THE GROSS EQUATION OF STATE 5.1 Nomenclature Binary interaction coefficients  BCH-CH, BCH-N2, BCH-CO2 , B N2-N2, B N2-CO2, BCO2-CO2, Bij  Ternary interaction coefficients C CH-CH-CH, C CH-CH-N2 , C CH-CH-CO2 , C CH-N2-N2, C CH-CO2-CO2 , C CH-N2-CO2, C  N2-N2-N2, C  N2-N2-CO2, C  N2-CO2-CO2, C CO2-CO2-CO2 CO2-CO2-CO2, C ijk  ijk  

Coefficients  Bmix  C m mix ix   B0, B1, B2  C 0, C 1, C 2  b0, b1, b2, c0, c1, c2  bi0, bi1, bi2, ci0, ci1, ci2 

Second virial coefficien coefficientt of the mixture (dm3/mol) Third virial coefficie coefficient nt of the mixture (dm6/mol2) Coefficients in the second virial equation for the CH-CH interaction Coefficients in the third virial equation for the CH-CH interaction Constants in Table 8 Constants in Table 9

Properties d    H CH CH 

Molar density (mol/dm3) Molar ideal gross heating value of the equivale equivalent nt hydrocarbon (kJ/mol) at 25 °C

 HN oi   N   P   R  T    xCH   x N2   xCO2   xi, x j, xk    Z  

Molar ideal gross heating value of component i (kJ/mol) at 25 °C Number of components in the mixture Absolute pressure (MPa) Gas constant [J/(mol∙K)] [J/(mol∙K)]   Absolute temperature temperature (K) Mole fraction of the equivalent hydrocarbon hydrocarbo n Mole fraction of nitrogen Mole fraction of carbon dioxide Mole fractions of components i, j, and k  in  in the mixture Compressibility Compressibili ty factor

5.2 Equation of State for Compressibility Factor The GROSS equation of state approximates a natural gas mixture by treating it as a mixture of three components: an equivalent hydrocarbon component (i.e., a pseudo-hydrocarbon component), nitrogen, and carbon dioxide. The equivalent hydrocarbon CH is used to collectively represent all the hydrocarbons found in the gas mixture. Nitrogen and carbon dioxide are the diluent components. The GROSS equation of state allows for the characterization of a natural gas by a number of different methods. These methods include knowledge of the heating value, relative density, or mole fractions of the components in the mixture. Two methods were available in the 1994 edition of AGA 8, labeled as Method 1 and Method 2. Two additional methods have been added in this document to allow direct calculations from the GROSS equation of state without the need for the iterative procedures required by Methods 1 and 2. These new methods are labeled as Method 0 and Method 3. A description of each method and the required inputs are given below.

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

23 

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Method 0 Inputs: Mole fractions fractions of the components in the mixture. mixture. Method 0 allows for the direct calculation of the equivalent hydrocarbon heating value [ H CH CH shown in Equation (5-9)] Equation (5-9)]   from composition. compositio n. No iterative procedure is required to set up the method. (This is the method that was used in the development of the GROSS equation of state, which was subsequently published in 1990, see Reference [3]). [3]). The second and third virial coefficients are calculated directly from H CH CH and the compositions of nitrogen and carbon dioxide. With the virial coefficients, pressure and compressibility factor can be calculated as a function of density and

temperature. of pressure temperature, themethod procedure described in Section Section 6 can be used to obtainFor theinputs density. Methodand 0 is the preferred when a composition analysis is available, and the DETAIL method cannot be used. Method 1 Inputs: Volumetric heating value of the mixture, relative density (specific gravity), and the mole fraction of carbon dioxide. Method 1 requires an iterative procedure that determines the molar heating value of the equivalent hydrocarbon H CH inputs to this method. The iterative CH and the mole fraction of nitrogen from the inputs method is given in Appendix A. Once  H CH CH  and  x N2  have been determined, pressures and compressibility factors are calculated as done in Method 0. Reference conditions must be specified for the relative density and volumetric heating value. Method 2

Inputs: Relative density and mole fractions of determines nitrogen andthe carbon Method 2 requires an iterative procedure that molardioxide. heating value of the equivalent hydrocarbon H CH CH. The iterative method is given in Appendix A. Once H CH CH has been determined,  pressures and compressibility factors are calculated calculated as done in Method 0. Reference conditions conditions must be specified for the relative density. Method 3 Inputs: Molar mass of the mixture and mole fractions of nitrogen and carbon dioxide. Method 3 is similar to Method 0 except that the molar mass of the mixture is used as an input, and the molar heating value of the equivalent hydrocarbon  H CH CH  is determined from the molar mass through Equation (A-16), Equation (A-16), as  as explained in Appendix A. No iterative procedure is required to set up the method, no reference state is needed, and all subsequent calculations are done as in Method 0. The T he constants G1 and G2 in Equation (A-16) Equation (A-16) were determined in Reference [3] through [3] through a fit of heating values as a function of molar mass, and properties are slightly less accurate than

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

those obtained with Method Method 0 through the use of a gas analysis. This method is useful for GROSS equation of state applications where network bandwidth restrictions might prohibit the transmission of the full compositional data to a gas flow computer in the field.

In Methods 1 and 2, the user may still find that the compositional analysis is available at some point throughout the measurement process (see introduction to Section A.3). Method 0 (or 3) should then be used rather than the methods given in Appendix A. The GROSS equation of state calculates compressibility factors for natural gas that contain component concentrations in the ranges given in Table 2. However, it should only be used for real natural gas, i.e., with heavy hydrocarbon tail, and not for synthetic gas such as LNG (in which case the uncertainty estimate should be reassessed). Equations, constants, and parameters needed to calculate compressibility factors for natural gas mixtures with the GROSS equation of state are presented in this section. An uncertainty discussion is given in Appendix B. The GROSS equation of state is a virial type model. It is based on the work of Schouten et al. (1990) (see Reference [3]). [3]). It is also known as the SGERG model (see Reference [4]), [4]), and should not be confused with the GERG-2008 equation of state described in Part 2. The SGERG model was developed with SI units. These units 24 

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are used here for the purpose of maintaining continuity with the original work. The original formulation included hydrogen and carbon monoxide as inputs for coke/oven gas applications. These gases rarely occur in North American pipeline applications and are not included in this document. A virial equation of state is a polynomial expansion in density, where the second virial coefficient  B  determines the departure of  Z   from unity at low densities, the third virial coefficient C   contributes more to the departure of Z   from from an ideal gas state as density increases, and so on. Each density term is preceded by these virial coefficients, which are functions of temperature and composition. The application of the virial equation of state via model truncates equation for the compressibility after the third virial coefficient termthe C . GROSS This truncation provides the highvirial accuracy calculations for natural gas factor pipeline transmission and distribution conditions only at pressures up to the limit in Table 2. The GROSS model expresses the compressibility compressib ility factor in terms of the molar density d , the mixture second virial coefficient Bmix, and the mixture third virial coefficient C mix mix as given in the following equations:

 Z   1  B   mix d     C mix d 2    Bmix 

3

(5-1)

3

  B  x  x

ij i  j

 

(5-2)

i1 j 1

 C mix

3

3

3

 i 1 j 1 k 1

C ijk  xi x    j xk   

(5-3)

where  Bij is the component interaction second virial coefficient for the i j  ,j pair, C ijk    is the component interaction ijk  is third virial coefficient for i,  jj,k , and  xi,  x j, and  xk   are the mole fractions of the gas components. The number of components in the gas gas mixture is set to 3: the equiva equivalent lent hydrocarbon, hydrocarbon, nitrogen, and carbon carbon dioxide. The mole fraction of the equivalent hydrocarbon is

 xCH    1  x N  2   xCO2 .

(5-4)

The  Bij and C ijk    terms in Equations (5-2) Equations (5-2) and  (5-3)   (5-3) are the interaction virial coefficient terms. They are ijk  terms temperature dependent functions. Expanding Equations (5-2) Equations (5-2) and  (5-3)   (5-3) for  Bmix  and C mix mix identifies all the terms needed to implement the SGERG model, given in the following equations: `  `  `    ,   , `  `  `  `    ,   ,   , `    , `  `    ,   , `  `    , `    ,   , `    ,   , `  `    ,   , `    ,   , `    , `    ,   , `  -

 Bmix

2 2   BCHCH xCH  B N  N  x N2  BCO CO  xCO  2 BCH N  xCH x N  2 BCHCO   xCH xCO  2 B N CO  x N 2

2

2

2

2

2

2

2

2

2

2

2

xCO2 2

 

(5-5)

3 3 C mix  C CH CH CH xCH  C  N 2  N 2  N 2 x N3 2  C CO2 CO2 CO2 xCO 2 2 2  x N  3C CH CHCO  xCH  xCO  3C CH CH  N  xCH 2

 3C CH  N  3C  N

2

2

2

2  xCH x N2 2  3C CH CO 2 CO2 xCH xCO 2

2  N 2

 

(5-6)

2  x N2 2 xCO2  3C  N 2 CO 2 CO2 x N 2 xCO 2

2  N 2  CO 2

 6C CH  N

 xCH x N 2 xCO2

2  CO 2

The following sections provide the equations needed to compute the second and third virial interaction terms for Equations (5-5) Equations  (5-5) and  (5-6).   (5-6).  25 

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5.3 Interaction Virial Coefficient Terms for Nitrogen and Carbon Dioxide The Bij values for the terms involving only nitrogen and carbon dioxide are expressed in dm3/mol and are given by

 Bij  b0   b1T     b2T 2 ,

(5-7)

where values for b0, b1, and b2 are given in Table 8, and T  is   is the temperature in kelvins. Similarly, the C ijk   values ijk  values 6

2

for the terms involving only nitrogen and carbon dioxide are expressed in dm /mol , and are given by C ijk   c0   c1T     c2T 2 , (5-8) where values for c0, c1, and c2 are also given in Table 8. Table 8 –  Interaction Virial Coefficient Coefficient Terms for Nitrogen and Carbon Dioxide b0 (dm3/mol)

 Bij Binary set

 N2-N2   N2-CO2  CO2-CO2 

0.1446  – 0.1446 0.339693  – 0.339693 0.86834  – 0.86834 c0 (dm6/mol2)

 Ternary set C ijk  ijk  Ternary

/(mol∙∙K)] b1 [dm3/(mol 0.740910×10 – 3  0.161176×10 – 2  0.403760×10 – 2  c1 [dm6/(mol2∙K)]

/(mol∙∙K 2)]  b2 [dm3/(mol 0.911950×10 – 6   – 0.911950×10 0.204429×10 – 5   – 0.204429×10 0.516570×10 – 5   – 0.516570×10 c2 [dm6/(mol2∙K 2)] 

 N2-N2-N2   N2-N2-CO2 

0.784980×10 – 2  0.552066×10 – 2 

0.398950×10 – 4   – 0.398950×10 0.168609×10 – 4   – 0.168609×10

0.611870×10 – 7  0.157169×10 – 7 

 N2-CO2-CO2  CO2-CO2-CO2 

0.358783×10 – 2  0.205130×10 – 2 

0.806674×10 – 5  0.348880×10 – 4 

0.325798×10 – 7   – 0.325798×10 0.837030×10 – 7   – 0.837030×10

5.4 Interaction Virial Coefficient Terms for the Equivalent Hydrocarbon The only remaining virial coefficient terms needed to compute the compressibility factor of a natural gas from Equations (5-1), (5-5), (5-1), (5-5), and   and  (5-6)  (5-6) are the quantities involving the equivalent hydrocarbon CH. The second and third interaction virial coefficients for the equivalent hydrocarbon must be calculated from the molar ideal gross heating value of the equivalent hydrocarbon ( H CH CH in kJ/mol at 25 °C). When a gas analysis is available, the molar gross heating value H CH CH can be determined as

   N   H CH    xi HN    io ( 25 C)    / xCH ,   i1

(5-9)

where  HN oi is the gross component molar heating value (for the ideal gas) in kJ/mol at 25 °C and is available in AGA 5,  Natural Gas Energy Measurement , GPA 2172, Calculation of Gross Heating Value, Relative Density, Compressibility Compressibil ity and Theoretical Hydrocarbon Liquid Content for Natural Gas Mixtures for Custody Transfer , or ISO 6976,  Natural Gas  –   Calculation of Calorific Values, Density, Relative Density and Wobbe Index from Composition. When the gas composition is not known, the value of H CH method s CH must be determined by one of the methods summarized in Appendix A. The equations for the second and third interaction interaction virial coefficients for the equivale equivalent nt hydrocarbon are 2  BCH-CH  B0   B   1 H CH  B2 H CH and

(5-10)

2   0   C 1 H CH  C 2 H CH C CH-CH-CH  C  ,

(5-11)

where B0, B1, B2, C 0, C 1, and C 2 are temperature dependent functions defined as 2

 B  b  b T     b T  , i  0,1,2  and C i  ci 0  ci1T     ci 2T 2 , i  0,1,2 . i

i0

i1

i2

(5-12) (5-13) 26 

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

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The constants in Equations (5-12) Equations (5-12) and  (5-13)  (5-13) are given in Table 9. Table 9 –  9 –  Virial  Virial Coefficient Terms for the Equivalent Hydrocarbon bi0 

i 3

 B0 (dm /mol)  B1 [dm3/(mol /(mol∙∙K)] 3 /(mol∙∙K 2)]  B2 [dm /(mol

6

2

C 0 (dm /mol ) C 1 [dm6/(mol2∙K)] C 2 [dm6/(mol2∙K 2)]

bi2 

bi1 

0 1 2

0.425468  – 0.425468 0.877118×10 – 3  0.824747×10 – 6   – 0.824747×10

0.286500×10   0.556281×10 – 5   – 0.556281×10 0.431436×10 – 8 

0.462073×10 – 5   – 0.462073×10 0.881510×10 – 8  0.608319×10 – 1111   – 0.608319×10

i

ci0 

ci1 

ci2 

0 1 2

 – 2

 – 2

0.302488  – 0.302488 0.646422×10 – 3  0.332805×10 – 6   – 0.332805×10

0.195861×10   0.422876×10 – 5   – 0.422876×10 0.223160×10 – 8 

0.316302×10 – 5   – 0.316302×10 0.688157×10 – 8  0.367713×10 – 1111   – 0.367713×10

The interaction second virial coefficient term for the equivalent hydrocarbon CH with nitrogen N 2  is calculated as



 T ) 2  BCHCH  B N2 N2 / 2 ,  BCH N2  0.72  1.875  10 5 (   320  

(5-14)

where T  is  is given in kelvins. For the equivalent hydrocarbon CH with carbon dioxide CO 2, the relation is



 BCH CO2    0.865  B  CH  CH BCO2 CO 2



1  2

.

(5-15)

The interaction third virial coefficient terms for nitrogen and carbon dioxide are calculated with the following equations:









2  C CH C CHCH N2  0.92   0.0013T   270 CH CH C     N 2  N 2 - N 2

C CH N 2  N 2  0.92   0.0013T   270  C CH CH-CH C  N2 2  N 2  N 2

C CHCH CO  2

 0.92C CH  2 CH   -CHC CO  CO  CO 2



2



1  3

2

2 C CH  CO 2  CO  2  0.92 C CH    CH  CHC CO 2  CO 2 - CO 2

1  3

1  3

 

(5-16) (5-17) (5-18)



1  3

 



C CH  N 2  CO     2  1.10 C CH CH  CH   C   N 2  N 2  N 2 C  CO 2  CO 2  CO 2

(5-19)



1  3

 

(5-20)

The equation for calculating the pressure with the GROSS equation of state is obtained by substituting Equation (5-1) Equation  (5-1) into Equation (2-5), Equation (2-5), resulting  resulting in





2 P  dR dRT  T  1   Bmix    C mix mix d  mix d  .

(5-21)

The derivative of pressure with respect to density is useful in iterative routines to determine the density with pressure and temperature inputs, as given by

 P      3C mix d 2  .    RT 1  2 Bmixd   d  T 

(5-22)

Section 6 describes an iterative method to obtain the density in the equation of state.

27  --```,,````,,,`,``,,``,`,,`,,-`-`,,`,,`,`,,`---

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6 COMPUTATION OF DENSITIES AND COMPRESSIBILITY FACTORS Flow rate calculations for gas metering applications typically require values of both the compressibility factor Z  at   at the flowing temperature and pressure, along with the compressibility factor at base conditions  Z  b. This calculation requires first the determination of the density at flowing conditions. Procedures for these computations for the DETAIL and GROSS equations of state are given below and in the supplementary material for this document.

6.1 Iterative Procedure to Determine Density from Temperature and Pressure There are many types of iterative methods that could be implemented to determine density, which is an independent variable (along with temperature) in the equation of state. Each has advantages (such as bounded regions that guarantee a root) and disadvantages (such as low speed of calculation or non-bounded procedures). The iterative process in the supplementary material uses a Newton’s method for rapid convergence. Because Becau se  pressures and and densities densities can be be very small small values, the natural natural log of these these values values is used. used. `  `  `    ,   , `  `  `  `    ,   ,   , `    , `  `    ,   , `  `    , `    ,   , `    ,   , `  `    ,   , `    ,   , `    , `    ,   , `  -

The iterative method starts with the calculation of density from the ideal-gas law, given the input temperature and pressure, and then converts it to the logarithm of the specific volume,

vln

  RT      ln  d   ln input  ,

(6-1)

  Pinput   where vln = ln(v). With the calculated density, the pressure used in the iteration (labeled Pcalc here) is calculated from either the DETAIL or GROSS equation of state, along with the first partial of pressure with respect to density. From Newton’s method, a new density (or logarithm of the specific volume in this case) is calculated from the difference between the calculated and known values of pressure and the partial derivative,

 lnv       lnPcalc   lnPinput ,   ln   P  T  

vln,new  vln,old   

(6-2)

where  

1

 lnv   P   v   P  P   d  T  .  P  T    d     lnP T   v  

(6-3)

The density is updated from vln,new as

d   exp ex  p   vln,new .

(6-4)

  is replaced with the new calculated value vln,new, and the iteration continues until the difference The variable vln,old  is in the pressures is less than some tolerance value.

28 

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6.2 Computer Programs for the Calculation of Properties The two equations of state (DETAIL and GROSS) have been incorporated into efficient computer  programs to compute the compressibility compressibility factor  Z , the molar density d , the mass density   , and the supercompressibility factor F  pv. For the DETAIL method, the other thermodynamic variables given in Section 5 are also calculated. The computer programs can be used for the following purposes:  

direct use in the computation of  Z , d ,   , and F  pv ,

 

as a guide for f or the development of subroutines for computations of these properties for incorporation in other computer code, such as orifice flow computer programs,

 

for verification purposes when new flow programs are developed, and

 

to produce tabulations of  Z ,   , or F  pv for different gas mixture compositions.

The computer programs and their documentation are given in Appendix C and the supplementary material for this document. Tables of computed compressibility factors are provided for the DETAIL and GROSS equations of state in Appendix B and in the supplementary material. These tables can be used to verify computer programs. The tables cover a wide range of gas types.

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

29 

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7 ASSIGNMENT OF TRACE COM COMPONENTS PONENTS In order to calculate the thermodynamic properties of a natural gas or similar mixture that contains components that do not appear in Table 1, it is necessary to assign each component to one of the 21 major or minor components for which the DETAIL equation of state was developed. Recommendations for appropriate assignments are given in Table 10. Each recommendation is based on an an assessment of which substance is likely to give the lowest overall uncertaint uncertainty y for the complete set of thermodynamic properties. Because, no single assignment is likely to be equally satisfactory for all properties, it is reasonable that the user may prefer an alternative assignment for a particular application in which, for example, only a single property is needed. Implementations that include assignments for trace components need to be carefully documented.

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Table 10 –  10 –  Assignment   Assignment of Components for Single-phase Thermodynamic Properties Only Component  Formula  Recommended assignment  2,2-Dimethylpropane (Neopentane)  C5H12  n-Pentane  2-Methylpentane  C6H14  n-Hexane  3-Methylpentane  C6H14  n-Hexane  2,2-Dimethylbutane  C6H14  n-Hexane  2,3-Dimethylbutane  C6H14  n-Hexane  Ethylene (Ethene)  C2H4  Ethane  Propylene (Propene)  C3H6  Propane  1-Butene  C4H8  n-Butane  cis-2-Butene  C4H8  n-Butane  C4H8  trans-2-Butene  n-Butane  2-Methylpropene  C4H8  n-Butane  1-Pentene  C5H10  n-Pentane  Propadiene  C3H4  Propane  1,2-Butadiene  C4H6  n-Butane  1,3-Butadiene  C4H6  n-Butane  Acetylene (Ethyne)  C2H2  Ethane  Cyclopentane  C5H10  n-Pentane  Methylcyclopentane  C6H12  n-Hexane  Ethylcyclopentane  C7H14  n-Heptane  Cyclohexane  Methylcyclohexane  Ethylcyclohexane  Benzene  Toluene (Methylbenzene)  Ethylbenzene  o-Xylene  All other C6 hydrocarbons 

C6H12  C7H14  C8H16  C6H6  C7H8  C8H10  C8H10 

n-Hexane  n-Heptane  n-Octane  n-Pentane  n-Hexane  n-Heptane  n-Heptane  n-Hexane 

All other C7 hydrocarbons 

n-Heptane 

All other C8 hydrocarbons 

n-Octane 

All other C9 hydrocarbons 

 Nonane  n- Nonane

All other C10 hydrocarbons 

n-Decane 

All higher hydrocarbons 

n-Decane 

Methanol (Methyl alcohol) 

CH4O 

Methanethiol Ammonia   (Methyl mercaptan)  Hydrogen cyanide  Carbonyl sulfide (Carbon oxysulfide)  Carbon disulfide  Sulfur dioxide   Nitrous oxide   Neon 

CH S    NH 3  CHN  COS  CS2  SO2   N2O   Ne 

4

Ethane  Propane   Methane Ethane  n-Butane  n-Pentane  n-Butane  Carbon dioxide  Argon

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8 REFERENCES 1  Starling, K.E., R.T Jacobsen, S.W. Beyerlein, C.W. Fitz, W.P. Clarke, E.W. Lemmon, Y.C. Chen, and E. Rondon, GRI High Accuracy Natural Gas Equation of State for Gas Measurement Applications –  Applications – 1991 1991 Revision of A.G.A. No. 8 Equation, Technical Reference Document, GRI-91/0184, 1991. 2  Savidge, J.L., S.W. Beyerlein, and E.W. Lemmon, Technical Reference Document for the 2nd  Edition of AGA Report Number 8, GRI-93/0181, 1993. 3  Schouten, J.A., J.P.J. Michels, and M. Jaeschke, Calculation of the Compressibility Factor of Natural Gases Based on the Calorific Value and the Specific Gravity,  Int. J. Thermophys., 11(1):145-156, 1990. 4  Jaeschke, M. and A.E. Humphreys, GERG Technical Monograph 5, Fortschritt-Berichte VDI Reihe 6, No. 266, 1991. 5  Lemmon, E.W., Better Defining the Uncertainties for the AGA 8 Equation, Catalog No. PR-381-12604-R01, Pipeline Research Council International, Inc., 2013. 6  Lemmon, E.W., M.L. Huber, and M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2013. 7  Lemmon, E.W., M.O. McLinden, and W. W Wagner, agner, Thermodynamic Properties of Propane. III. A Reference Equation of State for Temperatures from the Melting Line to 650 K and Pressures up to 1000 MPa,  J. Chem.  Eng. Data, 54:3141-3180, 2009. 8  Lemmon, E.W. and K.E. Starling, Speed of Sound and Related Thermodynamic Properties Calculated from the AGA Report No. 8 Detail Characterization Method Using a Helmholtz Energy Formulation, proceedings of the American Gas Association Conference and Biennial Exhibition, 2003. 9  Jaeschke, M. and P. Schley, Ideal-gas Thermodynamic Properties for Natural-Gas Applications,  Int. J. Thermophysics, 16, 1381-1392, 1995.

10  10  AGA Report No. 10, Speed of Sound in Natural Gas and Other Related Hydrocarbon Gases, Transmission Measurement Committee. 11  11  Schouten, J. and J. Michels, Evaluation of the PVT Reference Data on Natural Gas Mixtures, Gas Research Institute, 1992. 12  12  Jaeschke, M. and A.E. Humphreys, GERG Databank of High Accuracy Compressibility Factor Measurements, GERG Technical Monograph 4, Fortschritt-Berichte VDI Reihe 6, No. 251, 1990. 13  13  Younglove, B.A., N.V. Frederick, and R.D. McCarty, Speed of Sound Data and Related Models for Mixtures of Natural Gas Constituents, NIST Monograph 178, 1993.

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APPENDIX A –  GROSS  GROSS EQUATION OF STATE

(Informative) A.1 Nomenclature   Bmix  C m mix ix  d   Gr   G1, G2   H CH CH  o  HN     HV    M    M CH CH   M  N2   M CCO2 O2  P  Pd   Pgr    R  T   T d  d   T ggr r   T h   xCH   x N2   xCO2   xi   Z      

Second virial coefficient of the mixture (dm3/mol) Third virial coefficient coefficient of the mixture (dm6/mol2)  Molar density (mol/dm3) Relative density (specific gravity) of the mixture Constants used in the relation between M CH CH and H CH CH  Molar ideal gross heating value of the equivale equivalent nt hydrocarbon (kJ/mol) at 25 °C Molar ideal gross heating value (kJ/mol) at 25 °C Volumetric gross heating value (MJ/m3) Molar mass (molecular weight) (g/mol) Molar mass of the equivalent hydrocarbon (g/mol) Molar mass of nitrogen (28.0135 g/mol†) Molar mass of carbon dioxide (44.01 g/mol†) Absolute pressure (MPa) Reference pressure for molar density (MPa) Reference pressure for relative density (MPa) Gas constant [8.31451 J/(mol∙K)†] Absolute temperature temperature (K) Reference Reference temperature temperature for molar density (K) Reference temperature for relative density (K) Reference temperature for heating value (K) Mole fraction of the equivalent hydrocarbon hydrocarbo n Mole fraction of nitrogen Mole fraction of carbon dioxide Mole fraction of component i in the gas mixture Compressibility Compressibili ty factor Mass density (kg/m3)

†

The values given do not represent the most current scientific values, but are used here to conform with the 1994 edition of AGA 8 so that calculated property values match the original equation.

A.2 Reference Conditions When a body of information has been developed for a quantity such as the molar heating value at specific conditions of temperature and pressure, it is common to refer to these as the reference conditions. In the gas industry, reference conditions are also commonly referred to as base conditions, normal conditions, standard conditions, etc. A number of specific temperature-pressure conditions are used for reference conditions for natural gas volumetric properties (density, specific volume, or compressibility factor) as outlined in AGA 5,  Natural Gas  Energy Measurement , and GPA 2172, Calculation of Gross Heating Value, Relative Density, Compressibility Compressibility and Theoretical Hydrocarbon Liquid Content for Natural Gas Mixtures for Custody Transfer . In the U.S. gas industry, the reference conditions that are the basis for a gas contract are commonly referred to as the base conditions. For inter-statee custody transfer, the reference conditions/base inter-stat conditions/bas e conditions are 60 °F and 14.73 psia. In much of Europe, the reference conditions 15 °C and 0.101325 MPa are referred to as standard conditions, and the reference conditions 0 °C and 0.101325 MPa are commonly referred referre d to as normal conditions. The reference conditions for tabulations of the supercompressibility factor F  pv are 60 °F and 14.73 psia. Because there is a plethora of choices 33 

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

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for reference conditions as well as names such as standard conditions, normal conditions, and base conditions, the temperature and pressure reference conditions should be clearly specified. The reference conditions 25 °C and 0.101325 MPa are commonly used in the scientific literature for experimental data tabulations of molar enthalpies of formation of compounds from the elements. The molar enthalpies of formation of the compounds involved in combustion are used for calculations of component molar heating values at the reference conditions. A molar heating value for a compound at specified conditions that is different from the reference conditions can then be determined from the molar heating value at the reference conditions the in enthalpy difference between the two conditions for the stoichiometric amounts of the compounds plus involved the combustion reaction. The volumetric heating value is the molar heating value multiplied by the molar density. Separate reference conditions occur for the volumetric heating value when the reference conditions are different for the molar heating value and the molar density. Therefore, the reference conditions for both the molar heating value and the molar density must be specified to obtain the volumetric heating value. When the complete compositional analysis of the natural gas is not known, heating values of reliable accuracy can be measured with combustion calorimeters. Natural gas heating values can also be estimated from limited characterization information such as relative density, nitrogen content, and carbon dioxide content, although the resulting estimates of heating values generally have greater uncertainties than measurements from combustion calorimeters or calculations with complete compositional analyses.

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

A.3 GROSS Equation of State Computation Procedures

The methods for use of the GROSS equation of state have been changed in this edition. Because the gas composition is often available for use in calculations of thermodynamic properties, the methods given below are not required and one can proceed directly to the calculation of compressibility factor through the use of Method 0 outlined in Section 5 without the use of the gross volumetric heating value or relative density. In cases where a gas analysis is not available, either Method 1 or 2 given below is required to obtain the  H CH CH  value needed in Equations   (5-10) and (5-11) of the GROSS equation of state. These methods can be implemented when two Equations  particular sets of three three of the following four characte characterization rization parameters parameters aare re availa available: ble: * volumetric gross heating value * relative density (specific gravity) * mole fraction of nitrogen * mole fraction of carbon dioxide Method 1 is used for inputs of heating value, relative density, and carbon dioxide content. Method 2 is used for inputs of relative density, nitrogen content, and carbon dioxide content. Iterative procedures are required to obtain the necessary parameters in the SGERG model with Methods 1 and 2. These procedures are based on satisfying satisfyin g rigorous mole, mass, and energy balance equations. General equations specific to both models are given  below, and the details details of the methods are are explained explained in Se Sections ctions A.3.1 A.3.1 and A.3.2. A.3.2. One additional method, Method 3, is available when only the molar mass of the mixture and the mole fractions of nitrogen and carbon dioxide are available. This method is not iterative, and is mostly identical to Method 0, except in the calculation of the molar heating value of the equivalent hydrocarbon.

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o

The volumetric gross heating value  HV   is is the product of the molar ideal gross heating value  HN   and the real molar density d  of  of the gas mixture,

    o T h  d T d , Pd   .  HV T h , T d  , Pd     HN 

(A-1)

The reference conditions T h for the molar gross heating value may differ from the reference conditions T dd    and Pd  for  for the molar density. T h, T dd  , and Pd  must  must be specified to obtain the reference conditions for the volumetric heating value. o

The molar ideal gross heating value  HN   at 25 °C is  

 HN o 25 C   ZRT d  / Pd   HV T  h , T d , Pd    1  1.027  10

4

T h  298.15 ,

(A-2)

where T  is  is given in kelvins and Z  is  is the compressibility factor at the reference conditions T dd  and    and Pd . This is only an approximate equation equation for natural gas. In this equation, the volumetric gross he heating ating value  HV  is   is given in 3 MJ/m  at the reference conditions T h and the real molar density at the mixture reference conditions T dd  and    and Pd . AGA 5, Natural Gas Energy Measurement , should be consulted for additional information on heating values and reference states. The relative density (specific gravity) Gr  at  at the reference conditions T gr   and Pgr  is  is defined by the relation gr  and

Gr T gr , Pgr      T gr , Pgr  ,   ref  T gr , Pgr 

(A-3)

where   rref  where     is the real mass density of the reference fluid (previously defined as that for air, see GPA 2145, Table ef  is of Physical Properties for Hydrocarbons and Other Compounds of Interest to the Natural Gas Industry , for additional information), T ggr r   is the reference temperature, and Pgr   is the reference pressure. (The reference conditions indicated with a subscript "gr " are generally the same as those labeled with the subscript " d ", ", but used here for situations situations where the two are are not identica identical.) l.) In this relation for Gr (T gr  ), both the gas mixture density gr , Pgr ),      ((T ggr r , Pgr ) and the reference density   density   ref (T ggr r , Pgr ) must be at the same temperature-pressure conditions T gr   and Pgr . gr  and From Equation (2-6) Equation (2-6) for the real mass density of both the gas mixture and reference fluid, the following relation results

 MZ ref  T gr  , Pgr  Gr  T gr  ,  Pgr 



   M   Z T  ref 

gr 

, Pgr   .

(A-4)

The relative density is not a constant but varies with both  T gr    and Pgr . The molar mass of the reference gr  and fluid  M   M rref   is 28.9625 g/mol. The molar ma mass ss (molecular (molecular weight) M  of  of the mixture can be estimated from Equation ef  is (A-4) as a function of the relative density with the relation



 

 M   Gr  T gr , Pgr   Z  T gr , Pgr 

28.9625 g/mol

 1

Pgr   RT gr 

 0.12527  5.91 10

-4

,

T gr   6.62  10 T gr  -7

2

(A-5)



where the equation in parenthesis in the denominator represents the second virial coefficient of the reference fluid (air in this situation).

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A.3.1 Method 1. Volumetric Gross Heating Value, Relative Relative Density, and Mole Fraction of CO2  The procedures for calculating the ideal molar gross heating value of the equivalent hydrocarbon  H CH CH and the nitrogen mole fraction x N2 based on inputs of volumetric gross heating value, relative density, and mole fraction of carbon dioxide is outlined below. o

The compressibility Z   is is initially set to 1, and the molar ideal gross heating value HN   at 25 °C is calculated from Equation (A-2). Equation (A-2).   The molar mass  M  is   is calculated from Equation (A-5). Equation (A-5).   The mole fraction of the equivalent hydrocarbon is

 xCH 





 M    xCO 2  1 M  N 2  xCO 2 M CO 2  G2 HN o G1  M  N 2

,

(A-6)

where G1 = –  2.709328 g/mol and G2 = 0.021062199 g/kJ. The mole fraction of nitrogen  x N2 is   2.709328

 x N2   1  x  CH    xCO2 .

(A-7)

The molar gross heating value of the equivalent hydrocarbon H CH CH is

 H CH 



 HN o

.

(A-8)

 xCH  BCH-CH  is calculated with this value from Equation (5-10),  (5-10),  and  Bmix  is calculated with Equation (5-2). (5-2).   The compressibility compressibi lity factor is then updated as

 Z new    1  

 Bmix Pgr   RT gr 

.

(A-9)

The calculation procedure is iterative. These equations are repeated, replacing  Z  with   with  Z new new  iteratively until the -11 absolute value of ( Z/Z new    –    –     1) 1) is less than the convergence criterion (5×10  in double precision or 5×10-7 in single new  precision). This is not a rigorous calculation calculation for the compressibility factor because because it does not include the third virial coefficient C m mix ix; however, this contribution is mostly negligible near atmospheric pressure.

A.3.2 Method 2. Relative Density and Mole Fractions of N2 and CO2  The procedure for calculating the heating value of the equivalent hydrocarbon  H CH CH based on inputs of relative density at the reference conditions T ggr r  and  and Pgr  and  and mole fractions of N 2 and CO2 is outlined below. In this method the mole fraction of the equivalent hydrocarbon xCH is determined by

 xCH    1  x N  2   xCO2  

(A-10)

The molar mass of the equivalent hydrocarbon  M CH CH is

 M CH 

 M   x N2 M  N 2  xCO2 M CO2  xCH

,

(A-11)

where the molar mass of the mixture  M   is calculated from Equation (A-5) with an initial value for the compressibility factor Z  set  set to 1. 36 

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

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The molar gross heating value of the equivalent hydrocarbon H CH CH is

 H CH



 M    CH

 G1

G2

,

(A-12)

where G1 = –     – 2.709328 2.709328 g/mol and G2 =  0.021062199 g/kJ.  BCH-CH  is calculated with Equation (5-10) Equation (5-10) and  Bmix  is calculated with Equation (5-2). Equation (5-2). The  The compressibility compressibility factor is then updated as

 Z new    1  

 Bmix Pgr   RT gr 

.

(A-13)

The calculation procedure is iterative. These equations are repeated, replacing  Z  with   with  Z new new  iteratively until the -11 absolute value of ( Z/Z new  –  1)  1) is less than the convergence criterion (5×10  in double precision or 5×10-7 in single new  –   precision). This is not a rigorous calculation calculation for the compressibility factor because because it does not include the third virial coefficient C m mix ix; however, this contribution is mostly negligible near atmospheric pressure. The molar heating value can be calculated with

 HN o 25  C   H    CH xCH .

(A-14)

A.3.3 Method 3. Molar Mass and Mole Fractions of N2 and CO2  The procedure for calculating the heating value of the equivalent hydrocarbon  H CH CH based on inputs of molar mass M  and  and mole fractions of N2 and CO2 is outlined below. In this method the molar mass of the equivalent hydrocarbon M CH CH is

 M CH 

 M   x N 2 M  N 2  xCO 2 M CO 2

1  x N  2  xCO 2

.

(A-15)

The molar gross heating value of the equivalent hydrocarbon H CH CH is

 H CH



 M    CH

 G1

G2

,

(A-16)

where G1 = –  2.709328 g/mol and G2 = 0.021062199 g/kJ.   2.709328

37 

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

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APPENDIX B –  EXAMPLES  EXAMPLES AND COMPARISON TO MEASUREMENTS

(Informative) B.1 Nomenclature AAD

Average absolute deviation

BIAS  N   RMS Std. Dev.  Z    Z ccalc alc   Z ddiff  iff    Z ddiff, iff,i  (  Z  Z ddiff  iff ) max   Z exp exp 

Bias Number of data points Root mean squared deviation Standard deviation Compressibility Compressibili ty factor Calculated compressibility compressibilit y factor Relative percentage difference between calculated and experimental compressibility compressibilit y factors th Zdiff  for  for the i  data point Maximum value of Z ddiff iff Experimental compressibility compressibilit y factor

B.2 Calculation Examples This appendix provides example calculations that can be used to verify computer programs. Table B.1  provides five reference reference natural gas com compositions. positions. Relativ Relativee densities and volumetric volumetric gross heating va values lues at 60 °F and 14.73 psia calculated from the compositions given in Table B.1 are given in Table B.2. Tables B.3 and B.4  provide computed computed compressibility compressibility factors from the DETAIL and GROSS equatio equations ns of state for the compositions in Table B.1 at various temperatures and pressures that can be used to verify calculations, and Table B.5 provides values for the speed of sound. The Excel worksheet used to generate the outputs is given in the supplementary supplementar y material. Table B.1 –  B.1 –  Compositions  Compositions of Natural Gas in Mole Percent Component mole percent  Component  Methane  Nitrogen Carbon dioxide Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane

Gulf coast 96.5222 0.2595 0.5956 1.8186

Amarillo 90.6724 3.1284 0.4676 4.5279

Ekofisk 85.9063 1.0068 1.4954 8.4919

High N2  81.441 13.465 0.985 3.3

High CO2-N2  81.212 5.702 7.585 4.303

0.4596 0.0977 0.1007 0.0473 0.0324 0.0664

0.828 0.1037 0.1563 0.0321 0.0443 0.0393

2.3015 0.3486 0.3506 0.0509 0.048 0.0

0.605 0.1 0.104 0.0 0.0 0.0

0.895 0.151 0.152 0.0 0.0 0.0

38 

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

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Table B.2 –  B.2 –  Input  Input and Internal Values for the Gases in Table B.1 for the GROSS Equation of State Gulf coast

Amarillo

Ekofisk

High N2 

High CO2-N2 

1036.04 0.581047 0.5956

1034.84 0.608632 0.4676

1108.10 0.649485 1.4954

906.634 0.644855 0.985

933.075 0.685939 7.585

917.201 909.542

942.046 908.413

996.948 972.294

930.347 796.127

944.254 819.022

0.581047 0.2595 0.5956

0.608632 3.1284 0.4676

0.649485 1.0068 1.4954

0.644855 13.465 0.985

0.685939 5.702 7.585

917.092 909.250

941.910 908.039

996.812 971.870

930.205 795.790

944.110 818.667

40.7259 0.581202

40.6797 0.608804

43.5627 0.649717

35.6381 0.645006

36.6798 0.686144

0.5956

0.4676

1.4954

0.985

7.585

917.200 909.539

942.049 908.418

996.951 972.297

930.348 796.129

944.256 819.024

0.581202 0.2595 0.5956

0.608804 3.1284 0.4676

0.649717 1.0068 1.4954

0.645006 13.465 0.985

0.686144 5.702 7.585

917.093 909.251

941.911 908.040

996.814 971.872

930.206 795.791

944.113 818.669

†

U.S. customary units    Inputs for Method Method 1  (BTU/ft3)  HV  (BTU/ft Gr   CO2 (mole %)  Intermediate  Intermedia te values for for Method 1  H CH CH (kJ/mol) at 25 °C o

 HN   (kJ/mol) at 25 °C  Inputs for Method Method 2 Gr    N2 (mole %) CO2 (mole %)  Intermediate  Intermedia te values for for Method 2  H CH CH (kJ/mol) at 25 °C o

 HN   (kJ/mol) at 25 °C

SI units†   Inputs for Method Method 1  (MJ/m3)  HV  (MJ/m Gr  

CO2 (mole %)  Intermediate values for  Intermediate for Method 1  H CH CH (kJ/mol) at 25 °C o

 HN   (kJ/mol) at 25 °C  Inputs for Method Method 2 Gr    N2 (mole %) CO2 (mole %)  Intermediate  Intermedia te values for for Method 2  H CH CH (kJ/mol) at 25 °C o

 HN   (kJ/mol) at 25 °C †

 HV  is  is the volumetric gross heating value and Gr  is the relative density. The reference conditions for the U.S. customary units section is 60 °F and 14.73  psia for both the heating value value and density. For the SI section, ref reference erence conditions are 15 °C for heating value and 0 °C and 0.101325 MPa for density.                     `   ,   ,         `   ,         `   ,   ,         `   ,   ,         `             `       ,   ,         `   ,   ,         `   ,         `         `   ,   ,         `         `   ,         `   ,   ,   ,         `         `         `         `   ,   ,         `         `         `         -

39 

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Table B.3 –  B.3 –   Natural Natural Gas Compressibility Factors for Program Verification Purposes in U.S. Customary Units †  Gulf coast

Amarillo

Ekofisk

High N2 

High CO2-N2 

 DETAIL equation equation of state state  32 14.73 32 600 32 1200 60 14.73 60 600 60 1200 100 14.73 100 600 100 1200 150 14.73 150 600 150 1200

0.997406 0.893928 0.795680 0.997858 0.914141 0.837692 0.998363 0.935904 0.881410 0.998828 0.955278 0.919249

0.997302 0.889390 0.786763 0.997771 0.910480 0.830705 0.998294 0.933136 0.876265 0.998776 0.953263 0.915582

0.996780 0.864910 0.733467 0.997327 0.890563 0.789205 0.997938 0.917786 0.845491 0.998499 0.941741 0.893106

0.997670 0.906452 0.823883 0.998089 0.924700 0.860575 0.998556 0.944418 0.899227 0.998985 0.962006 0.932968

0.997207 0.884920 0.776728 0.997692 0.906897 0.822957 0.998233 0.930426 0.870585 0.998730 0.951272 0.911491

GROSS equation of state, Method 0  32 14.73 32 600 32 1200 60 14.73 60 600 60 1200 100 14.73 100 600

0.997407 0.893976 0.795667 0.997853 0.914052 0.837501 0.998359 0.935894

0.997308 0.889647 0.787231 0.997770 0.910564 0.830909 0.998293 0.933255

0.996791 0.865184 0.733689 0.997329 0.890645 0.789388 0.997940 0.918041

0.997680 0.906836 0.824222 0.998094 0.924988 0.860987 0.998556 0.944561

0.997220 0.885302 0.776972 0.997699 0.907231 0.823588 0.998237 0.930807

0.881489 0.998813 0.954836 0.918522

0.876630 0.998764 0.952923 0.915055

0.846140 0.998496 0.941684 0.892924

0.899552 0.998966 0.961385 0.931925

0.871580 0.998719 0.951013 0.911233

GROSS equation of state, Method 1  32 14.73 32 600 32 1200 60 14.73 60 600 60 1200 100 14.73 100 600 100 1200 150 14.73 150 600 150 1200

0.997407 0.894010 0.795735 0.997854 0.914080 0.837554 0.998359 0.935915 0.881529 0.998814 0.954851 0.918550

0.997309 0.889697 0.787330 0.997771 0.910603 0.830986 0.998294 0.933285 0.876686 0.998765 0.952945 0.915095

0.996792 0.865248 0.733828 0.997330 0.890695 0.789489 0.997941 0.918079 0.846211 0.998497 0.941711 0.892976

0.997681 0.906878 0.824302 0.998094 0.925021 0.861051 0.998556 0.944586 0.899599 0.998966 0.961404 0.931958

0.997221 0.885351 0.777070 0.997700 0.907269 0.823663 0.998238 0.930836 0.871635 0.998720 0.951034 0.911273

GROSS equation of state, Method 2  32 14.73 32 600 32 1200 60 14.73 60 600 60 1200 100 14.73 100 600 100 1200 150 14.73 150 600 150 1200

0.997409 0.894074 0.795871 0.997855 0.914133 0.837664 0.998360 0.935956 0.881612 0.998814 0.954882 0.918610

0.997311 0.889781 0.787510 0.997773 0.910673 0.831130 0.998295 0.933339 0.876794 0.998766 0.952985 0.915174

0.996795 0.865355 0.734070 0.997332 0.890781 0.789676 0.997943 0.918145 0.846348 0.998498 0.941760 0.893075

0.997682 0.906947 0.824446 0.998096 0.925079 0.861167 0.998557 0.944631 0.899688 0.998967 0.961437 0.932024

0.997222 0.885432 0.777247 0.997701 0.907336 0.823803 0.998239 0.930887 0.871739 0.998721 0.951073 0.911349

Temp. (°F)

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

100 150 150 150

Pressure (psia)

1200 14.73 600 1200

†

 Inputs to GROSS Methods 1 and 2 come from Table B.2.

40 

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Table B.4 –  B.4 –   Natural Natural Gas Compressibility Factors for Program Verification Purposes in SI units †  Gulf coast

Amarillo

Ekofisk

High N2 

High CO2-N2 

 DETAIL equation equation of state state  0 0.101325 0 6 0 12 20 0.101325 20 6 20 12 40 0.101325 40 6 40 12 60 0.101325 60 6 60 12

0.997412 0.847589 0.734037 0.997975 0.885078 0.802268 0.998409 0.912380 0.851843 0.998749 0.932930 0.888883

0.997308 0.840933 0.723739 0.997893 0.880119 0.794318 0.998343 0.908558 0.845670 0.998695 0.929919 0.884020

0.996787 0.803397 0.657514 0.997469 0.852050 0.743111 0.997994 0.886634 0.805678 0.998405 0.912304 0.852060

0.997675 0.866943 0.774260 0.998197 0.900309 0.833366 0.998599 0.924793 0.876739 0.998913 0.943293 0.909387

0.997214 0.834033 0.709585 0.997818 0.875026 0.783867 0.998283 0.904631 0.837684 0.998646 0.926803 0.877727

GROSS equation of state, Method 0  0 0.101325 0 6 0 12 20 0.101325 20 6 20 12 40 0.101325 40 6

0.997413 0.847622 0.733669 0.997971 0.884997 0.801569 0.998405 0.912424

0.997314 0.841279 0.724320 0.997892 0.880284 0.794289 0.998342 0.908792

0.996799 0.803620 0.658976 0.997471 0.852208 0.743900 0.997997 0.887075

0.997685 0.867395 0.773499 0.998201 0.900708 0.833122 0.998598 0.925005

0.997226 0.834411 0.709644 0.997824 0.875566 0.784805 0.998287 0.905262

0.851503 0.998739 0.932603 0.887985

0.845778 0.998687 0.929746 0.883426

0.806486 0.998404 0.912462 0.851833

0.876561 0.998899 0.942796 0.908201

0.838982 0.998641 0.926851 0.877932

GROSS equation of state, Method 1  0 0.101325 0 6 0 12 20 0.101325 20 6 20 12 40 0.101325 40 6 40 12 60 0.101325 60 6 60 12

0.997413 0.847673 0.733747 0.997971 0.885036 0.801630 0.998406 0.912453 0.851551 0.998739 0.932626 0.888023

0.997315 0.841351 0.724430 0.997893 0.880337 0.794373 0.998342 0.908833 0.845844 0.998688 0.929778 0.883478

0.996800 0.803717 0.659123 0.997472 0.852276 0.744008 0.997998 0.887126 0.806569 0.998405 0.912502 0.851902

0.997686 0.867455 0.773593 0.998202 0.900752 0.833194 0.998599 0.925039 0.876617 0.998899 0.942823 0.908245

0.997227 0.834482 0.709753 0.997825 0.875618 0.784888 0.998288 0.905302 0.839047 0.998641 0.926883 0.877985

GROSS equation of state, Method 2  0 0.101325 0 6 0 12 20 0.101325 20 6 20 12 40 0.101325 40 6 40 12 60 0.101325 60 6 60 12

0.997415 0.847768 0.733921 0.997973 0.885110 0.801767 0.998407 0.912512 0.851659 0.998740 0.932673 0.888109

0.997317 0.841479 0.724663 0.997894 0.880436 0.794556 0.998344 0.908910 0.845988 0.998689 0.929840 0.883593

0.996802 0.803884 0.659413 0.997474 0.852401 0.744237 0.998000 0.887222 0.806747 0.998406 0.912579 0.852045

0.997688 0.867559 0.773781 0.998203 0.900833 0.833341 0.998600 0.925103 0.876734 0.998900 0.942875 0.908340

0.997229 0.834606 0.709983 0.997826 0.875712 0.785065 0.998289 0.905376 0.839185 0.998642 0.926942 0.878095

Temp. (°C)

40 60 60 60

†

`  `  `    ,   , `  `  `  `    ,   ,   , `    , `  `    ,   , `  `    , `    ,   , `    ,   , `  `    ,   , `    ,   , `    , `    ,   ,

Pressure (MPa)

12 0.101325 6 12

 Inputs to GROSS Methods 1 and 2 come from Table B.2. `  -

41 

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Table B.5 –  B.5 –  Natural  Natural Gas Speed of Sound Calculations from the DETAIL Equation of State for Program Verification Purposes Temp.

Pressure

Gulf coast

Amarillo

Ekofisk

High N2 

High CO2-N2 

1376.60

1342.94

ft/s 1292.33

1310.35

1265.81

1318.41 1303.31 1412.36 1367.54 1359.35 1460.82 1430.71 1430.54 1517.63 1500.97 1508.34

1282.60 1266.74 1377.74 1331.02 1321.91 1424.94 1393.18 1392.06 1480.32 1462.26 1468.71

1213.75 1186.06 1325.59 1263.14 1242.82 1370.74 1325.95 1315.05 1423.84 1395.13 1393.39

1266.84 1263.30 1344.51 1312.27 1314.00 1390.87 1371.07 1378.98 1445.31 1436.91 1450.70

1205.98 1187.95 1298.60 1252.15 1241.11 1343.12 1311.36 1308.48 1395.47 1377.13 1381.90

U.S. customary units °F 32 32 32 60 60 60 100 100 100 150 150 150

psia 14.73 600 1200 14.73 600 1200 14.73 600 1200 14.73 600 1200 SI units

°C

MPa

m/s

0

0.101325

419.588

409.328

393.904

399.395

385.819

0 0 20 20 20 40 40 40 60 60 60

5 10 0.101325 5 10 0.101325 5 10 0.101325 5 10

399.337 402.828 433.516 419.292 423.185 446.689 437.013 441.898 459.204 453.052 458.970

388.304 391.991 422.883 407.997 411.795 435.714 425.457 430.145 447.914 441.245 446.925

366.146 369.013 406.859 386.433 387.916 419.137 404.202 406.370 430.831 420.134 423.389

384.553 390.693 412.701 402.896 409.351 425.307 419.322 426.488 437.297 434.281 442.197

364.887 367.458 398.592 383.711 386.542 410.701 400.369 404.188 422.230 415.420 420.294

42  --```,,````,,,`,``,,``,`,,`,,-`-`,,`,,`,`,,`---

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B.3 Comparisons of Calculated Properties with Measurements Compressibility factors and densities calculated with both equations of state were compared with experimentally measured values on five simulated natural gas mixtures (Reference [2]). [2]). These mixtures were gravimetrically prepared to represent key natural gas samples occurring in North America and Europe. Table B.1  provides the compositions compositions of these samples. The uncertainty of these reference reference data data for temp temperatures eratures from –  from – 10 10 °F to 170 °F (250 K to 350 K) and pressures to 1750 psia (12 MPa) at a 95 % confidence level is 0.07 % in density. The uncertainty between –  between – 10 10 °F to 170 °F (250 K to 350 K) and pressures from 1750 psia to 5200 psia (12 MPa to 36 MPa) is less than 0.2 % in density (References [11,12]). [11,12]). Computed compressibility factors and densities from the DETAIL equation of state agree on average within 0.025 % of a best fit of the experimental experimental data in the region from 35 °F to 170 °F and pressures up to 1750  psia (275 K to 350 K and pressures up to 12 MPa). MPa). At conditions up to 5200 psia psia (36 (36 MPa), the agreemen agreementt bet between ween calculated values and a best fit of the experimental data above 35 °F (275 K) is 0.1 %. For high pressure reservoir applications, the DETAIL equation of state predicts compressibility factors often better than 0.2 % when compared to the PVT reference database. Computed compressibility factors and densities from the GROSS equation of state agree on average within 0.04 % of a best fit of the experimental data in the region from 35 °F to 170 °F and pressures up to 1750 psia (275 K to 350 K and pressures up to 12 MPa) (References (References [2] and [2] and [3]). [3]). Both equations of state were used for compressibility factor and density calculations for 4850 natural gas data points in the GERG data bank (Reference [12]). [12]). These samples were not gravimetrically prepared. The compositions were determined by gas chromatography. The uncertainty in the chromatographic analysis and component identification is not insignificant when considering calculation uncertainties of 0.05%. Statistical analyses of the differences between calculated and experimental compressibility factors were performed to t o evaluate the uncertainties in the calculated compressibility factors and densities. Statistics were calculated with the following equations where N  is  is the number of data points:

  Z calc    Z exp      Z   100%   exp    

 Z diff   

AAD 

1

(B-1)

 N 

  Z diff,  N 

(B-2)

  Z   N 

(B-3)

i

 i 1

BIAS  1

 N 

diff,i

 i 1

 1  N  2 Std. Dev.       Z diff,i   BIAS     N   1 i1

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

 1  N  2 RMS RM S       Z diff,i     N  i1

1

1

2

(B-4)

2

(B-5)

Max. Dev.    Z diff  max   max

(B-6)

Calculations Calculatio 96 natural compositions in the range 17 °F to 143 °F (265 K to 333 K) with pressures up ns towere 1750performed psia (12 for MPa). These gas natural gas compositions were classified into seven groups according to composition: 43 

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 

Group 1 consists of 14 natural gas compositions containing more than 9.5 mole percent nitrogen.

 

Group 2 consists of 8 natural gas compositions containing more than 4 mole percent carbon dioxide.

 

Group 3 consists of 27 natural gas compositions containing more than 8 mole percent ethane.

 

Group 4 consists of 13 natural gas compositions containing more than 2 mole percent hydrogen.

 

Group 5 consists of 11 natural gas compositions containing more than 4 mole percent nitrogen and more than 4 mole percent ethane.

 

Group 6 consists of 12 natural gas compositions containing more than 94 mole percent methane.

 

Group 0 consists of 11 natural gas blends that do not fit within the criteria for Groups 1 to 6.

A summary of the statistical analyses of the differences between calculated and experimental compressibility factors and densities for the seven groups of natural gas is given in Table B.6, as well as calculations from Part 2 for comparison. comparison. For the DETAIL equation of state, the uncertainties in calculated compressibility factors are smallest for the natural gas compositions with more than 94 mole percent methane (Group 6), for which the standard deviation is 0.034 0.03 4 % and the t he maximum deviation de viation for f or 530 data points poi nts is 0.148 %. The uncertainties un certainties in i n calculated compressibility factors are largest for the natural gas compositions with more than 9.5 mole percent nitrogen (Group 1), for which the standard deviation is 0.061 % for 660 data points. The maximum deviation deviation point in the total of 4850 data points occurs for the natural gas compositions with more than 8 mole percent ethane (Group 3); this maximum deviation is 0.256 %. Overall, for the total of 4850 data points, the standard deviation is 0.049 %, the root mean square deviation is 0.050 %, the bias is –  is – 0.010 0.010 %, and the average absolute deviation is 0.036 %. For the GROSS equation of state (Method 0), the uncertainties in calculated compressibility factors are smallest for the natural gas compositions with more than 94 mole percent methane (Group 6), for which the standard deviation is 0.036 % and the maximum deviation deviation for 530 data points is is –   – 0.137 0.137 %. %. Aside from the group with high hydrogen content (Group 4), the uncertainties in calculated compressibility factors are largest for the natural gas compositions with more than 8 mole percent ethane (Group 3), for which the standard deviation is 0.061 % for 1403 data points. The maximum deviation point in the total of 4850 data points occurs for the natural gas compositions with more than 8 mole percent ethane (Group 3); this maximum deviation is 0.579 %. Overall, for the total of 4850 data points, the standard deviation is 0.057 %, the root mean square deviation is 0.058 %, the  bias is  – 0 0.012 .012 %, and the average absolute deviation is 0.038 %. Table B.6 also shows the uncertainties for the GERG-2008 equation of state, which is described in Part 2 of this document. The uncertainty in computed supercompressibility factors F  pv is related to the uncertainties in the computed  Z  values of both the compressibility factor  at anyingiven andthe pressure and the factor  Z (60 (60 °F, 14.73 psia). If there were no uncertainty  Z (60 (60 temperature °F, 14.73 psia), uncertainty in compressibility F  pv would be one-half the uncertainty in Z . If the uncertainty in  Z ((60 60 °F, 14.73 psia) were equal to the uncertainty in  Z , the uncertainty in F  pv would be 0.707 times the uncertainty in Z . Because the uncertainty in Z (60 (60 °F, 14.73 psia) cannot exceed the uncertainty in  Z , the uncertainty in F  pv generally will be between 0.5 and 0.7 times the uncertainty in  Z . For the 4850 data points for the 96 natural gas compositions in the custody transfer region of Table B.6, the expected uncertainty in computed values of F  pv is 0.024 % to 0.035 % for both equations of state. With the DETAIL equation of state, if there were no uncertainty in the natural gas composition, then 95 % of the time the uncertainty in a calculated supercompressibility factor would not exceed 0.035 %, and would not be expected to exceed 0.13 % in Range A of Table 1 in the main document. For the GROSS equation of state, if there were no uncertainty in the natural gas characterization (heating value, relative density, and nonhydrocarbon content), then 95 % of the time the uncertainty in a calculated supercompressibility factor would not exceed 0.034 %, and would not be expected to exceed 0.16 % in Range A of Table 1 in the main document.

44 

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

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Table B.6 –  B.6 –   Statistical Statistical Analyses of the Differences Between Calculated and Experimental Compressibility Factors and Densities for Seven Natural Gas Groups Gas group no.

 No. of gas samples

 No. of  points

DETAIL equation of state 1 14 2 8 3 27 4 13 5 11 6 12 0 11

AAD %

Bias %

StdDev %

RMS %

MaxDev % 

660 477 1403 690 660 530 430

0.058 0.029 0.031 0.029 0.035 0.026 0.051

0.037  – 0.037 0.005 0.003  – 0.003 0.014  – 0.014 0.012  – 0.012 0.010 0.024  – 0.024

0.061 0.042 0.044 0.038 0.046 0.034 0.061

0.072 0.042 0.044 0.041 0.047 0.036 0.066

0.205 0.153 0.256 0.163 0.162  – 0.162 0.148 0.371  – 0.371

48 4850 50

0.036

0.010  – 0.010

0.049

0.050

0.371  – 0.371

GROSS equation of state, Method 0 1 14 660 2 8 477 3 27 1403 4 13 690 5 11 660 6 12 530 0 11 430

0.038 0.035 0.040 0.032 0.044 0.026 0.049

0.001  – 0.001 0.021 0.018  – 0.018 0.013  – 0.013 0.031  – 0.031 0.000 0.033  – 0.033

0.048 0.040 0.061 0.069 0.049 0.036 0.058

0.048 0.045 0.064 0.070 0.058 0.036 0.066

0.165  – 0.165 0.144  – 0.144 0.579 0.476  – 0.476 0.219  – 0.219 0.137  – 0.137 0.443  – 0.443

48 4850 50

0.038

0.012  – 0.012

0.057

0.058

0.579

GROSS equation of state, Method 1 1 14 660 2 8 477 3 27 1403 4 13 690 5 11 660 6 12 530 0 11 430

0.037 0.037 0.037 0.020 0.038 0.027 0.044

0.002 0.026 0.011  – 0.011 0.001 0.022  – 0.022 0.002 0.022  – 0.022

0.047 0.040 0.059 0.029 0.047 0.037 0.060

0.047 0.047 0.060 0.029 0.052 0.037 0.064

0.153  – 0.153 0.148 0.606 0.119 0.205  – 0.205 0.137  – 0.137 0 0.438  –  .438

48 4850 50

0.034

0.005  – 0.005

0.050

0.051

0.606

660 477 1403 690

0.060 0.036 0.040 0.026

0.043  – 0.043 0.022 0.029 0.007

0.058 0.047 0.044 0.034

0.073 0.052 0.053 0.035

0.210  – 0.210 0.186 0.282 0.142  – 0.142

All

All

All

96

96

96

GERG-2008 equation of state 1 14 2 8 3 27 4 13 5 6 0

11 12 11

660 530 430

0.029 0.027 0.051

0.003 0.013 0.001

0.042 0.033 0.068

0.042 0.035 0.067

0.164 0.136  – 0.136 0.363  – 0.363

All

96

4850

0.038

0.007

0.052

0.052

0.363  – 0.363

The uncertainties of calculated speeds of sound depend on temperature, pressure, and composition. The uncertainties were evaluated by comparing calculated values to experimentally measured speed of sound from  NIST Monograph Monograph 178 (Reference [13]). Calcula Calculations tions were were compared compared with experimentally experimentally measured values for 17 gravimetrically prepared natural gas mixtures over the range of –  of  – 10 10 °F to 165 °F (250 K to 350 K) and pressures up to 2500 psia (17 MPa). Some of the gas mixtures included in the uncertainty analyses are outside the range of Table 1. The measurements conducted demonstrate that the uncertainty in the speed of sound is within 0.1 % for Gulf Coast, Amarillo, and Ekofisk Ekofisk gas for pressures up to 1750 psia (12 MPa) and temperature temperaturess between –  between – 10 10 °F and 165 °F (250 K and 350 K). The uncertainty in the speed of sound is also within 0.1 % for other gas mixtures whose characteristics fall within the ranges of Table 1. Higher levels of uncertainty exist for gas mixtures outside of these ranges.

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

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APPENDIX C –  DESCRIPTION  DESCRIPTION OF THE SUPPLEMENTARY FILES (Informative)  1. Property Calculation Calculation & Verification  AGA8.xls  –   This Excel spreadsheet can be used to calculate thermodynamic properties of natural gas at

any composition, temperature, and pressure, or to determine the differences between calculated values from the DETAIL, GROSS, and GERG-2008 equations of state. To access this file, use the link:  http://www.techstreet.com/direct/aga/AGA8.xls   2. Directory: TestData  NG Compositions.xls Compositions.xls –  Contains  Contains 200 compositions collected from industry that represent the full spectrum from nearly 0 to 100 % methane. Test Data.xls –  Contains   Contains calculated data points at multiple temperatures and pressures. These data can be used for validation of applications incorporating the AGA 8 Parts 1 and 2 source code or for testing modifications of other code. Compositions of the data include both binary mixtures of every component, and the data from the  NG Compositions.xls spreadsheet. The data are given along the dew and bubble point curves. curves. Many Many of the data points are outside the ranges ranges of the AGA 8 Part Part 1 equations, and the the values values

should only be used to confirm that a separate application application is working correctly.  Deviation Calculator.xls Calculator.xls –  Calculates  Calculates the deviation at any temperature and pressure between the DETAIL and GERG-2008 equations equatio ns of state. The calculations will identify if the point is within the 2-phase or liquid  phase. This file file requires that that the Refprop Refprop program from NIST be installed installed on the machine machine performing performing the calculations (which is used to determine the phase of each point). The spreadsheet also contains the data from the NG Compositions.xls Compositions.xls file for comparisons of a large range of gas mixtures. The  AGA8.xls file in the AGA8CODE directory can also calculate deviations between the different models, including the GROSS model that is not available in this Excel file, but it does not locate the phase boundaries. For states known to be in the gas phase, the AGA8.xls file is the best method for calculating deviations, and does not require the Refprop program. Tables.xls –   –  Contains  Contains the calculations used to generate the tables in AGA 8 Parts 1 and 2 plus calculations to verify that the tables in the 1994 edition are duplicated correctly in this revision.

3. Directory: AGA8Code This directory contains three subdirectories, each containing identical code originally developed in VB, and then translated to Fortran and C. Instructions are available at the top of each file that help explain the use of the code. The Property Calculation & Verification file,  AGA8.xls, described above, is also included in this directory. The VBA code in the Excel file is identical to the code given in the VB subdirectory.  AGA8.xls  –   Contains the VB code in  AGA8.bas and allows for calculations within Excel to obtain  properties from the AGA 8 Parts Parts 1 and 2 equations. equations. C directory –  Contains  Contains C code implementing the AGA 8 Parts 1 and 2 equations. `  `  `    ,   , `  `  `  `    ,   ,   , `    , `  `    ,   , `  `    , `    ,   , `    ,   , `  `  `    ,   , `    ,   , `    , `    ,   , `  -

Fortran directory –  Contains   Contains Fortran code implementing the AGA 8 Parts 1 and 2 equations. The *.cmn files are ‘include’ files that contain all of the common blocks. VB directory  –  VB   VB code implementing the AGA 8 Parts 1 and 2 equations. The VB code is identical to that in the AGA8.xls file.

To access the files described in items 2 and 3 above, use the link: link:  https://pages.nist.gov/AGA8/  

46 

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4. Directory: 1994Code

This directory contains the original files for the code from the 1994 edition of AGA 8. These files include  AGA8PROG.EXE ,  AGA8PROG.FOR,  DETAILXZ.FOR, GROSSXZ.FOR, UNITS.FOR, and CONF.SAV . The four Fortran files were compiled to make the executable file, and the CONF.SAV file contains the settings specified by the user. 1994AGA8.doc  –   Contains all documentation concerning the use of these Fortran files from the 1994 edition that is not included in the 2017 this  this revision.

To access this file, use the link:  http://www.techstreet.com/direct/aga/1994code.zip  

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

47 

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

48 

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FORM TO PROPOSE CHANGES AGA Report No. 8, Part 1 Send to:

Operations and Engineering Section  Section  American Gas Association 400 North Capitol Street, NW, 4 th Floor Washington, DC 20001, U.S.A. Email:  [email protected] Email: [email protected]  

Name: ________________________________________________________________ Company:_____________________________________________________________ Address_______________________________________________________________ Tel. No. __________________ _______________________________ ______________ _ Fax No. ___ ________________ __________________________ _____________

Please indicate organization represented (if any): ______________________________________________________________________ Document title, year of publication, section/paragraph: ______________________________________________________________________ Proposal recommends (check one): new text revised text deleted text Proposal (include proposed new or revised wording or identification of wording to be format;; i.e., use underscore to denote deleted (use separate sheet): (Proposed text should be in legislative format wording to be inserted (inserted wording) and strike-through to denote wording to be b e deleted (deleted wording).

Statement of problem and substantiation for proposal, (use separate sheet): (State the  problem that will be resolved by your recomme recommendation; ndation; give the spec specific ific reason for your proposal including including copies of tests, research papers, etc.) This proposal is original material.

(Note: Original material is considered to be the submitter’s own idea based on or as a result of his/her own experience, thought or research and, to the best of his/her knowledge, is not copied from another source.)

This proposal is not original material; its source (if known) is as follows: ______________________________________________________________________   Type or print legibly. If supplementary material (photographs, diagrams, reports, etc.) is included, you may be required to submit sufficient copies for all members of reviewing committees or task forces.

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

 I hereby grant grant the Ame American rican Gas Gas Association Association the non-exclusive, non-exclusive, royalty-free royalty-free rights, rights, inclu including ding non-e non-exclusive, xclusive, rroyalty-free oyalty-free rights in copyright, in this proposal and I understand that I acquire no rights in any publication of the American Gas  Association in which this prop proposal osal in this this or another another similar or or analog analogous ous form is used. FOR OFFICE USE ONLY

Date: __________________________ Log # ______________________ __________________________ ____

 ___________________________________________________________________  _______________________________ ____________________________________ Signature (Required)

49 

Date Rec’d ____________________ _____________________  _  

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

50 

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American Gas Association 400 N. Capitol Street, NW, 4th Floor Washington, DC 20001 U.S.A. 202/824-7000 www.aga.org

Catalog No. XQ1704-1 April 2017

© 2017 American Gas Association. All rights reserved.