SIST EN ISO 20765-1:2018

Natural gas - Calculation of thermodynamic properties - Part 1: Gas phase properties for transmission and distribution applications (ISO 20765-1:2005)

This part of ISO 20765 specifies a method of calculation for the volumetric and caloric properties of natural gases, natural gases containing synthetic admixture and similar mixtures, at conditions where the mixture can exist only as a gas.
The method is applicable to pipeline-quality gases within the ranges of pressure and temperature at which transmission and distribution operations normally take place. For volumetric properties (compression factor and density), the uncertainty of calculation is about ± 0,1 % (95 % confidence interval). For caloric properties (for example enthalpy, heat capacity, Joule-Thomson coefficient, speed of sound), the uncertainty of calculation is usually greater.

Erdgas - Berechnung thermodynamischer Eigenschaften - Teil 1: Eigenschaften der Gasphase für Zwecke des Transports und der Verteilung (ISO 20765-1:2005)

Gaz naturel - Calcul des propriétés thermodynamiques - Partie 1: Propriétés de la phase gazeuse pour des applications de transport et de distribution (ISO 20765-1:2005)

L'ISO 20765-1:2005 spécifie une méthode de calcul des propriétés volumétriques et calorifiques des gaz naturels, de gaz naturels contenant un adjuvant synthétique et de mélanges similaires, dans des conditions telles que le mélange ne peut exister que sous forme gazeuse.
La méthode est applicable aux gaz de qualité réseau dans les plages de pression et de température auxquelles s'effectuent normalement les opérations de transport et de distribution. Pour les propriétés volumétriques (facteur de compression et masse volumique), l'incertitude de calcul avoisine ± 0,1 % (intervalle de confiance de 95 %). En revanche, l'incertitude de calcul est généralement plus élevée pour les propriétés calorifiques (par exemple l'enthalpie, la capacité thermique, le coefficient de Joule-Thomson, la vitesse du son).

Zemeljski plin - Izračun termodinamičnih lastnosti - 1. del: Lastnosti plinaste faze za prenos in distribucijo (ISO 20765-1:2005)

Ta del standarda ISO 20765 določa metodo za izračun volumetričnih in kaloričnih lastnosti zemeljskih plinov, zemeljskih plinov, ki vsebujejo sintetične dodatke, in podobnih mešanic pri pogojih, v katerih lahko mešanica obstaja samo v plinastem stanju.
Metoda se uporablja za pline iz cevovoda v razponu tlaka in temperature, v katerem običajno potekajo dejavnosti prenosa in distribucije. Negotovost izračuna za volumetrične lastnosti (kompresijski faktor in gostota) znaša približno ±0,1 % (95-odstotni interval zaupanja). Negotovost izračuna za kalorične lastnosti (na primer entalpija, toplotna kapaciteta, Joul-Thomsonov koeficient, hitrost zvoka) je običajno večja.

General Information

• Status: Published
• Public Enquiry End Date: 02-Feb-2017
• Publication Date: 07-Nov-2018
• ICS: 75.060 - Natural gas
• Technical Committee: DPL - Gas supply
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 29-Oct-2018
• Due Date: 03-Jan-2019
• Completion Date: 08-Nov-2018
• Ref Project: EN ISO 20765-1:2018 - Natural gas - Calculation of thermodynamic properties - Part 1: Gas phase properties for transmission and distribution applications (ISO 20765-1:2005)

Overview

EN ISO 20765-1:2018 (ISO 20765-1:2005 adopted by CEN) defines a standardized method to calculate thermodynamic properties of natural gas in the gas phase for transmission and distribution applications. The standard is intended for pipeline‑quality gases and sets out equations and procedures to compute volumetric properties (compression factor, density) and caloric properties (enthalpy, heat capacity, Joule–Thomson coefficient, speed of sound, etc.) for mixtures that remain in the single‑gas phase. The method is based on a fundamental Helmholtz free energy formulation and leverages the structure of the AGA8 approach to provide analytical derivatives for reliable implementation.

Key topics and requirements

• Scope: Gas‑phase thermodynamic properties for conditions typical of gas transmission and distribution; not for two‑phase or dense‑fluid ranges.
• Fundamental basis: Equation of state expressed as Helmholtz free energy (ideal + residual parts), enabling calculation of both volumetric and caloric properties from analytical derivatives.
• Composition input: Detailed molar (component) analysis - a 21‑component representation is specified; components with mole fraction > 0.00005 should normally be included.
• State variables: Temperature and pressure are typical inputs; the standard gives conversion procedures to density where required.
• Accuracy / uncertainty:
  • Volumetric properties (compression factor, density): ≈ ±0.1 % (95 % confidence).
  • Caloric properties: generally larger uncertainty; the standard documents the expected accuracy and how input uncertainty propagates.
• Implementation guidance: Analytical formulas and normative annexes provide symbols, equations, documentation and implementation notes to avoid numerical differentiation.
• Normative and informative annexes: Include the Helmholtz ideal gas formulation, detailed equation parameters, implementation examples and trace component assignment guidance.

Applications

• Pipeline and distribution network modeling: Accurate density and compressibility for flow and hydraulic calculations.
• Custody transfer and metering: Compression factor and density calculations for volume/energy conversion in billing.
• Energy and process simulations: Enthalpy and heat capacity data for thermodynamic modeling, pressure‑letdown and heating/cooling calculations.
• Instrumentation and software: Embedded in gas property libraries, flow computers, energy calculators and SCADA analytics.
• Regulatory and standards compliance: Harmonizes thermodynamic property calculations across operators and jurisdictions.

Who should use this standard

• Gas transmission and distribution engineers
• Metering and custody transfer specialists
• Energy accountants and auditors
• Software developers of gas property libraries and flow computers
• Laboratories performing gas analysis and property calculations
• Regulators and standards bodies specifying calculation methods

Related standards (examples)

• ISO 12213-2 (calculation of compression factor using molar composition)
• ISO 14532 / ISO 7504 (gas analysis and vocabulary)

Keywords: EN ISO 20765-1:2018, ISO 20765-1, natural gas thermodynamic properties, Helmholtz free energy, compression factor, gas density, enthalpy, heat capacity, AGA8, pipeline‑quality gas.

Standards Content (Sample)

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Erdgas - Berechnung thermodynamischer Eigenschaften - Teil 1: Eigenschaften der Gasphase für Zwecke des Transports und der Verteilung (ISO 20765-1:2005)Gaz naturel - Calcul des propriétés thermodynamiques - Partie 1: Propriétés de la phase gazeuse pour des applications de transport et de distribution (ISO 20765-1:2005)Natural gas - Calculation of thermodynamic properties - Part 1: Gas phase properties for transmission and distribution applications (ISO 20765-1:2005)75.060Zemeljski plinNatural gasICS:Ta slovenski standard je istoveten z:EN ISO 20765-1:2018SIST EN ISO 20765-1:2018en,fr,de01-december-2018SIST EN ISO 20765-1:2018SLOVENSKI
STANDARD
EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM
EN ISO 20765-1
September
t r s z ICS
y wä r x r English Version
Natural gas æ Calculation of thermodynamic properties æ Part
sã Gas phase properties for transmission and Gaz naturel æ Calcul des propriétés thermodynamiques æ Partie
sã Propriétés de la phase gazeuse pour des
Erdgas æ Berechnung thermodynamischer Eigenschaften æ Teil
sã Eigenschaften der Gasphase für This European Standard was approved by CEN on
u s August
t r s zä
egulations which stipulate the conditions for giving this European Standard the status of a national standard without any alterationä Upætoædate lists and bibliographical references concerning such national standards may be obtained on application to the CENæCENELEC Management Centre or to any CEN memberä
translation under the responsibility of a CEN member into its own language and notified to the CENæCENELEC Management Centre has the same status as the official versionsä
CEN members are the national standards bodies of Austriaá Belgiumá Bulgariaá Croatiaá Cyprusá Czech Republicá Denmarká Estoniaá Finlandá Former Yugoslav Republic of Macedoniaá Franceá Germanyá Greeceá Hungaryá Icelandá Irelandá Italyá Latviaá Lithuaniaá Luxembourgá Maltaá Netherlandsá Norwayá Polandá Portugalá Romaniaá Serbiaá Slovakiaá Sloveniaá Spainá Swedená Switzerlandá Turkey and United Kingdomä
EUROPEAN COMMITTEE FOR STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre:
Rue de la Science 23,
B-1040 Brussels
t r s z CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Membersä Refä Noä EN ISO
t r y x wæ sã t r s z ESIST EN ISO 20765-1:2018

Reference numberISO 20765-1:2005(E)© ISO 2005
INTERNATIONAL STANDARD ISO20765-1First edition2005-09-15Natural gas — Calculation of thermodynamic properties — Part 1: Gas phase properties for transmission and distribution applications Gaz naturel — Calcul des propriétés thermodynamiques — Partie 1: Propriétés de la phase gazeuse utilisée pour des applications de transport et de distribution
ISO 20765-1:2005(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems Incorporated. Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
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ISO 2005 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO's member body in the country of the requester. ISO copyright office Case postale 56 • CH-1211 Geneva 20 Tel.
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www.iso.org Published in Switzerland
ii
ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
iiiContents Page Foreword.iv Introduction.v 1 Scope.1 2 Normative references.1 3 Terms and definitions.1 4 Thermodynamic basis of the method.2 4.1 Principle.2 4.2 The fundamental equation of Helmholtz free energy.3 4.3 Thermodynamic properties derived from the Helmholtz free energy.5 5 Method of calculation.8 5.1 Input variables.8 5.2 Conversion from pressure to reduced density.9 5.3 Implementation.9 6 Ranges of application.10 6.1 Pressure and temperature.10 6.2 Pipeline quality gas.10 7 Uncertainty.11 7.1 Uncertainty for pipeline quality gas.11 7.2 Impact of uncertainties of input variables.14 8 Reporting of results.14 Annex A (normative)
Symbols and units.16 Annex B (normative)
The Helmholtz free energy of the ideal gas.19 Annex C (normative)
The equation for the Helmholtz free energy.22 Annex D (normative)
Detailed documentation for the equation of state.24 Annex E (informative)
Assignment of trace components.30 Annex F (informative)
Implementation of the method.32 Annex G (informative)
Examples.35 Bibliography.42
ISO 20765-1:2005(E) iv
ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
vIntroduction This part of ISO 20765 specifies methods for the calculation of thermodynamic properties of natural gases, natural gases containing synthetic admixture, and similar mixtures. This part of ISO 20765 has four normative annexes and three informative annexes.
INTERNATIONAL STANDARD ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
1Natural gas — Calculation of thermodynamic properties — Part 1: Gas phase properties for transmission and distribution applications 1 Scope This part of ISO 20765 specifies a method of calculation for the volumetric and caloric properties of natural gases, natural gases containing synthetic admixture and similar mixtures, at conditions where the mixture can exist only as a gas. The method is applicable to pipeline-quality gases within the ranges of pressure, p, and temperature, T, at which transmission and distribution operations normally take place. For volumetric properties (compression factor and density), the uncertainty of calculation is about ± 0,1 % (95 % confidence interval). For caloric properties (for example enthalpy, heat capacity, Joule-Thomson coefficient, speed of sound), the uncertainty of calculation is usually greater. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 31-3, Quantities and units — Part 3: Mechanics ISO 31-4, Quantities and units — Part 4: Heat ISO 7504, Gas analysis — Vocabulary ISO 12213-2, Natural gas — Calculation of compression factor — Part 2: Calculation using molar-composition analysis ISO 14532, Natural gas — Vocabulary 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO 31-4, ISO 7504 and ISO 14532 and the following apply. NOTE See Annex A for the list of symbols and units used in this part of ISO 20765. 3.1 caloric property characteristic of a gas or homogeneous gas mixture which can be calculated from a fundamental equation of state NOTE The caloric properties to which this part of ISO 20765 can be applied are internal energy, enthalpy, entropy, isochoric heat capacity, isobaric heat capacity, Joule-Thomson coefficient, isentropic exponent and speed of sound. SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) 2
1) ppm is a depredated unit. SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
34.2 The fundamental equation of Helmholtz free energy 4.2.1 Background The AGA8 equation [1] was published in 1992 by the Transmission Measurements Committee of the American Gas Association, having been designed specifically as a means for the high accuracy calculation of compression factor. In this respect, it is already the subject of ISO 12213-2. Since then it has become increasingly apparent that the equation has excellent potential for use in the calculation of all thermodynamic properties of natural gas, even though the accuracy of calculation is less well documented. In order for the AGA8 equation to become useful for the calculation of all thermodynamic properties, there are two major requirements. a) The equation itself, published initially in a form explicit only for volumetric properties, has to be mathematically recast in a form explicit for the residual Helmholtz free energy. In fact, although not published as such, the original development of the equation was as a fundamental equation in the form of Helmholtz free energy. This formulation [2] is essential in that all residual thermodynamic properties can be calculated from the Helmholtz free energy and its derivatives with respect to the state conditions of temperature and density. b) For the calculation of caloric properties, a formulation is required for the Helmholtz free energy of the ideal gas as a function of temperature. Most previous formulations for the ideal gas have been explicit in the isobaric heat capacity and so, again, the chosen formulation [3], [4] has to be recast so as to be explicit in the Helmholtz free energy. Again, derivatives of the Helmholtz free energy with respect to the state conditions are needed. An important aspect of the formulations chosen for both the ideal and residual parts of the Helmholtz free energy is that the derivatives required for calculating the thermodynamic properties can be given in analytical form. Hence, there is no need for numerical differentiation or integration within any computer program that implements the procedures. As a result, numerical problems are avoided and calculation times are shorter. The method of calculation described is very suitable for use within process simulation programs and, in particular, within programs developed for use in natural gas transmission and distribution applications. 4.2.2 The Helmholtz free energy The Helmholtz free energy, f, of a homogeneous gas mixture at uniform pressure and temperature can be expressed as the sum of a part f o describing the ideal gas behaviour and a part fr describing the residual or real-gas behaviour, as given in Equation (1): ()()()or,,,,,,fXfXfXρΤρΤρΤ=+ (1) which, rewritten in the form of dimensionless reduced free energy ϕ = f/(R⋅T), becomes Equation (2): ()()()or,,,,,,XXXϕδτϕδτϕδτ=+ (2) where X is a vector that defines the composition of the mixture; τ is the inverse (dimensionless) reduced temperature, related to the temperature, T, as given in Equation (3): /LTτ= (3) where L = 1 K. SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) 4
,
,,fTXhTXRTTsTXρρ=−⋅−⋅ (5) The enthalpy, ho, and entropy, so, can in turn be expressed in terms of the isobaric heat capacity, co,p, of the ideal gas as given in Equations (6) and (7), where the implied limits of integration are T and T: ()oo,po,, dhTXcTh=+∫ (6) o,poo,1(,,)dlnlnlnNiiicTsTXTRRsRxxTTρρρ=⎛⎞⎛⎞=−⋅−⋅+−⋅⋅⎜⎟⎜⎟⎝⎠⎝⎠∑∫ (7) The reference state of zero enthalpy and zero entropy is here adopted as T = 298,15 K and p = 0,101 325 MPa for the ideal unmixed gas. The integration constants, o,h and o,s, are then determined so as to conform to this definition. The reference (ideal) density, ρ, is given by ρ = p/(R⋅T). The reduced Helmholtz free energy ϕo = fo/(R⋅T) can then be written, using Equations (6) and (7), as a function of δ, τ and X, as given in Equation (8): ()o,po,po,o,o21,,d1dlnlnlnNiiicchsXxxRLRRRττδϕδτττττδττ=⋅⎛⎞⎛⎞=−+−+++−+⋅⎜⎟⎜⎟⋅⋅⋅⎝⎠⎝⎠∑∫∫ (8) See Annex B for details of this formulation. 4.2.4 The residual part of the Helmholtz free energy The residual part of the reduced Helmholtz free energy is obtained, for the purposes of this part of ISO 20765, by use of the AGA8 equation. Written for the compression factor as a function of reduced density, inverse reduced temperature and composition, the AGA8 equation has the form of Equation (9): ()()1858313131expnnnnnuubkknnnnnnnnBZCCbckcKδδττδδδ==⋅=+−⋅+⋅⋅−⋅⋅−⋅∑∑ (9) SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
5where B is the second virial coefficient; bn, cn, kn, un are coefficients of the equation and functions of composition; Cn is a function of composition. The compression factor, Z, is related to the residual part of reduced free energy, ϕr, as given in Equation (10): r,1Zδϕδ=+⋅ (10) where r,ϕδis the partial derivative of ϕr with respect to reduced density at constant 2 and X. Elimination of Z between Equations (9) and (10), and integration with respect to reduced density leads to the Equation (11) for the residual part of the reduced Helmholtz free energy: 1858r31313(,,)exp()nnnnuubknnnnnBXCCcKδϕδτδττδδ==⋅=−⋅+⋅⋅−⋅∑∑ (11) See Annexes C and D for details of this formulation. 4.2.5 The reduced Helmholtz free energy The fundamental equation [Equation (2)] for the reduced Helmholtz free energy, ϕ, makes it possible, through use of Equation (8) for the ideal part, ϕo, and Equation (11) for the residual part, ϕr, to calculate all thermodynamic properties analytically. The reduced Helmholtz free energy, ϕ=, =therefore can be written as given in Equation (12): ()o,po,po,o,21185831313,,d1dlnlnln.exp()nnnnNiiiuubknnnnncchsXxxRRRRBCCcKττδϕδτττττδττδδττδδ===⋅⎛⎞⎛⎞=−+−+++−+⋅+⎜⎟⎜⎟⋅⋅⎝⎠⎝⎠⋅+−⋅+⋅⋅−⋅∑∫∫∑∑ (12) 4.3 Thermodynamic properties derived from the Helmholtz free energy 4.3.1 Background All of the thermodynamic properties can be written explicitly in terms of the reduced Helmholtz free energy, ϕ, and various derivatives thereof. The required derivatives, ϕτ, ϕττ, ϕδ=, ϕδδ and ϕτδ, are defined as given in Equations (13): ,Xϕϕττδ∂⎛⎞=⎜⎟⎝⎠∂
22,Xϕϕτττδ⎛⎞∂=⎜⎟∂⎝⎠
,Xϕϕδδτ∂⎛⎞=⎜⎟⎝⎠∂
22,Xϕϕδδδτ⎛⎞∂=⎜⎟∂⎝⎠
,X,Xϕϕτδτδτδ⎡⎤∂∂⎛⎞=⎢⎥⎜⎟⎝⎠∂∂⎢⎥⎣⎦ (13) Each derivative is the sum of an ideal part (see Annex B) and a residual part (see Annex C). The substitutions given in Equations (14) and (15) help to simplify the appearance of the relevant relationships: ()221,X2δϕϕδϕδϕδδδδδτ⎡⎤∂⋅⎢⎥==⋅⋅+⋅⎢⎥∂⎢⎥⎣⎦ (14) SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) 6
ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
74.3.2.3 Enthalpy The expression for the enthalpy, h, is given by Equation (20): hHMRTRTuUMZZRTRTτϕδϕτδ⋅=⋅⋅=⋅+⋅⋅=+=+⋅⋅ (20) 4.3.2.4 Entropy The expression for the entropy, s, is given by Equation (21): sSMRRuUMRTRTτϕϕϕϕτ⋅==⋅−⋅=−=−⋅⋅ (21) 4.3.2.5 Isochoric heat capacity The expression for the isochoric heat capacity, cv, is given by Equation (22): 2vvcCMRRτϕττ⋅==−⋅ (22) 4.3.2.6 Isobaric heat capacity The expression for the isobaric heat capacity, cp, is given by Equation (23): pp22212v212v21cCMRRcRCMRϕτϕϕϕϕϕϕττ⋅==−⋅+=+⋅=+ (23) 4.3.2.7 Joule-Thomson coefficient The expression for the Joule-Thomson coefficient, µ, is given by Equation (24): ()2122212p12p111RDRMRcRCMµµρϕϕϕτϕϕϕϕϕϕττ⋅⋅⋅⋅=−=−⋅⋅⎛⎞=−⎜⎟⎝⎠⎛⎞=−⎜⎟⋅⎝⎠ (24) SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) 8
ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
9If the mole fractions of heptanes, octanes, nonanes and decanes are unknown, then the use of a composite C6+ fraction may be acceptable. The user should carry out a sensitivity analysis in order to test whether a particular approximation of this type degrades the result. NOTE If the composition is known by volume fractions, these will need to be converted to mole fractions using the method given in ISO 6976 [5]. 5.2 Conversion from pressure to reduced density Combination of Equations (4), (9) and (18) results in Equation (27): ()()18583313131expnnnnnuubkknnnnnnnnpKBZCCbckcRLKτδδττδδδδ==⋅⋅⋅==+−⋅+⋅⋅−⋅⋅−⋅⋅⋅∑∑ (27) If the input variables are available as pressure, inverse reduced temperature and composition, Equation (27) may be solved for the reduced molar density, δ.= The variable quantities B(2,X), Cn(X), K(X) and the coefficients bn, cn, kn and un in Equation (27) may be obtained from equations and tabulations given in Annex D (Equations (D.1), (D.6) and (D.11), and Table D.1, respectively) for these quantities. Numerical values for all pure-component and binary interaction parameters that are also required for the evaluation of Equations (D.1), (D.6) and (D.11) are given in Tables D.2 and D.3, respectively. The solution may be obtained by any suitable numerical method but, in practice, a standard form of equation-of-state density-search algorithm may be the most convenient and satisfactory. Such algorithms usually use an initial estimate of the density (often the ideal-gas approximation) and proceed, by iterative calculations of p and δ, in order to find the value of δ that reproduces the known value of p to within a pre-established level of agreement. A suitable criterion in the present case is that the pressure calculated from the calculated reduced molar density, δ, shall reproduce the input value of p to within 1 part in 106. 5.3 Implementation The required set of input variables is now available. With this revised set of input variables, reduced density, δ, inverse reduced temperature, 2, and composition, X, it is now possible to use the fundamental equation to calculate the reduced Helmholtz free energy and the other thermodynamic properties. Equation (12) formulates the reduced Helmholtz free energy as ϕ = ϕo + ϕr. Equation (11) formulates the residual part of the Helmholtz free energy ϕr as a function of reduced density, δ, inverse reduced temperature, 2, and the molar composition, X. The ideal part, ϕo, formulated in Equation (8), may be developed as given by Equation (B.3) of Annex B so as to express ϕ as given in Equation (28): {}o,1o,2o,o,o,o,o,1o,o,o,o,18313()()lnlnsinh()lncosh().lnsinh()lncosh()lnlnln.nNiiiiiiiiiiiiiiunnnxAABCDEFGHIJxBCCKϕτττττδττδτδδτ=θθ=⎡⎤⎡⎤=⋅+⋅+⋅+⋅⋅−⋅⋅+⎣⎦⎣⎦⎛⎞⎛⎞⎡⎤⎡⎤+⋅⋅−⋅⋅++++⎜⎟⎜⎟⎣⎦⎣⎦⎝⎠⎝⎠⋅+−⋅+⋅∑∑5813exp()nnnubknncτδδ=⋅−⋅∑ (28) Values for all of the coefficients o,1()iA, o,2()iA and Bo,i to Jo,i for the ideal gas are given in Annex B for all of the 21 possible component gases. Derivatives of ϕ==with respect to (reduced) density and (inverse reduced) temperature, which are needed for the evaluation of the various thermodynamic properties, may be obtained from Equations (C.2) to (C.6) given in Annex C. Finally, the various thermodynamic properties may be evaluated by means of Equations (17) to (26). Values for the coefficients bn, cn, kn and un and the quantities Cn, which are functions of composition, are given in Annex D. A more detailed description of the implementation procedure is given in Annex F. SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) 10
6.2 Pipeline quality gas Pipeline quality gas shall be taken as a natural (or similar) gas with mole fractions of the various major and minor components that fall within the ranges given in Table 2. Possible trace components of natural gases, and details of how to deal with these, are discussed in Annex E. The total combined content of all trace components shall not exceed 0,000 5 mole fraction. Table 2 — Ranges of mole fractions for major and minor components of natural gas Number i Component Range mole fraction 1 nitrogen 0 u xN2 u 0,20 2 carbon dioxide 0 u xCO2 u 0,20 3 methane 0,7 u xCH4 u 1,00 4 ethane 0 u xC2H6 u 0,10 5 propane 0 u xC3H8 u 0,035 6 + 7 n-butane + iso-butane 0 u xC4H10 u 0,015 8 + 9 n-pentane + iso-pentane 0 u xC5H12 u 0,005 10 n-hexane 0 u xC6H14 u 0,001 11 n-heptane 0 u xC7H16 u 0,000 5 12 + 13 + 14 n-octane + n-nonane + n-decane 0 u xC8+ u 0,000 5 15 hydrogen 0 u xH2 u 0,10 17 carbon monoxide 0 u xCO u 0,03 18 water 0 u xH2O u 0,000 15 20 helium 0 u xHe u 0,005 16 oxygen 0 u xO2 u 0,000 2 19 hydrogen sulfide 0 u xH2S u 0,000 2 21 argon 0 u xAr u 0,000 2 SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
117 Uncertainty 7.1 Uncertainty for pipeline quality gas 7.1.1 Uncertainty diagrams for methane As a guide to the uncertainty which may be expected for mixtures containing a mole fraction of methane close to unity, Figures 1 to 3 present uncertainty diagrams for pure methane for compression factor, speed of sound and enthalpy, respectively. The uncertainty, expressed as a 95 % confidence limit, given for each region represents the largest value within the region of the sum of (a) the uncertainty in well-documented reference data, and (b) the difference between the reference data and the value of the property calculated using the method presented in this part of ISO 20765. The reference data used are calculated from equations given in Reference [6].
Key X temperature, expressed in kelvin Y pressure, expressed in megapascals a Region of uncertainty of ± 0,08 %. b Region of uncertainty of ± 0,04 %. Figure 1 — Uncertainty diagram for Z, the compression factor of methane
Key X temperature, expressed in kelvin Y pressure, expressed in megapascals a Region of uncertainty of ± 0,20 %. b Region of uncertainty of ± 0,05 %. Figure 2 — Uncertainty diagram for w, the speed of sound of methane SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) 12
Key X temperature, expressed in kelvin Y pressure, expressed in megapascals a Region of uncertainty of ± 3 kJ/kg. b Region of uncertainty of ± 2 kJ/kg. c Region of uncertainty of ± 1 kJ/kg. Figure 3 — Uncertainty diagram for H, the enthalpy of methane 7.1.2 Uncertainty diagrams for natural gas As a guide to the uncertainty that can be expected for natural gases, Figures 4, 5 and 6 present uncertainty diagrams for compression factor, speed of sound and enthalpy, respectively. The uncertainty, expressed as a 95 % confidence limit, given for each region represents the largest difference, for a wide range of natural gases, between the directly measured property and the value calculated using the method presented in this part of ISO 20765. For the compression factor, the directly measured values are taken from Reference [7]; for speed of sound, the values are taken from Reference [8] and for the enthalpy, the values are taken from Reference [9]. NOTE 1 For all gases, the uncertainty diagram for density is identical in form to that for compression factor. NOTE 2 For all gases, the uncertainty in the isentropic exponent is approximately twice the uncertainty in speed of sound. SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
13 Key X temperature, expressed in kelvin Y pressure, expressed in megapascals a Region of uncertainty of ± 0,4 %. b Region of uncertainty of ± 0,2 %. c Region of uncertainty of ± 0,1 %. Figure 4 — Uncertainty diagram for Z, the compression factor of natural gas
Key X temperature, expressed in kelvin Y pressure, expressed in megapascals a Region of uncertainty of ± 2,0 %. b Region of uncertainty of ± 0,8 %. c Region of uncertainty of ± 0,2 %. Figure 5 — Uncertainty diagram for w, the speed of sound of natural gas SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) 14
Key X temperature, expressed in kelvin Y pressure, expressed in megapascals a Region of uncertainty of ± 3 kJ/kg. b Region of uncertainty of ± 2 kJ/kg. Figure 6 — Uncertainty diagram for H, the enthalpy of natural gas For properties other than compression factor, density (for which the uncertainty diagram is the same as for compression factor), speed of sound and enthalpy, the paucity of experimental data of good (reference) quality makes it impossible to provide definitive numerical estimates of uncertainty. Nevertheless, it is possible to offer some guidelines. For gases at low pressures (below, say, 1 MPa) having approximately ideal behavior (compression factor greater than, say, 0,95), it is reasonable to expect all of the caloric properties to be predicted with a low uncertainty. This follows from the fact that, in this restricted case, the greater part of each property derives from the ideal part of the Helmholtz free energy that, being derived directly from high-accuracy data for the ideal isobaric heat capacity (see Annex B), is itself known with high accuracy. In this case, the density, compression factor, speed of sound, isochoric and isobaric heat capacities, isentropic exponent and Joule-Thomson coefficient are probably all predicted within 0,1 %. 7.2 Impact of uncertainties of input variables The user should recognize that uncertainties in the input variables, usually pressure, temperature and composition by mole fractions, will have additional effects upon the uncertainty of any calculated result. In any particular application where the additional uncertainty could be of importance, the user should carry out sensitivity tests to determine its magnitude. 8 Reporting of results When reported in accordance with the units given in Annex A, results for the thermodynamic properties shall be quoted with the number of digits after the decimal point as given in Table 3. The report shall identify the temperature, pressure (or density) and detailed composition to which the results refer. The method of calculation used shall be identified by reference to this document, e.g. ISO 20765-1. For validation of computational procedures, it can be useful to carry extra digits (see example calculations in Annex G). SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
15Table 3 — Reporting of results Symbol Property Units Decimal places Z compression factor — 4
molar density kmol/m3 3 D density kg/m3 2 u molar internal energy kJ/kmol 0 U specific internal energy kJ/kg 1 h molar enthalpy kJ/kmol 0 H specific enthalpy kJ/kg 1 s molar entropy kJ/(kmol·K) 2 S specific entropy kJ/(kg·K) 3 cv molar isochoric heat capacity kJ/(kmol·K) 2 Cv specific isochoric heat capacity kJ/(kg·K) 3 cp molar isobaric heat capacity kJ/(kmol·K) 2 Cp specific isobaric heat capacity kJ/(kg·K) 3 µ Joule-Thomson coefficient K/MPa 2
isentropic exponent — 2 w speed of sound m/s 1 SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) 16
Symbols and units Symbol Meaning Source of values Units an constants in Equations (D.2) and (D.6) Table D.1 --- (Ao,1)i coefficient in the ideal gas equation [Equation (B.3)] Table B.1 --- (Ao,2)i coefficient in the ideal gas equation [(Equation (B.3)] Table B.1 --- bn constants in the real gas equation [(Equation (9)] Table D.1 --- B second virial coefficient Equation (D.1) m3/kmol Bo,i coefficient in the ideal gas equation [Equation (B.3)] Table B.1 --- *nB quantities in Equation (D.1) Equation (D.2) --- *nijB binary interaction parameter in Equation (D.2) Equation (D.3) --- cn constants in the real gas equation [Equation (9)] Table D.1 --- cp molar isobaric heat capacity Equation (23) kJ/(kmol·K) cv molar isochoric heat capacity Equation (22) kJ/(kmol·K) Co,i coefficient in the ideal gas equation [Equation (B.3)] Table B.1 --- Cn coefficients in the real gas equation [Equation (9)] Equation (D.6) --- Cp specific isobaric heat capacity Equation (23) kJ/(kg·K) Cv specific isochoric heat capacity Equation (22) kJ/(kg·K) D specific (mass) density Equation (18) kg/m3 Do,i coefficient in the ideal gas equation [Equation (B.3)] Table B.1 --- Ei energy parameter in Equations (D.4) and (D.7) Table D.2 --- Eo,i coefficient in the ideal gas equation [Equation (B.3)] Table B.1 --- Eij binary interaction energy parameter in Equation (D.2) Equation (D.4) --- *nijE binary interaction energy parameter in Equation (D.4) Table D.3 --- f molar Helmholtz free energy Equation (1) kJ/kmol fn constants in Equations (D.3) and (D.6) Table D.1 --- F constant in Equation (D.6) Equation (D.10) --- Fi high temperature parameter in Equations (D.3) and (D.10) Table D.2 --- Fo,i coefficient in the ideal gas equation [Equation (B.3)] Table B.1 --- gn constants in Equations (D.3) and (D.6) Table D.1 --- G constant in Equation (D.6) Equation (D.8) --- Gi orientation parameter in Equations (D.5) and (D.8) Table D.2 --- Go,i coefficient in the ideal gas equation [Equation (B.3)] Table B.1 --- Gij binary interaction orientation parameter in Equation (D.3) Equation (D.5) --- *nijG binary interaction orientation parameter in
Equations (D.5) and (D.8) Table D.3 --- SIST EN ISO 20765-1:2018

ISO 20765-1:2005(E) © ISO 2005 – All rights reserved
17h molar enthalpy Equation (20) kJ/kmol H specific enthalpy Equation (20) kJ/kg Ho,i coefficient in the ideal gas equat
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