# ISO 20765-1-2005

Reference number ISO 20765-12005E © ISO 2005INTERNATIONAL STANDARD ISO 20765-1 First edition 2005-09-15 Natural 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 20765-12005E 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 pering 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. 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ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. 41 22 749 01 11 Fax 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii © ISO 2005 – All rights reservedISO 20765-12005E © ISO 2005 – All rights reserved iii Contents Page Foreword iv Introduction v 1 Scope 1 2 Normative references 1 3 Terms and definitions .1 4 Thermodynamic basis of the 2 4.1 Principle2 4.2 The fundamental equation of Helmholtz free energy.3 4.3 Thermodynamic properties derived from the Helmholtz free energy 5 5 of calculation8 5.1 variables8 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 variables 14 8 Reporting of results.14 Annex A normative Symbols and units16 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 inative Assignment of trace components .30 Annex F inative Implementation of the .32 Annex G inative Examples .35 Bibliography 42 ISO 20765-12005E iv © ISO 2005 – All rights reservedForeword ISO the International Organization for Standardization is a worldwide federation of national standards bodies ISO member bodies. The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission IEC on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 20765-1 was prepared by Technical Committee ISO/TC 193, Natural gas, Subcommittee SC 1, Analysis of natural gas. ISO 20765 consists of the following parts, under the general title Natural gas Calculation of thermodynamic properties ⎯ Part 1 Gas phase properties for transmission and distribution applications The following parts are under preparation ⎯ Part 2 Single phase properties gas, liquid and dense-fluid for extended ranges of application ⎯ Part 3 Two-phase properties vapour-liquid equilibria ISO 20765-12005E © ISO 2005 – All rights reserved v Introduction This part of ISO 20765 specifies s 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 anns and three inative anns. INTERNATIONAL STANDARD ISO 20765-12005E© ISO 2005 – All rights reserved 1 Natural gas Calculation of thermodynamic properties Part 1 Gas phase properties for transmission and distribution applications 1 Scope This part of ISO 20765 specifies a 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 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. ISO 20765-12005E 2 © ISO 2005 – All rights reserved3.2 equation of state mathematical relationship between state variables of a gas or homogeneous gas mixture NOTE In this part of ISO 20765, it is useful to distinguish between two types of equation of state, namely 1 volumetric equation of state, in which the relationship is between the state variables pressure, temperature and the volume occupied by a given amount of substance, and 2 fundamental equation of state, in which the relationship is between the density, temperature and the Helmholtz free energy. 3.3 residual property that part of a thermodynamic property which results from the non-ideal real-gas behaviour of a gas or homogeneous gas mixture, i.e. the difference between a thermodynamic property of a real gas or gas mixture and the same thermodynamic property for the same gas or gas mixture, in the ideal state, at the same state conditions of temperature and density 3.4 thermodynamic property volumetric or caloric property 3.5 volumetric property characteristic of a gas or homogeneous gas mixture that can be calculated from a volumetric equation of state NOTE The volumetric properties to which this part of ISO 20765 can be applied are compression factor and density. 4 Thermodynamic basis of the 4.1 Principle The recommended is based on the concept that pipeline-quality natural gas is completely characterized for the calculation of its thermodynamic properties by component analysis. Such an analysis, together with the state variables of temperature and density, provides the necessary data for the . In practice, the state variables available as data are more usually temperature and pressure and, in this case, it is necessary first to convert these to temperature and density. Equations are presented which express the Helmholtz free energy of the gas as a function of density, temperature and composition, from which all of the thermodynamic properties can be obtained in terms of the Helmholtz free energy and its derivatives with respect to temperature and density. The uses a detailed molar composition analysis in which all components present in amounts exceeding 0,000 05 mole fraction [50 molar ppm 1 ] should be represented. For a typical natural gas, this might include alkane hydrocarbons up to about C 7or C 8 , together with nitrogen, carbon dioxide and helium. Typically, isomers for alkanes above C 5may be lumped together by molecular weight and treated collectively as the normal isomer. For some natural gases, it may be necessary to take into consideration additional components such as C 9and C 10hydrocarbons, water vapour and hydrogen sulfide. For manufactured gases, hydrogen and carbon monoxide should be considered. More precisely, the uses a 21-component analysis in which all of the major and minor components of natural gas are included see 6.2. Any trace component present but not identified as one of the 21 specified components may be reassigned appropriately to a specified component. 1ppm is a depredated unit. ISO 20765-12005E © ISO 2005 – All rights reserved 3 4.2 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 explicit only for volumetric properties, has to be mathematically recast in a 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 of Helmholtz free energy. This ulation [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 ulation is required for the Helmholtz free energy of the ideal gas as a function of temperature. Most previous ulations for the ideal gas have been explicit in the isobaric heat capacity and so, again, the chosen ulation [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 ulations 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 . 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 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 uni pressure and temperature can be expressed as the sum of a part fodescribing the ideal gas behaviour and a part f rdescribing the residual or real-gas behaviour, as given in Equation 1 or ,, ,, ,, f Xf Xf X ρΤ ρΤ ρΤ 1 which, rewritten in the of dimensionless reduced free energy ϕ f /R⋅T, becomes Equation 2 or ,, ,, ,, XXX ϕδτ ϕ δτ ϕ δτ 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 / L T τ 3 where L 1 K. ISO 20765-12005E 4 © ISO 2005 – All rights reservedNote that Equations 1 and 2 are written in terms of the molar density, ρ , and reduced density, δ, respectively, not in terms of the more commonly available variable of pressure, p. This is because, from statistical thermodynamics, the Helmholtz free energy appears as a natural consequence of the number and types of molecular interactions in a mixture and, therefore, becomes a natural function of the molar density and mole fractions of the molecules. The reduced density, δ, is related to the molar density, ρ, as shown in Equation 4 3 K δ ρ ⋅ 4 where K is a mixture size parameter. The ideal part, ϕ o , of the reduced Helmholtz free energy is obtained from equations for the isobaric heat capacity in the ideal gas state see 4.2.3, and the residual part, ϕ ris , from the AGA8 equation of state see 4.2.4. 4.2.3 The Helmholtz free energy of the ideal gas The Helmholtz free energy of an ideal gas can be expressed in terms of the enthalpy, h o , and entropy, s o , as given in Equation 5 ooo ,, , ,, f TX hTX RTTs TX ρρ − ⋅ − ⋅ 5 The enthalpy, h o , and entropy, s o , can in turn be expressed in terms of the isobaric heat capacity, c o,p , of the ideal gas as given in Equations 6 and 7, where the implied limits of integration are T θand T oo , po , θ , d hTX c Th ∫6 o,p oo , θ θθ 1 ,, d l n l n l n N ii i c T s TX T R R s R x x TT ρ ρ ρ ⎛⎞ ⎛⎞ − ⋅− ⋅− ⋅⋅ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ∑ ∫7 The reference state of zero enthalpy and zero entropy is here adopted as T θ 298,15 K and p θ 0,101 325 MPa for the ideal unmixed gas. Th