AGA 8 PART 2-2017 Thermodynamic Properties of Natural Gas and Related Gases GERG C2008 Equation of State (First Edition XQ1704-2).pdf

1、 AGA Report No. 8 Thermodynamic Properties of Natural Gas and Related Gases GERG2008 Equation of State First Edition April 2017 Prepared by Transmission Measurement Committee Part 2 AGA Report No. 8 Part 2 Thermodynamic Properties of Natural Gas and Related Gases GERG2008 Equation of State Prepared

2、by Transmission Measurement Committee First Edition April 2017 Copyright 2017 American Gas Association All Rights Reserved Catalog No. XQ1704-2 ii iii DISCLAIMER AND COPYRIGHT The American Gas Associations (AGA) Operations and Engineering Section provides a forum for industry experts to bring their

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15、ggested revisions in an amended publication of the document. Copyright 2017, American Gas Association, All Rights Reserved. iv FOREWORD AGA Report No. 8, Part 2, provides technical information necessary to compute thermodynamic properties including compressibility factors, densities, speeds of sound

16、, and dew and bubble points for natural gas and related gases. It is based on the research performed at the Ruhr University in Bochum, Germany, and published in 2006 as the doctoral dissertation of Oliver Kunz under the direction of Prof. Dr.-Ing. Wolfgang Wagner. The equations in the dissertation a

17、re commonly referred to as the GERG-2004 and GERG-2008 equations of state in acknowledgement of partial sponsorship of the research by the Groupe Europeen de Recherches Gazieres (GERG). Because these equations are used both in this document and the International Standards Organization document ISO 2

18、0765: Natural Gas Calculation of Thermodynamic Properties, Part 2: Single-Phase Properties (Gas, Liquid, and Dense Fluid) for Extended Ranges of Application, 2015 edition, calculations of properties should have the same values. The companion publication, AGA Report No. 8, Part 1, provides calculatio

19、n methods for the DETAIL and GROSS equations of state as in the 1994 edition of AGA Report No. 8, but the temperature, pressure, and composition limits for different levels of uncertainties have been modified. The documentation of programs for calculating properties from the methods described in thi

20、s 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 composi

21、tion, 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 r

22、elated 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. Some material described in Part 2 also applies to Part 1, and vice versa, and is

23、 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 in Part 2 (and which is applied for this purpose to the GROSS, DETAIL, and GERG-2008 equations of state in the programs in the suppl

24、ementary material). Similarly, Part 2 outlines the method for reporting calculated results and uncertainties from the equations in both parts, and also describes the experimental database available for natural gas mixtures (both binary and multicomponent systems), much of which was used in the devel

25、opment 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 whereas Part 2 extends these ranges to cover all mole fractions of these components in both the vapor and liquid phases. As with the DETAIL eq

26、uation of state in Part 1, use of the GERG-2008 equation in Part 2 requires that the mixture be completely characterized by a component analysis before thermodynamic properties can be calculated. Because the mixture model combines the contributions from the pure fluid equations of state, the composi

27、tion must be specified for each component. For a C6+ fraction, the amount of the fraction must be distributed among the heavy hydrocarbons. For a typical natural gas, this might include alkane hydrocarbons up to about C7 or C8 together with nitrogen and carbon dioxide. Additional components includin

28、g nonane, decane, water, hydrogen sulfide, and helium may be present, and should not be lumped with other components as their presence can have a significant impact on some properties. Dew and bubble-points are influenced by the presence of the cryogens hydrogen, carbon monoxide, and oxygen in manuf

29、actured gases. Trace components other than the 21 available in the model must be reassigned appropriately depending on the desired properties (see Section 8). Alkane isomers are typically combined by molar mass or boiling point with the normal alkanes and treated collectively for density or VLE appl

30、ications. The use of a composite C6+ fraction for the heavy hydrocarbon compounds may be sufficient for density or speed of sound calculations, but detrimental in the determination of the dew point. Vapor-liquid equilibrium (VLE) calculations (which includes dew points) are most accurate when the co

31、mpositions are known for all of the components in the mixture. Small amounts of heptanes, octanes, nonanes, decanes, and water have a significant impact on the dew-point state of the mixture. Analyses of the sensitivity of VLE calculations can help determine whether a particular approximation is sui

32、table for a particular application. The independent variables in the Helmholtz energy equation of state are density, temperature, and molar composition. These properties must be known before all other thermodynamic properties can be calculated directly. When only pressure, temperature, and molar com

33、position are available as the input variables, it is necessary to use an iterative solution to determine the density required as the independent variable in the equation of state. Multiple iterative solutions are available for such density-search algorithms, with the appropriate method dependent on

34、the complexity of an application. If all state points are known to be single phase and within the gas region, the most successful search algorithms generally make use of the first and possibly second derivatives of pressure with respect to density to quickly locate the root. Away from the critical r

35、egion, such an algorithm can converge within four to six steps depending on the value of the initial guess, the magnitude of the pressure or density (with dense states requiring additional steps to locate the root), and the desired tolerance in the search algorithm. Multi-term equations of state hav

36、e several roots in the two-phase region, and verification that a root is stable adds to the complexity of the procedure. The composition in mole fractions is required for the following 21 components: methane, nitrogen, carbon dioxide, ethane, propane, isobutane, n-butane, isopentane, n-pentane, n-he

37、xane, n-heptane, n-octane, n-nonane, n-decane, hydrogen, oxygen, carbon monoxide, water, hydrogen sulfide, helium, and argon. The allowable ranges of mole fractions are defined in Section 5. The compositions of all mole fractions shall sum to one. Compositions given in volume or mass fractions need

38、to be converted to mole fractions, see GPA 2177, Analysis of Natural Gas Liquid Mixtures Containing Nitrogen and Carbon Dioxide by Gas Chromatography or ISO 14912, Gas Analysis Conversion of Gas Mixture Composition Data. 3 2 DEFINITIONS AND GENERAL EQUATIONS 2.1 Definitions of Phase Regions As in Pa

39、rt 1, Part 2 puts forth a new approach to define the gas phase, dense phase, and liquid phase of a mixture. Figure 1 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 n

40、onane 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 when the path is such that it does not cross the phase boundary, defin

41、ed regions are useful to give a general indication of the fluids 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 groups po

42、int of view. Most of these bounding techniques 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. As shown in Figure 1, the three phase regions are now define

43、d 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

44、 125 % of the critical density. The dense phase of a fluid is any single-phase 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 1, including the cricondentherm (maximum 2-phase t

45、emperature), 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

46、 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

47、 can be used to determine the critical density of a mixture, such as the tools available in Reference 4 that use the GERG-2008 equation of state 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 th

48、at is in the general vicinity of the true critical point of the mixture when volume translation 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 density would then be the reciprocal of the critical volume)

49、. The approach taken depends on the needs of a particular application. 4 Figure 1. Example of gas, liquid, and dense phase regions of a natural gas mixture. 2.2 Nomenclature a Molar Helmholtz energy (J/mol) B Second virial density coefficient (dm3/mol) c Density exponent cp Molar isobaric heat capacity J/(molK) cv Molar isochoric heat capacity J/(molK) C Third virial coefficient (dm6/mol2) d Molar density (mol/dm3) d Density exponent Dc Critical density (mol/dm3) fi Fugacity of component i (MPa) F Mixture parameter g Molar Gibbs energy (J/mol) h Molar enthalpy (J/mol)