Prof. Wagner
Software for the Reference Equation of State GERG2008 for Natural Gases and Other Mixtures
Information about the several Windows operating systems and Excel versions are given at the end of this software description.
For the description of the reference equation of state GERG2008 for natural gases and other mixtures see this page.
For the reference equation of state GERG2008 for natural gases and similar mixtures, software is available that allows the calculation of more than 20 thermodynamic properties of binary mixtures, natural gases and other multicomponent mixtures. These mixtures can be composed of any of the 21 components listed in the following table. The software enables to calculate thermodynamic properties in the homogeneous gas, liquid and supercritical regions, and allows to perform vapourliquid equilibrium (VLE) calculations. The VLE calculation options comprise flash, phase envelope, dew point and bubble point calculations for any binary and multicomponent mixture defined above.
The software package contains a dynamic link library (DLL) and a Microsoft Excel AddIn. With the AddIn file, the property functions exported by the DLL can be added to the standard function volume of Microsoft Excel. This allows for a very simple use of the DLL from within Microsoft Excel. Furthermore, all of the exported property functions and subroutines of the DLL can be called from userspecific programs written in Fortran, C and Visual Basic. A corresponding import library file provides the information that is required for this purpose.
There are two software versions available:
• A “classical” version, where the pressure p, temperature T and total composition x (mole fractions) are the input quantities.
• An advanced version, where in addition to pressure, temperature and total composition (p,T,x ), the following combinations of input quantities can be used:
 pressure, total enthalpy and total composition (p,h,x )
 pressure, total entropy and total composition (p,s, x )
 temperature, total volume and total composition (T,v,x )
 total internal energy, total volume and total composition (u,v,x ).
The routines developed for these additional calculation options are based on special algorithms that use modern numerical procedures. They enable fast and stable property calculations. The input variables (p,h,x ) and (p,s,x ) are of particular interest for compressor and flow calculations.
For given values of the input quantities (p,T,x ) in the classical version, or (p,T,x ), (p,h,x ), (p,s,x ), (T,v,x ) and (u,v,x ) in the advanced version, the following thermodynamic properties of binary and multicomponent mixtures can be calculated with the help of the DLL:
ρ 
Density 
v 
Volume 
Z 
Compressibility factor 
h 
Enthalpy 
s 
Entropy 
c_{p} 
Isobaric heat capacity 
c_{v} 
Isochoric heat capacity 
w 
Speed of sound 
κ 
Isentropic exponent, κ = − (v/p) (∂p/∂v)_{s} 
μ 
JouleThomson coefficient; μ = (∂T/∂p)_{h} 
_{δT} 
isothermal throttling coefficient; δ_{T }= (∂h/∂p)_{T } 
u 
Internal energy 
g 
Gibbs free energy, g = h − Ts 
a 
Helmholtz free energy, a = u − Ts 
(∂p/∂T)_{ρ} 
Partial derivative of pressure with respect to temperature at constant density 
(∂p/∂ρ)_{T} 
Partial derivative of pressure with respect to density at constant temperature 
(∂ρ/∂T)_{p} 
Partial derivative of density with respect to temperature at constant pressure 
(∂p/∂v)_{T} 
Partial derivative of pressure with respect to volume at constant temperature 
(∂v/∂T)_{p} 
Partial derivative of volume with respect to temperature at constant pressure 
(∂s/∂p)_{T} 
Partial derivative of entropy with respect to pressure at constant temperature 
f_{i} 
Fugacity of component i 
ln φ_{i} 
Logarithm of the fugacity coefficient of component i, φ_{i} =f_{i}/(x_{i} p) 
ln K_{i} 
Logarithm of the Kfactor of component i, K_{i} = y_{i}/x_{i} 
β 
Molar vapour fraction, β = n _{vap}/n _{tot} 
β_{m} 
Mass vapour fraction, β_{m} = m _{vap}/m _{tot} 
β_{v} 
Volume vapour fraction, β_{v} = v _{vap}/v _{tot} 
M 
Molar mass 
All these properties can be calulated as molar or specific values.
Examples of calculations executed with the software are shown as screenshots on this page.
The DLL and the die ExcelFiles .xla, .xlam, .xls, xlsm are configurated in such away that they can be used under the several Windows operating systems [Windows 2000 to XP (32 Bit) Windows 7 and 8 (32 Bit/64 Bit)] and under the several Excel versions [2003 to 2013 (32 Bit)].
The GERG2008 software is now available as a 64Bit version, which can be, under the 64Bit operating systems of Windows XP to Windows 2010 and the supplied 64bit Excel Addins, incorporated into the 64Bit versions of Excel 20102016. Using the supplied LIB file, the software can also be integrated into other 64Bit applications (e.g. Matlab).
.Net DLLs are also available.
The software for GERG2008 is not free of charge.
Contact :
Prof. em. Dr.Ing. W. Wagner
Tel. +49 (0)234 3229033
Fax +49 (0)234 3214945
This email address is being protected from spambots. You need JavaScript enabled to view it.
Range of Validity and Estimated Uncertainties of the Equation of State GERG2008
The equation of state GERG2008 are valid in the gas phase, in the liquid phase, in the supercritical region and for vapourliquid equilibrium (VLE) states. The entire range of validity regarding the calculation of thermodynamic properties of natural gases, other multicomponent mixtures and binary mixtures of naturalgas components is divided, as follows, into three different parts. The uncertainty estimations given for the different ranges of validity are based on the representation of experimental data for various thermodynamic properties of binary and multicomponent mixtures by the reference equation of state GERG2008.
Normal range of validity
The normal range of validity covers temperatures of
90 K ≤ T ≤ 450 K
and pressures of
p ≤ 35 MPa.
This range corresponds to the use of the equation in both standard and advanced technical applications using natural gases and similar mixtures, e.g. pipeline transport, naturalgas storage and processes with liquefied natural gas.
In the gas phase, the uncertainty of the equations in density and speed of sound is 0.1% over the temperature range from 250 K / 270 K to 450 K at pressures up to 35 MPa. This uncertainty statement is valid for various types of natural gases and also holds for many binary and other multicomponent mixtures that consist of the 18 naturalgas components covered by GERG2004 and of the 21 components covered by GERG2008. The equation GERG2008 represent accurate data for isobaric enthalpy differences of binary and multicomponent mixtures to within their experimental uncertainty, which is in the range of (0.2–0.5)%.
In the liquid phase of many binary and multicomponent mixtures, the uncertainty of GERG2008 in density amounts to (0.10.5)%, in enthalpy differences (0.51)% and in heat capacities (12)%.
Due to the limited and poor data, the vapourliquid equilibrium (VLE) is described with lower accuracy. Hence, accurate vapourpressure data for binary and ternary mixtures consisting of the naturalgas main components are reproduced by the equations to within their experimental uncertainty, which is approximately (1–3)%.
Extended range of validity
The extended range of validity covers temperatures of
60 K ≤ T ≤ 700 K
and pressures of
p ≤ 70 MPa.
The uncertainty of the equations in gasphase density at temperatures and pressures outside the normal range of validity is roughly estimated to be about (0.2–0.5)%.
For certain mixtures, the extended range of validity covers temperatures up to 900 K and pressures up to 100 MPa and more. For example, the equations accurately describe gasphase density data for air within (0.1–0.2)% at temperatures up to 900 K and pressures up to 100 MPa.
The calculation of properties beyond the extended range of validity
When accepting larger uncertainties, GERG2008 can be reasonably used outside the extended range of validity. For example, density data for certain binary mixtures are described within about 1% at pressures up to 300 MPa.
Software for the Industrial Formulation IAPWSIF97 for Water and Steam
Information about the several Windows operating systems and Excel versions as well as about 64 Bit DLLs and .Net DLLs are given at the end of this software description.
1. Short information about IAPWSIF97
The Industrial Formulation IAPWSIF97 consists of a set of equations for different regions, which covers the following range of validity:
0 °C ≤ t ≤ 800 °C, p ≤ 1000 bar (100 MPa)
800 °C < t ≤ 2000 °C, p ≤ 500 bar (50 MPa)
The figure above shows the five regions into which the entire range of validity of IAPWSIF97 is divided. Regions 1 and 2 are both individually covered by a fundamental equation for the specific Gibbs free energy g(p,T), region 3 by a fundamental equation for the specific Helmholtz free energy f(ρ,T), and the saturation curve, corresponding to region 4, by a saturationpressure equation p_{s}(T). The hightemperature region 5 is also covered by a g(p,T) equation. These five equations, shown in rectangular boxes in the figure, form the so called basic equations.
In addition to these basic equations, socalled backward equations are provided for regions 1 to 4. These backward equations were developed in the following combinations of variables: For regions 1 and 2 as equations of the form T(p,h), T(p,s), and p(h,s), for region 3 as equations of the form T(p,h), v(p,h), T(p,s), v(p,s), p(h,s) and v(p,T). The backward equation for the entire region 4 is a saturationtemperature equation T_{s}(p), and for the technically most important part of region 4 (s ≥ s’’ (623.15 K)), there is a saturationtemperature equation of the form T_{s}(h,s). In the figure above, in addition to the (framed) basic equations, all of these types of backward equations (marked in grey) are assigned to the corresponding region of IAPWSIF97.
With these backward equations, properties dependent on the input quantities (p,h), (p,s), (h,s), in region 3 also on the input quantities (p,T), are calculable without iterations, and thus very fast.
Further details of IAPWSIF97 see here.
Furthermore, the book
Wagner, W., Kretzschmar, H.J. International Steam Tables  Properties of Water and Steam Based on the Industrial Formulation IAPWSIF97. SpringerVerlag (Berlin), 2008
comprehensively describes IAPWSIF97. This book also contains the IAPWS equations for the most important transport properties and some other properties, and two wall charts, a Mollier h,s diagram and a T,s diagram. For more details (contents, sample pages, etc.) see here.
2. Software for IAPWSIF97
On the basis of IAPWSIF97, including all of the backward equations as well as the IAPWS equations for the transport properties and three further properties, there is a software package for the calculation of more than 25 properties. This software was especially established regarding an optimal programming to achieve short computing times.
When applying the software, it is not necessary to know which region of IAPWSIF97 the property to be calculated belongs to. Based on the given input quantities, the software automatically determines which equation of IAPWSIF97 has to be applied.
With our software package, the following thermodynamic properties, transport properties and three further properties of water and steam can be calculated:
2.1 Thermodynamic properties
Based on the corresponding equations of IAPWSIF97 the thermodynamic properties listed in Table 1 can be calculated with the software:
Table 1. Calculable thermodynamic properties
Symbol Property 
p 
Pressure 

T 
Temperature 

v 
Specific volume 

ρ 
Density 

h 
Specific enthalpy 

s 
Specific entropy 

cp 
Specific isobaric heat capacity 

u 
Specific internal energy 

c_{v} 
Specific isochoric heat capacity 

x 
Vapour fraction 

w 
Speed of sound 

g 
Specific Gibbs free energy g = h − Ts 

f 
Specific Helmholtz free energy f = u − Ts 

z 
Compression factor 

f* 
Fugacity 

α_{v } 
Isobaric cubic expansion coefficient, α_{v } = v^{− }^{1} (∂v/∂T)_{p } 

α_{p} 
_{ } Relative pressure coefficient, α = v^{−1} (∂v/∂T)_{p} 

β_{p} 
Isothermal stress coefficient, β = p^{−1} (∂p/∂T)_{v} 

κ 
Isentropic exponent, κ = − (v/p) (∂p/ ∂v)_{s} 

κ_{T} 
Isothermal compressibility, κ_{T } = –v^{ }^{1} (∂v/∂p)_{T } 

µ 
Joule‑Thomson coefficient, µ = (∂T/∂p)_{h } 

(∂v/∂p)_{h} 
Partial derivative 

(∂ρ/∂p)_{h} 
Partial derivative 

(∂v/∂h)_{p} 
Partial derivative 

(∂ρ/∂h)_{p} 
Partial derivative 

(∂h/∂p)_{T} 
Partial derivative 

x 
Vapour fraction 

________________________________________________________ 
All these properties can be calculated in the entire range of validity of IAPWSIF97, see Sec. 1. Concerning region 4 (twophase region), the properties ν, ρ, h, s, u, f, g and x can also be calculated within the twophase region. The other properties can only be calculated on the phase boundaries (saturatedliquid line and saturatedvapour line) because they are not defined within the twophase region.
2.2 Transport properties and further properties
The software allows the calculation of transport properties, dielectric constant, refractive index, and surface tension listed in Table 2.
Table 2. Calculable transport and further properties
Symbol 
Property 
η 
Dynamic viscosity 
v 
Kinematic viscosity, v = η / ρ 
λ 
Thermal conductivity 
Pr 
Prandtl number, Pr = η c_{p}/ λ 
a 
Thermal diffusivity, a = λ /(ρc_{p}) 
ε 
Relative static dielectric constant 
n 
Refractive index 
σ 
Surface tension 
_____________________________________________________
The internationally agreed equations for calculating these properties, which do not belong to IAPWSIF97, are described in Ref. [165] and in the corresponding IAPWS Releases, see www.iapws.org. It should be noted that these equations are functions of temperature and density (not pressure). This fact has consequences for the necessity of iterations. The surface tension is a function of temperature only. Except for the dielectric constant ε, all the other properties can be calculated in the entire range of validity of IAPWSIF97, see Sec. 1.
The range of validity of the equation for ε is limited to 873.15 K, but the equation can be reasonably extrapolated up to 1073.15 K. The surface tension σ(T) refers only to the twophase region, region 4.
2.3 Combinations of input variables for calculating the several properties
2.3.1 Regions 15
For regions 13 and 5 (singlephase regions) and region 4 (twophase region), all properties listed in Tables 1 and 2 can be calculated as a function of the pairs of input variables shown in Table 3. For region 5, properties for input variables other than (p,T) are calculated via iterations only; there are no backward equations. Properties in region 4 cannot be calculated for the combination (p,T) as input variables, because p and T are not independent of each other in this region.
Table 3. Possible combinations of input variables for calculations in regions 1 to 5; for region 4, (p,T) cannot be used 
(p,T) 
(T,h) 
(ν,h) 
(h,s) 
(p,h) 
(T,s) 
(ν,s) 

(p,s) 
(T,ν) 


(p,ν) 
(T,ρ) 


The most important properties can directly be calculated from the functions in the software for the pairs of input variables listed in Table 3. The calculation of further properties as functions of all the pairs of input variables is possible by corresponding combinations of functions in the software.
2.3.2 Calculations for region 4 (twophase region) only
For region 4 [saturation pressure p_{sat} , saturation temperature T_{sat}, saturatedliquid line [('), x = 0, bubble line], saturatedvapour line [("), x = 1, dew line], twophase region (0 < x < 1)], the properties in the left column of Table 4 can be calculated from the functions given in the software for all listed input variables.
Table 4. Calculable properties for the entire region 4 (saturatedliquid line, saturatedvapour line and within the twophase region) from the corresponding functions listed in the software 
Calculable properties 
Input variables^{1} 
Explanations 
p_{sat} 
T, h, s, ρ, x 
^{1}In addition to the input variables given here, the properties can also be calculated using the corresponding input variables listed in Table 3 [except for 
T_{sat } 
p, h, s, ρ 

v, h, s 
(T,x), (p,x) 

ν, f, g 
(T,x), (p,x) 

x 
(p,h), (p,s), (p,v) 
Those properties listed in Tables 1 and 2 that are not given in the left column of Table 4 cannot be calculated within the twophase region (0 < x < 1) but only on the saturatedliquid and saturatedvapour line; these properties are not defined within the twophase region.
2.4 Dynamic Link Library for userspecific calculations
For the integration of IAPWSIF97 into user specific applications, the software contains a Dynamic Link Library (DLL). This DLL contains numerous functions thath enable the calculation of all properties listed above dependend on all combinations of input variables listed below. The user can choose between the calculation of properties with the backward equations of IAPWSIF97 or with iterations using only the basic equations. The calls of the functions of the DLL are made via simple names of functions that are based on the property to be calculated and the selected input variables. For example, the enthalpy h for given values of temperature T and pressure p is calculated from function HBPT.
The software allows the selection whether the backward equations should be used or only basic equations with iterations if iterations are necessary for the calculation of the corresponding property.
The software contains a .LIB file that allows the integration of the DLL into user specific Fortran programs, C programs, and Visual Basic.
In addition, the software contains an AddIn file that allows a simple integration of the DLL into Microsoft Excel. In this way, the considered properties can directly be calculated from within an Excel spreadsheet by calling the name of the corresponding function with the required input values.
As an example, the following screenshot shows the results of the calculation of all the properties for T = 300 K and p = 1 MPa. For T = 300 K, all properties on the saturatedliquid line and saturatedvapour line were calculated as well. For the vapour fraction x = 0.5, all properties that are defined within the twophase region are also calculated. All these properties were calculated at once. This Excel spreadsheet contains all the functions that are provided by the software. Of course, a userspecific Excel spreadsheet can be designed.
Example screenshot of calculations with the software package IAPWSIF97 from within a Microsoft Excel spreadsheet.
All functions that can be called from the DLL are specified in the file MANUAL.PDF that is also part of this software.
The DLL and the die Excelfiles .xla, .xlam, .xls, xlsm are configurated in such a way that they can be used under the several Windows operating systems [Windows 2000 to XP (32 Bit), Windows 7 and 8
(32 Bit/64 Bit)] and under the several Excel versions [2003 to 2013 (32 Bit)].
The IAPWSIF97 software is now available as a 64Bit version, which can be, under the 64Bit operating systems of Windows XP to Windows 2010 and the supplied 64bit Excel Addins, incorporated into the 64Bit versions of Excel 20102016. Using the supplied LIB file, the software can also be integrated into other 64Bit applications (e.g. Matlab).
.Net DLLs are also available.
The software is not free of charge.
Contact:
Prof. em. Dr.Ing. W. Wagner
Tel. +49 (0)234 3229033
Fax +49 (0)234 3214945
This email address is being protected from spambots. You need JavaScript enabled to view it.
Reference Equation of State GERG2008 for Natural Gases and similar Mixtures
The accurate knowledge of the thermodynamic properties of natural gases and other mixtures consisting of naturalgas components is of indispensable importance for the basic engineering and performance of technical processes. The processing, transportation through pipelines or by shipping, storage and liquefaction of natural gas are examples for technical applications where the thermodynamic properties of a variety of mixtures of natural gas components are required. For these processes, the design of fractionation units, compressors, heat exchangers, and storage facilities requires property calculations over wide ranges of mixture compositions and operating conditions in the homogeneous gas, liquid and supercritical regions, and for vapourliquid equilibrium (VLE) states. These data can be calculated in a very convenient way from equations of state.
There exists, however, not any equation of state for natural gases that is appropriate for all of the exemplified applications and that satisfies the demands on the accuracy in the description of thermodynamic properties over the entire fluid region. This statement not only includes the AGA8DC92 equation of state, which is only valid for a limited range in the homogeneous gas region. It also includes the different cubic equations of state and particularly the correlation equations applied for a limited range in the liquid region.
Therefore, we developed a widerange equation of state for natural gases and other mixtures that meets the requirements of standard and advanced natural gas applications. This research project was supported by the European naturalgas companies E.ON Ruhrgas (Germany), Enagás (Spain), Gasunie (The Netherlands), Gaz de France (France), Snam Rete Gas (Italy) and Statoil (Norway), which are members of GERG (Groupe Européen de Recherches Gazières).
The first version of the equation of state covers mixtures consisting of up to 18 components that are listed in the table; originally, nnonane, ndecane and hydrogen sulfide did not belong to these components. In contrast to the AGA8DC92 equation, there are basically no limitations in the concentration range. In 2004, the new equation of state was evaluated by the GERG group and then adopted under the name GERG2004 equation of state (or GERG2004 for short) as GERG reference equation of state for natural gases and similar mixtures (GERG standard).
In 2008, we finished the expansion of GERG2004 by incorporating the three components nnonane, ndecane and hydrogen sulphide. Thus, the equation can now be applied to mixtures consisting of an arbitrary combination of the 21 components listed in the table. This expanded equation of state is called GERG2008. Meanwhile the GERG2008 equation of state was adopted as an ISO Standard (ISO 207652) for natural gases and similar mixtures.
Structure of the equations of state GERG2004 and GERG2008
The GERG2008 is based on a multifluid mixture model, which is explicit in the reduced Helmholtz free energy α = a/(RT) as a function of the density ρ, the temperature T and the composition x (mole fractions) of the mixture. The structure of the equations of state is shown in the following figure.
Three elements are necessary to set up a multifluid mixture model:
• Pure substance equations of state for all components
• Reducing functions for density and temperature
• Departure functions
The reducing functions as well as the departure function were developed to describe the behaviour of the mixture and contain substance and mixture specific parameters. From the reducing functions, the reducing values ρ_{r} and T_{r} for the density and the temperature of the mixture are calculated. They only depend on the mixture composition and turn into the critical properties ρ_{c} and T_{c}, respectively, for the pure components. The departure function depends on the reduced density δ, the inversely reduced temperature τ ( τ = Tau in the figures) , and the composition x of the mixture. It contains the sum of binary specific and generalized departure functions, which can be developed for single binary mixtures (binary specific) or for a group of binary mixtures (generalized). The following equation illustrates this summation:
The mathematical structure of the part of the binary specific and generalized departure functions that depends on δ and τ is similar to the structure of pure substance equations of state and is determined by our method for optimizing the structure of equations of state. Furthermore, the departure functions contain a factor that only depends on the composition of the mixture. For further details see the references given at the end of this description.
In order to obtain a reference equation of state that yields accurate results for various types of natural gases and other multicomponent mixtures over wide ranges of composition, the reducing and departure functions were developed using only data for binary mixtures. The 21 pure components covered by GERG2008 result in 210 possible binary mixture combinations. Departure functions Δα^{r}_{ij }(δ,τ, x) were developed only for such binary mixtures for which accurate experimental data existed. For binary mixtures with limited or poor data, no departure functions were developed, and only the parameters of the reducing functions ρ_{r}(x) und T_{r}(x) were fitted; in case of very poor data, simplified reducing functions without any fitting were used.
The multifluid model used enables a simple inclusion of additional components in future developments. This means that, for example, the fitted parameters of the existing equation of state do not have to be refitted when incorporating new components. This also holds for the departure function with its optimized structure, which remains unchanged when expanding the model.
Range of validity and accuracy of GERG2004 and GERG2008
The entire range of validity of GERG2008 covers the following temperatures and pressures:
• Normal range: 90 K ≤ T ≤ 450 K p ≤ 35 MPa
• Extended range: 60 K ≤ T ≤ 700 K p ≤ 70 MPa.
Moreover, the equation can be reasonably extrapolated beyond the extended range, and each component can basically cover the entire composition range, i.e., (0100)%.
GERG2008 represents most of the experimental data, including the most accurate measurements available, to within their uncertainties. The uncertainty values given in the following correspond to the uncertainties of the most accurate experimental data.
In the gas region, the uncertainties in density and speed of sound are 0.1%, in enthalpy differences (0.20.5)% and in heat capacities (12)%. In the liquid region, the uncertainty in density is (0.10.5)%, in enthalpy differences (0.51)% and in heat capacities (12)%. In the twophase region, vapour pressures are calculated with a total uncertainty of (13)%, which corresponds to the uncertainties of the experimental VLE data. For mixtures with limited or poor data, the uncertainty values stated above can be somewhat higher.
These accuracy statements are based on the fact that GERG2008 represents the corresponding experimental data to within their experimental uncertainties (with very few exceptions).
Further details and an assignment of the uncertainties to the ranges of validity given above can be found here.
Quality of GERG2008 for “normal” natural gases and special mixtures
Comparisons with experimental data for natural gases show that the reference equation of state GERG2008 describes the thermodynamic properties in the “classical” naturalgas region more accurately than the current standard, the AGA8DC92 equation, which is a pure gas equation. For example, GERG2008 achieves important improvements in representing caloric properties (such as the speed of sound of natural gases) and significantly extends the range of composition, in which natural gases can be described in high accuracy. The pρT data of most natural gases in the “classical” naturalgas region are described by GERG2008 to within the required uncertainty of 0.1% in density (in the temperature range from 270 K to 450 K at pressures up to 35 MPa). Significant improvements were achieved for temperatures ranging from 250 K to 275 K.
In contrast to the AGA8DC92 equation, GERG2008 is also able to describe the liquid phase and vapourliquid equilibrium states with the highest possible accuracy. The experimental data for densities, enthalpy differences and heat capacities are represented to within the experimental uncertainties over the entire fluid region. Moreover, the vapour pressure can be calculated with comparatively high accuracy, which is, however, clearly lower than for the properties in the homogeneous liquid. Thus, GERG2008 also meets all requirements in accuracy for the liquid phase and the phase equilibrium. In comparison with cubic equations, significant improvements were achieved for the saturated liquid densities of liquefied natural gases (LNG) and LNGlike mixtures; the uncertainties were reduced from more than 10% to (0.10.5)%.
Aside from the accurate description of the thermodynamic properties of common natural gases, the so far achieved results have shown that GERG2008 also allows the at present most accurate description of natural gases consisting of high fractions of nitrogen, carbon dioxide, ethane or higher alkanes. Moreover, for the first time, GERG2008 also enables the accurate description of “Rich Natural Gas” (RNG), “Compressed Natural Gas” (CNG), “Liquefied Petroleum Gas” (LPG) and “Liquefied Natural Gas (LNG). Furthermore, GERG2008 is able to very accurately describe natural gases containing a high fraction of hydrogen and binary mixtures of naturalgas components with hydrogen as well as natural gases with a low calorific value, light oil and other mixtures related to natural gas. In addition, the properties of mixtures consisting of nontypical naturalgas components can be accurately calculated, including dry air, humid air, and binary and multicomponent mixtures of the flue gases water, carbon dioxide, carbon monoxide, nitrogen, oxygen and argon, in particular, gasphase properties. For such calculations, the values of temperature and pressure can exceed the limits defined for the extended range of validity of GERG2008. However, due to the lack of sufficiently accurate experimental data, the uncertainty in calculating the thermodynamic properties of such mixtures is higher than for natural gases and related mixtures.
The following statement should be a hint not to overestimate the high performance of the equation of state GERG2008. Formally, GERG2008 should cover (all) mixtures consisting of an arbitrary combination of the 21 considered components. Of course, there are a number of mixtures for which GERG2008 does not yield a satisfactory property description. Reasons for this might be, for example, the lack of accurate measurements (at the time when the equation of state was developed), mixture conditions that are far beyond the range of validity of GERG2008 (e.g., mixtures with large amounts of helium or hydrogen at cryogenic temperatures), and mixtures that were not in the main focus of this work (e.g., carbon dioxidewater and other gaseous components dissolved in liquid water).
Examples for the applications of GERG2008
Due to the wide range of validity, GERG2008 can be used for standard and extended applications with natural gases and other mixtures. This includes the following processes: The transport of natural gas through pipelines and its storage in underground storage facilities, providing compressed natural gas (CNG), the removal of undesired components from natural gas, the liquefaction of natural gas, advanced processes with liquefied natural gas and sour gas (natural gases containing water and hydrogen sulfide), the production of liquefied petroleumgas (LPG), working with light oil, coming applications of natural gas/hydrogen mixtures and also very efficient refrigeration processes with mixtures of naturalgas components (e.g., mixtures of propane and butane). Moreover, the application of GERG2004 and GERG2008 for processes with dry and humid air as well as mixtures of fluegas components is possible. The equation of state GERG2008 can also be used for the calculation of dew points of all the mixtures mentioned.
References
The equation of state GERG2004 is described in detail in the GERGMonograph TM15, where the complete numerical information and the comprehensive comparisons with experimental data are given. This reference reads:
Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M. The GERG2004 widerange equation of state for natural gases and other mixtures. GERG TM15 2007. Fortschr.Ber. VDI, Reihe 6, Nr. 557, VDI Verlag, Düsseldorf, 2007; also available as GERG Technical Monograph 15 (2007).
The expanded equation of state GERG2008 is described in the article:
Kunz, O., Wagner, W. The GERG2008 widerange equation of state for natural gases and other mixtures: An expansion of GERG2004. J. Chem. Eng. Data 57 (2012), 30323091.
Software for the reference equation of state GERG2008 for natural gases and other mixtures
For the reference equation of state GERG2008 described above, a comprehensive and userfriendly software package is available. The software enables to calculate several thermodynamic properties in the homogeneous gas, liquid, and supercritical regions and allows to carry out VLE calculations at arbitrary mixture conditions where the prior knowledge of the number of phases (one or two) is not required. The VLE calculation options include different flash options as well as phase envelope, dew point, and bubble point calculations.
For details about software see this page.
The Industrial Formulation IAPWSIF97 for Water und Steam
In 1997 the International Association for the Properties of Water and Steam (IAPWS) released the industrial standard “IAPWS Industrial Formulation for the Thermodynamic Properties of Water and Steam (IAPWSIF97)”. The IAPWSIF97 replaced the industrial standard IFC67, which had been valid until 1967.
The IAPWS Industrial Formulation 1997 consists of a set of equations for different regions, which cover the following range of validity:
0 °C ≤ t ≤ 800 °C, p ≤ 1000 bar (100 MPa)
800 °C < t ≤ 2000 °C, p ≤ 100 bar (50 MPa)
The figure above shows the five regions into which the entire range of validity of IAPWSIF97 is divided. The boundaries of the regions can be directly taken from the figure except for the boundary between regions 2 and 3; this boundary, which corresponds approximately to the isentropic line s = 5.047 kJ kg^{−1} K^{−1}, is defined by a corresponding auxiliary equation. Regions 1 and 2 are both individually covered by a fundamental equation for the specific Gibbs free energy g(p,T), region 3 by a fundamental equation for the specific Helmholtz free energy f(ρ,T), and the saturation curve, corresponding to region 4, by a saturationpressure equation p_{s}(T). The hightemperature region 5 is also covered by a g(p,T) equation. These five equations, shown in rectangular boxes in the figure, form the socalled basic equations.
In order to achieve a high accuracy of the industrial standard IAPWSIF97, it has been coupled to the scientific standard for the calculation of the thermodynamic properties of water, the “IAPWS Formulation 1995 (see here). This coupling was achieved by fitting the basic equations of regions 1 to 3 and 5 of IAPWSIF97 to values of the specific volume v, specific enthalpy h, specific isobaric heat capacity c_{p} and speed of sound w calculated from IAPWS95. Accordingly, the basic equation for region 4, the saturationpressure equation, was fitted to the values of the saturation pressure p_{s} calculated from IAPWS95.
Based on “bank of terms” specially formulated for the basic equations for the regions 1 to 3 and 5, the final equations of IAPWSIF97 [117] were developed with the help of our structure optimization procedure.
In addition to these basic equations, socalled backward equations are provided for regions 1 to 4. These backward equations were developed in the following combinations of variables: For regions 1 and 2 as equations of the form T(p,h), T(p,s), and p(h,s), for region 3 as equations of the form T(p,h), v(p,h), T(p,s), v(p,s), p(h,s) and v(p,T). The backward equation for the entire region 4 is a saturationtemperature equation T_{s}(p), and for the technically most important part of region 4 (s ≥ s’’ (623.15 K)), there is a saturationtemperature equation of the form T_{s}(h,s). In addition to the (framed) basic equations, all of these types of backward equations (marked in grey) are assigned to the corresponding region of IAPWSIF97.
The backward equations are numerically very consistent with the corresponding basic equation. Thus, properties as functions of (p,h), (p,s), and (h,s) for regions 1 to 3, of (p) for the entire region 4, and of (h,s) for the technically most important part of region 4 can be calculated without any iteration. Due to the backward equation v (p,T) for region 3, the specific volume (and thus also all the other properties) can be calculated for this region without the necessity of its iteration from the basic equation f(ρ,T). Consequently, properties such as s(p,h) and h(p,s) can be calculated directly from the corresponding backward equation or in combination with the corresponding basic equation, for example, h(p,s) via the relation h(p,T(p,s)). As a result of this special concept of the industrial standard IAPWSIF97, all important combinations of properties can be calculated extremely quickly.
A complete description of the individual equations of IAPWSIF97 and a comprehensive steam table along with two wall charts, a Mollier h,s diagram and a T,s diagram, are given in the book
Wagner, W., Kretzschmar, H.J. International Steam Tables  Properties of Water and Steam Based on the Industrial Formulation IAPWSIF97. SpringerVerlag (Berlin), 2008.
Equations for the transport properties dynamic viscosity and thermal conductivity, as well as for the properties surface tension, dielectric constant and refractive index are also given in the book. Furthermore, the book presents pressuretemperature diagrams with isolines of all the properties tabulated and of further properties such as the specific internal energy, JouleThomson coefficient and a number of partial derivatives. A CD provides the interactive program “IAPWSIF97 Electronic Steam Tables” to calculate all of the properties contained in the book as function of pressure and temperature. In this way, users can produce “personal” steam tables. For more details (contents, sample pages, etc.) see here.
The international article on IAPWSIF97 of Wagner et al. [117] informs about the development of this formulation (requirements, concept, accuracy and consistency at the region boundaries).
Software for IAPWSIF97
For IAPWSIF97, including all of the backward equations and the equations for the transport properties, there is software for the calculation of more than 25 properties.
Details on the software for IAPWSIF97 can be found on this page.