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Prof. Wagner

Software for the Reference Equation of State GERG-2008 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 GERG-2008 for natural gases and other mixtures see this page.

For the reference equation of state GERG-2008 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 multi-component 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 vapour-liquid equilibrium (VLE) calculations. The VLE calculation options comprise flash, phase envelope, dew point and bubble point calculations for any binary and multi-component mixture defined above.

 

Components covered by the GERG-2008 equation of state.

 

The software package contains a dynamic link library (DLL) and a Microsoft Excel Add-In. With the Add-In 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 user-specific 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 multi-component mixtures can be calculated with the help of the DLL:

ρ

Density

v

Volume

Z

Compressibility factor

h

Enthalpy

s

Entropy

cp

Isobaric heat capacity

cv

Isochoric heat capacity

w

Speed of sound

κ

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

μ

Joule-Thomson coefficient; μ = (∂T/∂p)h

δT

isothermal throttling coefficient; δT = (∂h/∂p)T

u

Internal energy

g

Gibbs free energy, g = hTs

a

Helmholtz free energy, a = uTs

(∂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

fi

Fugacity of component i

ln φi

Logarithm of the fugacity coefficient of component i, φi =fi/(xi p)

ln Ki

Logarithm of the K-factor of component i, Ki = yi/xi

β

Molar vapour fraction, β = n vap/n tot

βm

Mass vapour fraction, βm = m vap/m tot

βv

Volume vapour fraction, βv = 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 Excel-Files .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 GERG-2008 software is now available as a 64-Bit version, which can be, under the 64-Bit operating systems of Windows XP to Windows 2010 and the supplied 64-bit Excel Add-ins, incorporated into the 64-Bit versions of Excel 2010-2016. Using the supplied LIB file, the software can also be integrated into other 64-Bit applications (e.g. Matlab).

.Net DLLs are also available.

The software for GERG-2008 is not free of charge.

 

Contact :

Prof. em. Dr.-Ing. W. Wagner
Tel. +49 (0)234 32-29033
Fax +49 (0)234 32-14945
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 GERG-2008

The equation of state GERG-2008 are valid in the gas phase, in the liquid phase, in the supercritical region and for vapour-liquid equilibrium (VLE) states. The entire range of validity regarding the calculation of thermodynamic properties of natural gases, other multi-component mixtures and binary mixtures of natural-gas 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 multi-component mixtures by the reference equation of state GERG-2008.

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, natural-gas 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 multi-component mixtures that consist of the 18 natural-gas components covered by GERG-2004 and of the 21 components covered by GERG-2008. The equation GERG-2008 represent accurate data for isobaric enthalpy differences of binary and multi-component mixtures to within their experimental uncertainty, which is in the range of (0.2–0.5)%.

In the liquid phase of many binary and multi-component mixtures, the uncertainty of GERG-2008 in density amounts to (0.1-0.5)%, in enthalpy differences (0.5-1)% and in heat capacities (1-2)%.

Due to the limited and poor data, the vapour-liquid equilibrium (VLE) is described with lower accuracy. Hence, accurate vapour-pressure data for binary and ternary mixtures consisting of the natural-gas 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 gas-phase 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 gas-phase 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, GERG-2008 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 IAPWS-IF97 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 IAPWS-IF97 

The Industrial Formulation IAPWS-IF97 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)

 

diagramm 5

Structure and regions of IAPWS-IF97.

 

The figure above shows the five regions into which the entire range of validity of IAPWS-IF97 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 saturation-pressure equation ps(T). The high-temperature 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, so-called 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 saturation-temperature equation Ts(p), and for the technically most important part of region 4 (s ≥ s’’ (623.15 K)), there is a saturation-temperature equation of the form Ts(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 IAPWS-IF97.

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 IAPWS-IF97 see here.

Furthermore, the book

Wagner, W., Kretzschmar, H.-J. International Steam Tables - Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97. Springer-Verlag (Berlin), 2008

comprehensively describes IAPWS-IF97. 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 IAPWS-IF97

On the basis of IAPWS-IF97, 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 IAPWS-IF97 the property to be calculated belongs to. Based on the given input quantities, the software automatically determines which equation of IAPWS-IF97 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 IAPWS-IF97 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

cv  

Specific isochoric heat capacity

x

Vapour fraction

w

Speed of sound

g

Specific Gibbs free energy g = hTs

f

Specific Helmholtz free energy f = uTs

z

Compression factor

f*

Fugacity

αv

Isobaric cubic expansion coefficient,  αv = v 1 (v/T)p    

αp

   Relative pressure coefficient,  α = v−1 (∂v/∂T)p

βp

Isothermal stress coefficient,  β = p−1 (∂p/∂T)v

κ

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

κT

Isothermal compressibility,  κT = 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 IAPWS-IF97, see Sec. 1. Concerning region 4 (two-phase region), the properties ν, ρ, h, s, u, f, g and x can also be calculated within the two-phase region. The other properties can only be calculated on the phase boundaries (saturated-liquid line and saturated-vapour line) because they are not defined within the two-phase 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, Prη  cp/ λ 

a

  Thermal diffusivity, aλ /(ρcp)

 ε  

  Relative static dielectric constant

  Refractive index

σ 

  Surface tension

_____________________________________________________

The internationally agreed equations for calculating these properties, which do not belong to IAPWS-IF97, 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 IAPWS-IF97, 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 two-phase region, region 4.

2.3 Combinations of input variables for calculating the several properties

2.3.1 Regions 1-5

 For regions 1-3 and 5 (single-phase regions) and region 4 (two-phase 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
(two-phase region) only
For region 4 [saturation pressure psat , saturation temperature Tsat, saturated-liquid line [('), x = 0, bubble line], saturated-vapour line [("), x = 1, dew line], two-phase 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 (saturated-liquid line, saturated-vapour line and within the two-phase region) from the corresponding functions listed in the software

Calculable properties

Input variables1

Explanations

psat

T, h, s, ρ, x 

1In addition to the input variables given here, the properties can also be calculated using the corresponding input variables listed in Table 3 [except for
the combination (p,T)]; the belonging functions are given in the software. The software finds out if the state point is in region 4.

Tsat

p, h, sρ 

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 two-phase region (0 < x < 1) but only on the saturated-liquid and saturated-vapour line; these properties are not defined within the two-phase region.

2.4 Dynamic Link Library for user-specific calculations

For the integration of IAPWS-IF97 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 IAPWS-IF97 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 Add-In 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 saturated-liquid line and saturated-vapour line were calculated as well. For the vapour fraction x = 0.5, all properties that are defined within the two-phase 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 user-specific Excel spreadsheet can be designed.


Example screenshot of calculations with the software package IAPWS-IF97 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 Excel-files .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 IAPWS-IF97 software is now available as a 64-Bit version, which can be, under the 64-Bit operating systems of Windows XP to Windows 2010 and the supplied 64-bit Excel Add-ins, incorporated into the 64-Bit versions of Excel 2010-2016. Using the supplied LIB file, the software can also be integrated into other 64-Bit 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 32-29033
Fax +49 (0)234 32-14945
This email address is being protected from spambots. You need JavaScript enabled to view it.

 

Reference Equation of State GERG-2008 for Natural Gases and similar Mixtures

 

The accurate knowledge of the thermodynamic properties of natural gases and other mixtures consisting of natural-gas 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 vapour-liquid 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 AGA8-DC92 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 wide-range 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 natural-gas 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, n-nonane, n-decane and hydrogen sulfide did not belong to these components. In contrast to the AGA8-DC92 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 GERG-2004 equation of state (or GERG-2004 for short) as GERG reference equation of state for natural gases and similar mixtures (GERG standard).

In 2008, we finished the expansion of  GERG-2004 by incorporating the three components n-nonane, n-decane 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 GERG-2008. Meanwhile the GERG-2008 equation of state was adopted as an ISO Standard (ISO 20765-2) for natural gases and similar mixtures.

 

Components, which were taken into account in the development of the equation of state GERG-2008. Yellow fields: natural gas main components; red fields: further hydrocarbons; blue fields: further components.
 

Structure of the equations of state GERG-2004 and GERG-2008

The GERG-2008 is based on a multi-fluid 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.

 

Multifluid model for the equation of state GERG-2008 for natural gases and similar mixtures.

 

Three elements are necessary to set up a multi-fluid 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 ρr and Tr for the density and the temperature of the mixture are calculated. They only depend on the mixture composition and turn into the critical properties ρc and Tc, 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:

 

Fig3 Multikomp mixt

The departure function for the mixture in a multi-fluid model as a double summation over all binary specific and generalized departure functions developed for the binary subsystems, that can be formed from the 21 components.

 

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 multi-component 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 GERG-2008 result in 210 possible binary mixture combinations. Departure functions Δαrij (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 ρr(x) und Tr(x) were fitted; in case of very poor data, simplified reducing functions without any fitting were used.

The multi-fluid 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 GERG-2004 and GERG-2008

The entire range of validity of GERG-2008 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., (0-100)%.

GERG-2008 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 (0.2-0.5)% and in heat capacities (1-2)%. In the liquid region, the uncertainty in density is (0.1-0.5)%, in enthalpy differences (0.5-1)% and in heat capacities (1-2)%. In the two-phase region, vapour pressures are calculated with a total uncertainty of (1-3)%, 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 GERG-2008 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 GERG-2008 for “normal” natural gases and special mixtures
Comparisons with experimental data for natural gases show that the reference equation of state GERG-2008 describes the thermodynamic properties in the “classical” natural-gas region more accurately than the current standard, the AGA8-DC92 equation, which is a pure gas equation. For example, GERG-2008 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” natural-gas region are described by GERG-2008 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 AGA8-DC92 equation, GERG-2008 is also able to describe the liquid phase and vapour-liquid 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, GERG-2008 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 LNG-like mixtures; the uncertainties were reduced from more than 10% to (0.1-0.5)%.

Aside from the accurate description of the thermodynamic properties of common natural gases, the so far achieved results have shown that GERG-2008 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, GERG-2008 also enables the accurate description of “Rich Natural Gas” (RNG), “Compressed Natural Gas” (CNG), “Liquefied Petroleum Gas” (LPG) and “Liquefied Natural Gas (LNG). Furthermore, GERG-2008 is able to very accurately describe natural gases containing a high fraction of hydrogen and binary mixtures of natural-gas 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 non-typical natural-gas components can be accurately calculated, including dry air, humid air, and binary and multi-component mixtures of the flue gases water, carbon dioxide, carbon monoxide, nitrogen, oxygen and argon, in particular, gas-phase properties. For such calculations, the values of temperature and pressure can exceed the limits defined for the extended range of validity of GERG-2008. 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 GERG-2008. Formally, GERG-2008 should cover (all) mixtures consisting of an arbitrary combination of the 21 considered components. Of course, there are a number of mixtures for which GERG-2008 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 GERG-2008 (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 dioxide-water and other gaseous components dissolved in liquid water).


Examples for the applications of GERG-2008
Due to the wide range of validity, GERG-2008 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 petroleum-gas (LPG), working with light oil, coming applications of natural gas/hydrogen mixtures and also very efficient refrigeration processes with mixtures of natural-gas components (e.g., mixtures of propane and butane). Moreover, the application of GERG-2004 and GERG-2008 for processes with dry and humid air as well as mixtures of flue-gas components is possible. The equation of state GERG-2008 can also be used for the calculation of dew points of all the mixtures mentioned.

References
The equation of state GERG-2004 is described in detail in the GERG-Monograph 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 GERG-2004 wide-range 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 GERG-2008 is described in the article:

Kunz, O., Wagner, W. The GERG-2008 wide-range equation of state for natural gases and other mixtures: An expansion of GERG-2004. J. Chem. Eng. Data 57 (2012), 3032-3091.

Software for the reference equation of state GERG-2008 for natural gases and other mixtures
For the reference equation of state GERG-2008 described above, a comprehensive and user-friendly 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 IAPWS-IF97 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 (IAPWS-IF97)”. The IAPWS-IF97 replaced the industrial standard IFC-67, which had been valid until 1967.

 

diagramm 5

Structure and regions of IAPWS-IF97.

 

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 IAPWS-IF97 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 saturation-pressure equation ps(T). The high-temperature 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 order to achieve a high accuracy of the industrial standard IAPWS-IF97, 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 IAPWS-IF97 to values of the specific volume v, specific enthalpy h, specific isobaric heat capacity cp and speed of sound w calculated from IAPWS-95. Accordingly, the basic equation for region 4, the saturation-pressure equation, was fitted to the values of the saturation pressure ps calculated from IAPWS-95.

Based on “bank of terms” specially formulated for the basic equations for the regions 1 to 3 and 5, the final equations of IAPWS-IF97 [117] were developed with the help of our structure optimization procedure.

In addition to these basic equations, so-called 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 saturation-temperature equation Ts(p), and for the technically most important part of region 4 (s ≥ s’’ (623.15 K)), there is a saturation-temperature equation of the form Ts(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 IAPWS-IF97.

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 IAPWS-IF97, all important combinations of properties can be calculated extremely quickly.

A complete description of the individual equations of IAPWS-IF97 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 IAPWS-IF97. Springer-Verlag (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 pressure-temperature diagrams with isolines of all the properties tabulated and of further properties such as the specific internal energy, Joule-Thomson coefficient and a number of partial derivatives. A CD provides the interactive program “IAPWS-IF97 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 IAPWS-IF97 of Wagner et al. [117] informs about the development of this formulation (requirements, concept, accuracy and consistency at the region boundaries).

 

Software for IAPWS-IF97

For IAPWS-IF97, 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 IAPWS-IF97 can be found on this page.