Prof. Wagner
The IAPWS95 Formulation for Water
In 1995 the International Association for the Properties of Water and Steam (IAPWS) released a new scientificstandard equation of state called ”The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use” (IAPWS95).The comprehensive article on the IAPWS95 formulation [127] contains detailed information about the following topics:

Necessity of a new scientificstandard equation of state for water

Phase equilibrium of water

Data used in the development of IAPWS95

Details on the development of IAPWS95

Numerical description of IAPWS95 and further details

Comparison of IAPWS95 with experimental data

Uncertainty of IAPWS95

Recommendation on an improvement of the data basis

Annex: Steam table based on IAPWS95
The following diagrams show the estimated uncertainties of IAPWS95 for the properties density, speed of sound, isobaric heat capacity in the homogeneous region and for the properties vapour pressure, saturated liquid and vapour density on the liquidvapour phase boundary.
The three diagrams for the homogeneous phases also show the range of validity of IAPWS95. Apart from this formal range of validity, IAPWS95 can be reasonably extrapolated for the properties pressure, density and enthalpy up to extremely high pressures, temperatures and densities. (about 80000 MPa, some thousand kelvins, about 2500 kg m^{−3})
Software
There is an extensive software package available for the use of IAPWS95, namely as the program FLUIDCAL in the version for the substance water, which is described in the section software of this website.
Due to the scientific relevance of IAPWS95, the software for the calculation of thermodynamic properties of water and steam based on IAPWS95 is available for universities free of charge.
Details on the software FLUIDCAL can be found on this page.
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
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Examples of calculations executed with the software for GERG2008
The following screenshots show examples of calculations carried out with the software for the GERG2008 reference equation of state for natural gases and other mixtures.
Example of the calculation of several thermodynamic properties for a 14component naturalgas mixture for typical pipeline conditions using the exported functions of the GERG2008 DLL from within a Microsoft Excel spreadsheet.
Example of the calculation of several thermodynamic properties for a 14component naturalgas mixture for vapourliquidequilibrium (VLE) conditions using the VBA function TPFLASH from within a Microsoft Excel spreadsheet.
Example of the calculation of several thermodynamic properties for an eightcomponent LNGlike mixture in the homogeneous liquid phase using the VBA function TPFLASH from within a Microsoft Excel spreadsheet.
Example of the phaseenvelope calculation for a 14component naturalgas mixture using the VBA function PHASENV from within a Microsoft Excel spreadsheet.
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Prof. Wagner
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 34