Prof. Wagner

The IAPWS-95 Formulation for Water

In 1995 the International Association for the Properties of Water and Steam (IAPWS) released a new scientific-standard equation of state called ”The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use” (IAPWS-95).The comprehensive article on the IAPWS-95 formulation [127] contains detailed information about the following topics:

  • Necessity of a new scientific-standard equation of state for water

  • Phase equilibrium of water

  • Data used in the development of IAPWS-95

  • Details on the development of IAPWS-95

  • Numerical description of IAPWS-95 and further details

  • Comparison of IAPWS-95 with experimental data

  • Uncertainty of IAPWS-95

  • Recommendation on an improvement of the data basis

  • Annex: Steam table based on IAPWS-95

The following diagrams show the estimated uncertainties of IAPWS-95 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 liquid-vapour phase boundary.

Uncertainty of IAPWS-95 in density (in pressure in the critical region, in pressure p, left diagram) and in speed of sound (right diagram).

 

Uncertainty of IAPWS-95 in isobaric heat capacity (left diagram) and on the vapour-liquid phase boundary in the three properties vapour pressure pσ, saturated-liquid density ρ' and saturated-vapour density ρ'' (right diagram).
 

 

The three diagrams for the homogeneous phases also show the range of validity of IAPWS-95. Apart from this formal range of validity, IAPWS-95 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 IAPWS-95, 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 IAPWS-95, the software for the calculation of thermodynamic properties of water and steam based on IAPWS-95 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 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
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Examples of calculations executed with the software for GERG-2008

 

The following screenshots show examples of calculations carried out with the software for the GERG-2008 reference equation of state for natural gases and other mixtures.

 

 Example of the calculation of several thermodynamic properties for a 14-component natural-gas mixture for typical pipeline conditions using the exported functions of the GERG-2008 DLL from within a Microsoft Excel spreadsheet.

 

Example of the calculation of several thermodynamic properties for a 14-component natural-gas mixture for vapour-liquid-equilibrium (VLE) conditions using the VBA function TPFLASH from within a Microsoft Excel spreadsheet.

 

Example of the calculation of several thermodynamic properties for an eight-component LNG-like mixture in the homogeneous liquid phase using the VBA function TPFLASH from within a Microsoft Excel spreadsheet.

 

Example of the phase-envelope calculation for a 14-component natural-gas mixture using the VBA function PHASENV from within a Microsoft Excel spreadsheet.

 

 

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