Thermodynamic and Transport Properties of Water and Steam

Contents

• Introduction to IAPWS-IF97
• Equations of IAPWS-IF97
• IAPWS Transport Properties
• Excel Add-In
• References

Introduction to IAPWS-IF97

Water is not only one of the most common substances and indispensable to life, it's also one of the most important media in engineering applications. Steam engines with water as the working fluid were at the beginning of the industrial revolution. The rise of electrical energy is connected to hydroelectric and steam power plants. Water is used as cooling medium or heat transfer fluid and it plays an important role for air-condition. For conservation or for reaching desired properties, water must be removed from substances (drying). In other cases water must be added (humidification). Also, many chemical reactions take place in hydrous solutions.

That's why a good deal of work has been spent on the investigation and measurement of water properties over the years. Thermodynamic, transport and other properties of water are known better than of any other substance. Accurate data are especially needed for the design of equipment in steam power plants (boilers, turbines, condensers). In this field it's also important that all parties involved, e.g., companies bidding for equipment in a new steam power plant, base their calculations on the same property data values because small differences may produce appreciable differences.

A standard for the thermodynamic properties of water over a wide range of temperature and pressure was developed in the 1960's, the 1967 IFC Formulation for Industrial Use (IFC-67). Since 1967 IFC-67 has been used for "official" calculations such as performance guarantee calculations of power cycles. The equations underlying IFC-97 are published for example in [1].

In 1997, IFC-67 has been replaced by a new formulation, the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam or IAPWS-IF97 for short. IAPWS-IF97 was developed in an international research project coordinated by the International Association for the Properties of Water and Steam (IAPWS). The formulation is described in a paper by W. Wagner et al., "The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam," ASME J. Eng. Gas Turbines and Power, Vol. 122 (2000), pp. 150-182 and several steam table books, among others ASME Steam Tables and Properties of Water and Steam by W. Wagner, Springer 1998.

IAPWS-IF97 uses some property constants of water for evaluating the equations for the thermodynamic properties. The reference values of these constants are as follows.

The value of the specific gas constant

R = 0.461 526 kJ/(kg K)

results from the recommended value of the molar gas constant

R_m = 8.314 51 kJ/(kmol K)

and the molecular weight of ordinary water

M = 18.015 257 kg/kmol

Values of the critical temperature, critical pressure and critical density are taken as

T_c = 647.096 K p_c = 220.64 bar = 322 kg/m³

The triple-point temperature as defined in the International Temperature Scale of 1990 (ITS-90) is

T_t = 273.16 K = 0.01 °C

and the corresponding pressure at the triple point

p_t = 611.657 Pa

Finally, the temperature at the normal boiling point (at a pressure of 1.013 25 bar) is

T_b = 373.1243 K = 99.9743 °C

Equations of IAPWS-IF97

The IAPWS-IF97 divides the thermodynamic surface into five regions (see figure below):

• region 1 for the liquid state from low to high pressures,
• region 2 for the vapor and ideal gas state,
• region 3 for the thermodynamic state around the critical point,
• region 4 for the saturation curve (vapor-liquid equilibrium),
• region 5 for high temperatures above 1073.15 K (800 °C) and pressures up to 10 MPa (100 bar).

For regions 1, 2, 3 and 5 the authors of IAPWS-IF97 have developed fundamental equations of very high accuracy. Regions 1, 2 and 5 are covered by fundamental equations for the Gibbs free energy g(T,p), region 3 by a fundamental equation for the Helmholtz free energy f(T,v). All thermodynamic properties can then be calculated from these fundamental equations by using the appropriate thermodynamic relations. For region 4 a saturation-pressure equation has been developed.

In chemical engineering applications mainly regions 1, 2, 4, and to some extent also region 3 are of interest. The range of validity of these regions, the equations for calculating the thermodynamic properties, and references are summarized in an Adobe pdf-file. The equations of the high-temperature region 5 should be looked up in the references.

For regions 1 and 2 the thermodynamic properties are given as a function of temperature and pressure, for region 3 as a function of temperature and density. For other independent variables an iterative calculation is usually required. So-called backward equations are provided in IAPWS-IF97 which allow direct calculation of properties as a function of some other sets of variables (see references).

Accuracy of the equations and consistency along the region boundaries are more than sufficient for engineering applications. Details can be found in the references.

IAPWS Transport Properties

The International Association for the Properties of Water and Steam (IAPWS) has not only developed an international standard for the thermodynamic properties of water and steam but also equations for transport properties and other properties [2-6]. We have summarized the equations for calculating the transport properties dynamic viscosity and thermal conductivity as well as the surface tension of the interface between the liquid and the vapor phase of water in an Adobe pdf-file . IAPWS also gives equations for the static dielectric constant and the refractive index of water which are of less interest in chemical engineering applications. If required these equations can be found in the references [2, 3].

The equations for dynamic viscosity and thermal conductivity are given as a function of temperature and density. The use of density as an independent variable makes it possible to calculate properties of the liquid and vapor phase using one single equation. In most cases, however, temperature and pressure are the independent variables and the density must be determined first from the IAPWS-IF97 equations.

Viscosity can be calculated for temperatures from 0 °C to 900 °C and for pressures up to at least 3000 bar depending on the temperature. The equation for thermal conductivity can be applied for temperatures from 0 °C to 800 °C and pressures up to at least 1000 bar. Surface tension can be calculated over the whole range where a liquid-vapor interface exists, i.e. from the triple point to the critical point of water. Accuracy of the equations is more than sufficient for engineering applications. Details can be found in the references [4-6].

Excel Add-In

Water97_v13.xla (version 1.3) is an Add-In for MS Excel which provides a set of functions for calculating thermodynamic and transport properties of water and steam using the industrial standard IAPWS-IF97.

Functions are available for calculating the following properties in the single-phase state for temperatures between 273.15 K and 1073.15 K and pressures between 0 and 1000 bar:

• density
• specific internal energy
• specific enthalpy
• specific entropy
• specific isobaric heat capacity
• specific isochoric heat capacity
• dynamic viscosity
• thermal conductivity

Additionally there are functions for calculating the boiling point temperature as a function of pressure and the vapor pressure as a function of temperature as well as above named properties for the saturated liquid and vapor state both as a function of temperature and pressure between the triple point and the critical point.

The functions are provided as an Add-In file for MS Excel. After downloading and decompressing the archive file the Add-In file "water97_v13.xla" may be loaded in Excel by going to Tools...Add-ins or by simply double clicking on "water97_v13.xla" in Explorer. The water property functions are then available just like built-in functions. In the function wizard list they can be found under User Defined.

The list of available functions with syntax, arguments, units, and examples can be found in the accompanying readme file.

You may use this add-in file for free. However, I retain all rights to it and it may not be sold or distributed as part of another package that is sold without my express permission. All files are provided "as is" without warranty of any kind.

While I can't provide full technical support I will do my best to answer questions or to help via e-mail (b.spang@hamburg.de) if you have any problems. Suggestions from users are also welcome.

• Download Add-In (iapwsif97_v13.zip, 51 kB)

References

1. Properties of Water and Steam in SI-Units, 2nd Revised and Updated Printing, Springer 1979.
2. William T. Parry et al., ASME International Steam Tables for Industrial Use, American Society of Mechanical Engineers 2000.
3. W. Wagner, A. Kruse, Properties of Water and Steam, Springer-Verlag, Berlin 1998.
4. IAPWS Release on the Viscosity of Ordinary Water Substance, IAPWS Secretariat 1997.
5. IAPWS Release on the Thermal Conductivity of Ordinary Water Substance, IAPWS Secretariat 1998.
6. IAPWS Release: "Surface Tension of Ordinary Water Substance", IAPWS Secretariat 1994.

IAPWS Releases are available from the Executive Secretary of IAPWS.

By: Dr. Bernhard Spang, Associate Content Writer (read the author's Profile)
b.spang@gmx.net