In 1997 the International Association for the Properties of Water and Steam (IAPWS) released the new industrial standard “IAPWS Industrial Formulation for the Thermodynamic Properties of Water and Steam (IAPWS-IF97)”. The IAPWS-IF97 replaces the old industrial standard IFC-67, which was valid until 1997.

Structure and regions of IAPWS-IF97

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 energy g(p,T), region 3 by a fundamental equation for the specific Helmholtz energy f(ρ,T), and the saturation curve, corresponding to region 4, by a saturation-pressure equation p_s(T). The high-temperature region 5 is also covered by a g(p,T) equation. These 5 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 c_p 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 p_s 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 [42].

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 T_s(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 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 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 f₃(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 dependent on 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 points requirements, concept, accuracy and consistency at the region boundaries.

Software for IAWPS-IF97

On the basis of IAPWS-IF97, including all of the backward equations as well as 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.