Equations of State

Under the direction of Prof. Wagner, the Chair of Thermodynamics at the Ruhr-University Bochum had dealt with the development of equations of state. As it is state-of-the-art today, these equations are established as fundamental equations in the form of the Helmholtz free energy. The equations cover the whole fluid region (gas, liquid, supercritical region, liquid-vapour phase boundaries) with one and the same equation. Due to the form of the equations of state as fundamental equations, all thermodynamic properties can be calculated from combinations of derivatives of such equations, which eliminates the necessity of the integration of pressure explicit equations of state for the calculation of caloric properties.

The characteristic feature of the "Bochum" equations of state is that their mathematical structure is not gained by "trial and error" based on experience, but by the use of a structure optimization method developed at the Chair of Thermodynamics.

Equations of state in reference quality

These equations of state consist of a substance specific form and cover the whole fluid region very precisely.

The IAPWS-95 formulation for water

The IAPWS-95 formulation is a good example of a reference equation of state. Due to the great scientific relevance of this international standard, the IAPWS-95 is described in a chapter of its own.

The Industrial formulation IAPWS-IF97 for water and steam

This special set of equations of state for water and steam was established upon an initiative of the international power-plant industry and the International Association for the Properties of Water and Steam (IAPWS). The IAPWS-IF97 enables the calculation of thermodynamic properties depending on different combinations of input variables at very low computing times.

Reference equation of state GERG-2008 for natural gases and similar mixtures

Due to the great importance of natural gas and related mixtures, an equation of state for natural gases and other mixtures consisting of up to 18 specified components was developed. This equation covers in highest possible accuracy the homogeneous gas, liquid and supercritical regions, and also the vapour-liquid equilibrium. This equation of state was adopted by the GERG (Groupe Europeen de Recherche Gazieres) under the name GERG-2004 as the GERG reference equation of state for natural gases. In the following years, GERG-2004 was expanded by three additional components. Since this development was finished in 2008, the expanded equation of state is called GERG-2008. GERG-2004 and GERG-2008 are not only valid for various types of natural gases but also for binary and other multi-component mixtures of an arbitrary combination of the 18 (GERG-2004) or 21 (GERG-2008) specified components. Meanwhile the GERG-2008 equation of state was adopted as an ISO Standard (ISO 20765-2) for natural gases and similar mixtures. Thus, GERG-2008 replaces GERG-2004. 

Software

Software for the calculation of numerous thermodynamic properties is available for all categories of equations of state listed above; for details see here.