Kunz O., Klimeck R., Wagner R., Jaeschke M. The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures

Groupe Européen de Recherches Gazières, 2007. — 555 p.
The accurate knowledge of the thermodynamic properties of natural gases and other mixtures of natural gas components is of indispensable importance for the basic engineering and performance of technical processes. The processing, transportation, and storage of natural gas requires property calculations for a wide range of mixture compositions and operating conditions in the homogeneous gas, liquid, and supercritical regions, and also for vapourliquid equilibrium states. These data can advantageously be calculated from equations of state. To overcome the weaknesses and limitations of existing equations of state used in the natural gas industry, several years ago the Chair of Thermodynamics of the Ruhr-niversität Bochum decided to develop a new wide-range equation of state for natural gases and other mixtures of a quality that enables the equation to be adopted as a standard international reference equation suitable for all natural gas applications where thermodynamic properties are required. The work was supported by the DVGW (German Technical and Scientific Association on Gas and Water) and European natural gas companies (E.ON Ruhrgas, Germany; Enagás, Spain; Gasunie, The Netherlands; Gaz de France, France; Snam Rete Gas, Italy; and Statoil, Norway), which are members of GERG (Groupe Européen de Recherches Gazières). Based on the new formulation, robust and efficient calculation routines (software) were developed in a second project, supported by the European natural gas companies mentioned before. The routines allow for “blind” calculations of the thermodynamic properties of mixtures at arbitrary conditions. This monograph thoroughly presents the new equation of state, adopted by GERG in 2004 and called GERG-2004 equation of state or GERG-2004 for short. Firstly, a brief introduction to existing mixture models with particular focus on the equations of state commonly used in the natural gas industry is given, followed by the basic requirements that were defined for the new model. Similar to recent developments, the new wide-range formulation is explicit in the Helmholtz free energy. The mixture model uses accurate equations of state in the form of fundamental equations for each mixture component along with formulations developed for binary mixtures that take into account the residual mixture behaviour. Therefore, the pure substance equations of state and the general characteristics of the modern approach are described. However, the descriptions should be considered as background information and are not necessarily required for those who are only interested in the structure of the new equation of state. In Chap. 6, an overview of the experimental data used for the development and evaluation of the new mixture model is given. The quality and the extent of the available data limit the achievable accuracy of the equation. Detailed information on the mathematical structure of the new equation of state, its range of validity, the uncertainties in different thermodynamic properties, and the development of the binary equations is provided in Chap. 7. Moreover, it offers guidelines for the calculation of thermodynamic properties from the new equation of state along with some fundamental principles regarding advanced mixture property calculations using second order convergence methods. This includes stability analysis, the solution to flash specifications, the calculation of saturation points, and the construction of phase envelopes. The quality and predictive power of the new formulation is discussed in Chap. 8 by comparisons with experimental data and with results obtained from previous mixture models. Finally, recommendations for the potential further extension of the new equation of state are given. The monograph is written in such a way that the complete numerical information, required for the calculation of thermodynamic properties from the new equation of state, such as density, enthalpy, entropy, isobaric heat capacity, and fugacity coefficients, is given in Chap. 7. However, special algorithms are needed to analyse the phase stability, i.e. to determine whether a mixture at the specified conditions is homogeneous or split in two (or more) phases, and to be able to perform phase equilibrium calculations. As mentioned above, the procedures used for this purpose in this work are also described in Chap. 7. The authors are grateful to the members of the GERG Working Group 1.34 and the GERG Working Group 1.46 for the financial support of the respective research projects and for their very helpful collaboration and their patience. We are also grateful to all of the experimentalists who carried out measurements for the equation project, as well as to those who provided us with recently measured data prior to their publication or with (older) data that are not available in the open literature. Our special thanks go to M. L. Michelsen for providing us with the computer codes of algorithms for phase equilibrium calculations and for his help in understanding the sophisticated procedures. Moreover, we thank G. Lauermann and the Gas Processors Association for providing us with the GPA Thermodynamic Database. We wish to express our warmest thanks to D. Lecaplain, J. Kirschbaum, J. Bierwirth, and K. Göckeler, who, in different ways, contributed to certain parts of this work. In particular, one of us (O. K.) is very grateful to A. Grevé for her assistance in writing this monograph and for typing most of the equations of the manuscript. Finally, we thank E. W. Lemmon for carefully reading the entire manuscript, for helpful discussions and suggestions, and for improving the English style.