Mixing Rules for Thermodynamic Equations of State

In many energy conversion and chemical engineering processes the working substances are fluids. For the rational use of energy in these processes, equations of state for the thermodynamic properties of the working fluids are crucial. Such equations may be either empirical or molecular based. The advantage of the latter is that the required input of experimental data is reduced from about 1000 to about 5 with a corresponding cost-reduction. In the last years, considerable progress was made in the development of molecular based equations of state for pure fluids. In nearly all chemical engineering processes, however, the working fluids are mixtures. Moreover, in energy conversion processes mixtures become increasingly important as working fluids for environmental reasons. Hence, the research challenge is to extend the molecular based equations of state to mixtures by developing mixing rules. For that purpose we will use models for the interactions between the molecules of the working fluids. The problem is to develop mixing rules which match with the interaction models. The performance of the mixing rules has to be checked by molecular computer simulations. Finally, the optimized mixing rules shall be made available in an easy-to-use software package for the calculation of the thermodynamic properties of the working fluids as was already done for pure fluids.

The aim of the project was the extension of the molecular based BACKONE equation of state for the thermodynamic properties of fluids to mixtures. For that purpose new mixing rules based on molecular theory were derived, which require for each binary mixture only one fitted parameter. The high quality of the new mixing rules was proven by comparison of calculated with experimental data. A presently hot example for application are the thermodynamic data of mixed refrigerants with low global warming potential. In addition a new molecular based equation of state for water was derived. The project resulted into 6 publications and 6 oral conference contributions. Text Quantities of a substance like pressure, temperature, density, energy, and entropy are called thermodynamic properties. These include also equilibria between different phases like liquid and vapor. Their knowledge is required for the design of nearly all energy and chemical engineering processes. The laws of thermodynamics tell us that the thermodynamic properties of a given substance call all be derived from a fundamental equation of state. The problem is then to construct the equations of state for the different substances. It is also obvious that the thermodynamic properties are ultimately determined by the forces between the molecules. In recent years there was remarkable progress in formulating the contributions to the equation of state arising from different intermolecular forces. Our group, in particular, had developed before the beginning of the present project the molecular based BACKONE equation of state. This equation allows the description of a class of pure substances within the technically required accuracy. The substances have to be molecularly simple with intermolecular forces of dispersion-, dipolar-, and quadrupolar type. This includes e.g. oxygen, carbon dioxide, alkanes, halogenated alkanes, aromates and ethers. In practical applications, however, frequently equations of state for mixtures are required. Hence, the problem to be solved in the project was the extension of BACKONE to mixtures. In the project new molecular based mixing rules have been derived using theory and computer simulations. These require for each binary mixture only one adjustable parameter. The high quality of the new mixing rules was proven by comparison between calculated and experimental data for mixtures of substances belonging to different molecular interaction classes. It has to be pointed out that for ternary mixtures no additional parameter is required and also that liquid - liquid equilibria can for the first time be described with the same binary parameter as vapor - liquid equilibria. Initially not intended, we also derived a new molecular based equation of state for water in order to be able to describe at a later stage also aqueous mixtures. A presently hot application are the thermodynamic properties of mixtures of refrigerants with small global warming potential. Other interesting applications refer to gas and petroleum engineering. Finally we want to mention the "Reinheitsgebot" for beer: the substances to be used for the production of beer may be only hop, malt and water. Therefore, carbon dioxide is only allowed to be added to the beer if it was produced during the fermentation, but this requires separation of the oxygen. Hence, the thermodynamic properties of the ternary mixture oxygen + nitrogen + carbon dioxide are needed.