A method that includes the use of modified equations of state has been developed to enable noniterative, efficient computation of the thermodynamic behaviors of gases and liquids at temperatures >100 K and pressures from 1 to 100 MPa. The method is intended to be particularly useful for calculating such quantities as partial molar volumes, enthalpies, entropies, compressibilities, and thermal expansivities of oxidant/fuel mixtures at given pressures, temperatures, and mass fractions in gas turbine and rocket engines.

The method is based partly on the concept of a reference state of a real gas, which state is similar to that of a perfect gas at the same temperature and pressure and is defined with respect to the condition of the real gas at a relatively low reference pressure. The method is also based partly on the use of departure functions to represent the deviations of thermodynamic functions of the real gas at high pressure from reference-state values of those functions.

The form of the departure functions is obtained from the Peng-Robinson equation of state:

p=RT/(v-bm)-am/(v²+2bmv-b²m),

where p is the absolute pressure, R is the molar ideal-gas constant,T is the absolute temperature, and v is the molar volume. The parameters am and bm are semiempirical terms calculated from critical-state properties; these parameters follow conventional mixing rules; namely,

am=ΣΣxixjaij and bmxibi,

where xi is the mole fraction of the ith molecular species.

One first applies the departure-function formalism to each of the pure constituents of a mixture, then reuses this formalism for the mixture as a whole. In the application to each pure constituent, one expresses the reference-state enthalpy and entropy as finite series of temperature- and pressure-dependent terms, the coefficients of which are established by least-squares fits to the best available empirical data on enthalpy and entropy (see table). This method follows the standard practice in calculating the properties of nonideal mixtures by use of accurately known properties of the pure constituents along with excess Gibbs energy and/or fugacity coefficients, which are defined by use of conventional mixing rules.

Reference-State Fits were made for seven substances in various pressure and temperature ranges. The fit for each substance is characterized by a maximum root-mean-square (rms) relative error at fixed pressure.

This work was done by Josette Bellan, Richard S. Miller, and Kenneth G. Harstad of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Physical Sciences category, or circle no. 128 on the TSP Order Card in this issue to receive a copy by mail ($5 charge).

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Equations of state for fluid mixtures at high pressures

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This article first appeared in the March, 1998 issue of NASA Tech Briefs Magazine.

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