Deriving Analytical Expressions for the Ideal Curves and Using the Curves to Obtain the Temperature Dependence of Equation-of-State Parameters

Abstract

Different equations of state (EOSs) have been used to obtain analytical expressions for the ideal curves, namely, the Joule-Thomson inversion curve (JTIC), Boyle curve (BC), and Joule inversion curve (JIC). The selected EOSs are the Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), Deiters, linear isotherm regularity (LIR), modified LIR (MLIR), dense system equation of state (DSEOS), and van der Waals (vdW). Analytical expressions have been obtained for the JTIC and BC only by using the LIR, MLIR, and vdW equations of state. The expression obtained using the LIR is the simplest. The experimental data for the JTIC and the calculated points from the empirical EOSs for the BC are well fitted into the derived expression from the LIR, in such a way that the fitting on this expression is better than those on the empirical expressions given by Gunn et al. and Miller. No experimental data have been reported for the BC and JIC; therefore, the calculated curves from different EOSs have been compared with those calculated from the empirical equations. On the basis of the JTIC, an approach is given for obtaining the temperature dependence of an EOS parameter(s). Such an approach has been used to determine the temperature dependences of A 2 of the LIR, a and b parameters of the vdW, and the cohesion function of the RK. Such temperature dependences, obtained on the basis of the JTIC, have been found to be appropriate for other ideal curves as well.

A theoretically modified PC-SAFT equation of state for predicting asphaltene onset pressures at low temperatures

“…Then, the comparisons between PC-SAFT and those correlations should be taken with caution. Parsafar and IzanIoo (see Figure7in[211]) realized a similar comparison for Ar, N 2 , and CO 2 among the Amagat curves predicted by other EoS models and the same empirical correlations here used[223]-[225].Finally, as seen from figures 2-66 to 2-72, Boyle and Charles curves behave contrary to the Amagat ones, showing a shrinkage of the respective envelopes as 𝑛 is increased. Notice that PC-SAFT has not problems in tracing the Boyle and Charles curves, but the Amagat curves are really a demanding test for this EoS.…”

“…Brown [210] reported a group of curves, known as Brown´s characteristic (ideal) curves, representing thermodynamic states at which one thermodynamic property of a real pure fluid matches that of an ideal gas [211]. To predict physically reasonable Brown ideal curves, such as the Amagat (Joule inversion), Boyle, and Charles (Joule-Thompson inversion) ones, is challenging for any equation of state (EoS) intended to represent the thermodynamics of a real pure fluid at any condition on the P-T phase diagram.…”

Generalized Cubic Equation of State Adjusted to the Virial Coefficients of Real Gases and Its Prediction of Auxiliary Thermodynamic Properties

“…Nevertheless, several studies that have considered the accuracy of these models in predicting the auxiliary thermodynamic properties should be mentioned. Some of them (see for example refs − ) have examined the Joule−Thomson inversion and the ideal gas curves. Others (see for example refs − ) have considered properties such as the isochoric and the isobaric heat capacities, sound velocities, etc.…”