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

Abstract

This study demonstrates that the overall reliability of a simplest cubic equation of state (EOS) might be improved by developing its accuracy in estimating the virial coefficients. In particular, it has been demonstrated that the progress can be achieved in predicting the sound velocities and, probably, the Joule−Thomson inversion curves. At the same time, the limitations of the simplest model are evident. In particular, it fails in predicting of the virial coefficients in the low temperature range. As a result, its predictions of the liquid phase properties are still imperfect. Further directions of development of the proposed EOS are discussed.

About the physical validity of attaching the repulsive terms of analytical EOS models by temperature dependencies

“…In addition, it can be seen that at high temperatures C V increases with the pressure. Surprisingly, the simple and theoretically baseless cubic EOS model [14] predicts most of the phenomena above qualitatively correct. In particular, it shows the increase of C V near the critical temperature, failing although in predicting the characteristic "peak" shape.…”

“…Solid lines: the EOS of Christoforakos and Franck [23]. Dotted lines: the recently proposed cubic EOS [14]. Dashed lines: Huang and Radosz's version of SAFT [1].…”

“…In order provide an answer to this question let us analyze the behavior of generalized functions at the limiting condition of the infinite pressure. Such an analysis has been proposed in the previous publication [14], however has not been successfully completed.…”

“…It has been demonstrated [19][20][21] that analytical EOS models may describe the complex phenomena such as the increase of C R V around the critical temperatures. This behavior can be generated even by the simple empirical temperature dependency for the attraction parameter of cubic EOS [14]:…”

“…A very important practical question is how much the prediction of the real fluids data at ordinary pressures is affected by the inconsistency taking place at the imaginary state of infinite pressure. In what follows we will compare the predictions of the isochoric heat capacity yielded by the recently proposed cubic EOS [14], the theo- …”