Analysis of Different EOSs in Predicting the Ideal Curve and Deriving the Temperature Dependencies of Their Parameters

Abstract

The regularity shown by different fluids along the contour of the ideal compressibility factor Z = P V /(RT ) = 1 in the temperature-density plane is used to test the accuracy of different equations of state and derive temperature dependencies of their parameters. For a wide range of pure fluids, this contour, known as the Zeno line, has been empirically observed to be nearly linear. The precision of the van der Waals (vdW) equation in predicting the Zeno line has been evaluated and shown that this equation predicts a linear relation between temperature and density on the Z = 1 contour, qualitatively. However, the line shows significant deviations from the experimental Zeno line. Experimental PVT data for CO 2 is used to obtain the temperature dependencies of the vdW parameters. The vdW equation with such temperature dependencies does not show a straight line for the Z = 1 contour. This means that the equation is not able to predict the Zeno line, both qualitatively and quantitatively. Also, the accuracy of the modified vdW equations in predicting the Zeno line has been investigated. It is shown that none of these equations can predict the Zeno line qualitatively. However, the predicted line on the Z = 1 contour given by some of these equations is near the experimental Zeno line. Assuming that the Zeno line must hold, the temperature dependence of the non-ideal thermal pressure, A , of the linear isotherm regularity as A = a + bT + c/T has been derived. Such a temperature dependence was confirmed by experimental data. The derived expression for A was used to obtain the temperature dependence of the thermal pressure coefficient, which is in accordance with experimental data. Also, the temperature dependencies of the parameters of the dense system equation of state

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

“…These EOSs are the RK, SRK, Deiters, LIR, modified LIR (MLIR) by Parsafar and Saydi [10], dense system equation of state (DSEOS), and vdW EOS that are given in the Appendix.…”

“…where a = −2αβB /R, b = −β 2 B /R, and c = A /R − α 2 B /R, and α, β, B , and A are constant parameters that depend on the selected fluid, then the LIR can predict the Zeno line [10]. We shall refer to the LIR with the temperature dependence of A 2 given in Eq.…”

“…12a. Parsafar and Saydi [10] have recently shown that the deviation given by the vdW EOS for the experimental Zeno line may be due to temperature dependences of the a and b parameters of this EOS. They have found temperature dependences of the a and b parameters in such a way that the EOS gives a more accurate prediction for the Zeno line.…”

“…As shown in this figure, the calculated values of A 2 are well fitted with Eq. (12), which was obtained on the basis of the Z = 1 contour [10].…”

“…Parsafar and Saydi [10] made such a study of the Zeno line. They showed that only the van der Waals (vdW) EOS is able to predict a linear relation between the density and temperature on the Z = 1 contour.…”