Category: Engineering Equations of State for PVT Properties

P7.1. For Tr < 1 and Pr ≈ Prsat, the Peng-Robinson equation of state has three roots corresponding to compressibility factors between zero and 10. The smallest root is the compressibility factor of the liquid. The largest root is the compressibility factor of the vapor and the middle root has no physical significance. This gives us a general method for finding the…

The simple physical observations and succinct mathematical models set forth in this chapter provide powerful tools for current chemical applications and excellent examples of model development that we would all do well to emulate. This chapter has illustrated applications of physical reasoning, dimensional analysis, asymptotic analysis, and parameter estimation that have set the standard for…

Molecular simulation provides a numerical connection between the intermolecular potential model and the macroscopic properties, but it does so one state point at a time. For an equation of state, we need an equation that makes this connection over all state points. The key to making this kind of connection is to consider the average…

In the previous sections we alluded to equations of state as empirical equations that may have appeared by magic. In this section and the next two, we attempt to de-mystify the origins behind equations of state by systematically describing the current outlook on equation of state development. It may seem like overkill to develop so…

The capability of a relatively simple equation to represent the complex physical phenomena illustrated in Figs. 7.5–7.6, and as shown later in Figs. 7.7 and 7.9, is a tribute to the genius of van der Waals. His method for characterizing the difference between subcritical and supercritical fluids was equally clever. He recognized that, at the critical point, Figure 7.7.…

There is one implication of non-ideal fluid behavior that should be clear from the equations presented above: Real fluids behave differently from ideal gases. How differently? An example provides the most straightforward answer to that question. Here we adapt some of the derivatives from Chapter 6. Example 7.6. Derivatives of the Peng-Robinson equation Determine , , and  for the…

To apply the relationships that we can develop for relating changes in properties to CP, CV, P, T, V, and their derivatives, we need really general relationships between P, V, and T. These relationships are dictated by the equation of state (EOS). Constructing an equation of state with a firm physical and mathematical foundation requires considering how the intermolecular forces…

At low reduced pressure, deviations from ideal gas behavior are sufficiently small that we can write our equation of state as explicit in a power series with respect to density. That is, where B, C, and D are the second, third, and fourth virial coefficients. This can be considered an expansion in powers of ρ. Coefficients C and D are rarely applied because…

P-V-T behavior can be generalized in terms of Tc, Pc, and ω. The original correlation was presented by Pitzer, and is given in the form  Pitzer correlation. where tables or charts summarized the values of Z0 and Z1 at reduced temperature and pressure. The broad availability of computers and programmable calculators is making this approach somewhat obsolete, but it is worthwhile to…

If we plot P versus ρ for several different fluids, we find some remarkably similar trends. As shown in Fig. 7.1 below, both methane and pentane show the saturated vapor density approaching the saturated liquid density as the temperature increases. Compare these figures to Fig. 1.4 on page 23, and note that the P versus ρ figure is qualitatively a mirror image of the P versus V figure.…