Caloric properties

The uncertainties in the equation of state are 0.1% in the saturated liquid density between 280 and 310 K, 0.5% in density in the liquid phase below 380 K, and 1% in density elsewhere, including all states at pressures above 100 MPa. The uncertainties in vapor pressure are 0.5% above 270 K (0.25% between 290 and 390 K), and the uncertainties in heat capacities and speeds of sound are 1%. These uncertainties (in caloric properties and sound speeds) may be higher at pressures above the saturation pressure and at temperatures above 320 K in the liquid phase and at supercritical conditions. 

Because energy usage and heat transfer are important in process operations, caloric properties (enthalpy, heat capacity) can be considered the second most important area. The enthalpy of vaporization is particularly important in vapor-liquid separations. 

The three approaches mentioned in the previous section may also be used to describe caloric properties (enthalpy, entropy, heat capacity) of mixtures. The same considerations mentioned earlier are also true for the application of mixture equations of state and corresponding-states methods for the prediction of caloric properties. 

The experimental determination of a fluid s T t and its inversion curve is difficult since very precise measurements of volumetric or caloric properties at conditions up to 5 times its critical temperature and 12 times its critical pressure. Experimental inversion curve data are therefore scarce, often unreliable [65], and mostly available only for pure fluids. 

Chapter 5 gives a comprehensive overview on the most important models and routes for phase equilibrium calculation, including sophisticated phenomena like the pressure dependence of liquid-liquid equilibria. The abilities and weaknesses of both models and equations of state are thoroughly discussed. A special focus is dedicated to the predictive methods for the calculation of phase equilibria, applying the UNIFAC group contribution method and its derivatives, that is, the Mod. UNIFAC method and the PSRK and VTPR group contribution equations of state. Furthermore, in Chapter 6 the calculation of caloric properties and the way they are treated in process simulation programs are explained. 

It should be clearly pointed out that there is no absolute value for the specific caloric quantities u, h, s, a, and g. Therefore, single values for caloric properties without the definition of a reference point are meaningless only differences between caloric properties can be interpreted. Any table for caloric properties should have defined a reference point where the particular caloric property is set to... 

For process simulators, a more sophisticated way is chosen which makes sure that the caloric properties are consistent even if chemical reactions occur. This is the case if the standard enthalpy of formation Ab° is taken as the reference point, This is explained in detail in the Section 3.1,5 and Chapters 6 and 12, The standard enthalpy of formation refers to the standard conditions To = 298,15 K and Po = 101325 Pa in the state of ideal gases (see Section 2.3), Therefore, the reference point for the specific enthalpy for a pure component is... 

Technical high-precision EOS are a remarkable compromise between keeping the accuracy and gain in simplicity. They can also be applied to substances where less extensive and less accurate experimental data are available. Furthermore, these equations should enable the user to extrapolate safely to the extreme conditions often encountered in industrial processes. For example, in the LDPE process ethylene is compressed to approx. 3000 bar, and it is necessary for the simulation of the process and the design of the equipment to have a reliable tool for the determination of the thermal and caloric properties. 

For the description of Cp or, respectively, cj,, highly flexible and accurate equations are necessary, as discussed in Section 3.2.4. From Cp or c, the various caloric properties can be obtained by integration (see Section 6.1). As reference points, the high-precision EOS use T f = 298.15 K and P r = 101 325 Pa in the ideal gas state, where h ( and Srcf are set to 0, even if this reference point is fictitious and the fluid regarded is in the liquid state. ... 

The advantage of the Helmholtz formulation is that all thermal and caloric properties can be calculated by means of simple derivatives of the Helmholtz energy a with respect to r and <5. For instance, the pressure can be obtained via... 

Concerning the caloric properties, the enthalpy of vaporization is linked to the vapor pressure curve via the Clausius-Clapeyron equation (Eq. (2.86)). Therefore, the quality is mainly determined by the ability of the ty-function in representing the vapor pressure data, which is usually sufficient (see above). The enthalpy of vaporization can easily be calculated with a cubic equation of state by subtracting the residua] parts of the enthalpy of vapor and liquid in the saturation state... 

Equations of state valid both for vapor and liquid phase as well as for pure components and mixtures provide all the necessary volumetric and caloric properties which are needed for process simulation except c p, where a correlation has to be provided. In case of the real liquid mixture behavior, the activity coefficient approach provides an alternative option which is still applied in most cases in chemical industry. This method is explained in detail in Chapter 5. It is more appropriate for low-pressure applications. Concerning the physical property calculation, it is more accurate, as all the properties are represented by separate correlations. The following section explains the correlation and estimation methods for the particular properties. 

The caloric properties of the VTPR equation of state are given by... 

In the following sections, expressions for the caloric properties are derived both for pressure-explicit and for volume-explicit equations of state, which have to be valid for the regarded temperature and pressure range. 

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