Thermodynamic properties fugacity coefficients

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

For liquid mixtures at low pressures, it is not important to specify with care the pressure of the standard state because at low pressures the thermodynamic properties of liquids, pure or mixed, are not sensitive to the pressure. However, at high pressures, liquid-phase properties are strong functions of pressure, and we cannot be careless about the pressure dependence of either the activity coefficient or the standard-state fugacity. 

It is believed that ASPEN provides a state-of-the-art capability for thermodynamic properties of conventional components. A number of equation-of-state (EOS) models are supplied to handle virtually any mixture over a wide range of temperatures and pressures. The equation-of-state models are programmed to give any subset of the properties of molar density, residual enthalpy, residual free energy, and the fugacity coefficient vector (and temperature derivatives) for a liquid or vapor mixture. The EOS models (named in tribute to the authors of such work) made available in ASPEN are the following ... 

In addition to these ordinary thermodynamic properties, the temperature and composition derivatives of the enthalpy and the fugacity coefficients are required in some calculations. 

These equations are restatements of Eqs. (6.37) and (6.38) wherein the restriction of the derivatives to constant composition is shown explicitly. They lead to Eqs. (6.40), (6.41), (6.42), and (11.20), which allow calculation of residual properties and fugacity coefficients from PVT data and equations of state. It is through the residual properties that this kind of experimental information enters into the practical application of thermodynamics. 

Use of generalized fugacity coefficients (e.g., see Example 1.18) eliminates some computational steps. However, the equation-of-state method used here is easier to program on a programmable calculator or computer. It is completely analytical, and use of an equation of state permits the computation of all the thermodynamic properties in a consistent manner. 

Finally, we must select appropriate methods of estimating thermodynamic properties. lime (op. cit.) used the SRK equation of state to model this column, whereas Klemola and lime (op. cit.) had earlier used the UNIFAC model for liquid-phase activity coefficients, the Antoine equation for vapor pressures, and the SRK equation for vapor-phase fugacities only. For this exercise we used the Peng-Robinson equation of state. Computed product compositions and flow rates are shown in the table below. 

The graphs are based on the Peng-Robinson equation of state (1) as improved by Stryjek and Vera (2, 3). The equations for thermodynamic properties using the Peng-Robinson equation of state are given in the appendix for volume, compressibility factor, fugacity coefficient, residual enthalpy, and residual entropy. Critical constants and ideal gas heat capacities for use in the equations are from the data compilations of DIPPR (8) and Yaws (28, 29, 30). 

Extensive thermodynamic properties of steam are available in the steam tables and these data offer a good comparison for the validity of the equation of state in the calculation of other thermodynamic properties. Figure 1 shows the fugacity coefficients of steam calculated from Equation 15. For comparison, Figure 1 also shows the fugacity coefficients of steam calculated from the steam tables. 

Values of the fugacity coefficients computed from the Starling modification of the B-W-R equation of state are 0.3894 and 0.9101, respectively (K. E. Starling, Fluid Thermodynamic Properties for Light Petroleum Systems, Gulf Publishing Co., Houston, Texas, 1973.)... 

In this chapter we have developed ways for computing conceptual thermodynamic properties relative to well-defined states provided by the ideal gas. We identified two ways for measuring deviations from ideal-gas behavior differences and ratios. Relative to the ideal gas, the difference measures are the isobaric and isometric residual properties, while the ratio measures are the compressibility factor and fugacity coefficient. These differences and ratios all apply to the properties of any single homogeneous phase (liquid or gas) composed of any number of components. 

Numerical calculations of phase equilibria require thermodynamic data or correlations of data. For pure components, the requisite data may include saturation pressures (or temperatures), heat capacities, latent heate, and volumetric properties. For mixtures, one requires a PVTx equation of state (for determination of d/), and/or an expression for the molar excess Gibbs energy (fw determination of yt). We have discussed in Sections 1.3 and 1.4 the correlating capabilities of selected equations of state and expressions for g, and the behavior of the fugacity coefficients and activity coefficients derived ftom them. 

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