Fugacity and compressibility factor

For purpose of calculations, physical properties of the liquid phase are considered independent of pressure (specific mass, viscosities and diffusivities). Concerning the gas phase, it is clear that these properties are functions of the pressure compressibility factors and fugacity coefficients are calculated by the... 

S, N2/H2O (29), CO2/H2O (30) and H2/H2O (21). Above 4500C, the icity coefficients for these species were all close to unity. Fugacity coefficients of radicals and transition states were assumed to ual one. The only correction made therefore was to include the compressibility factor and fugacity coefficient (when appropriate) of supercritical water as calculated from the steam tables (22). At most, this correction amounted to a factor of two and did not change the modeling results significantly. 

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. 

The first attempt to find exact shape factors is due to Leach,who equated the residual compressibility factor and fugacity coefficient of two fluids, with... 

Table 9.E.10 Performance of the SRK EoS in the Estimation of the Compressibility Factor and Fugacity Coefficient for i-Butane at 410 K as a Fimc-tion of Pressure. Values for z and from Goodwin and Haynes.

The acentric factor is used in thermodynamic correlations involving fugacity, compressibility factor, enthalpy, fugacity, and virial coefficients. The computer program PROG21 provides a routine for estimating the vapor pressure, and Table 2-1 shows P of water as a function of temperature. Figure 2-6 shows the vapor pressure of water as a function of temperature to its critical value of 374.2°C. For water, deviations of less... 

The applicability of the proposed equation was tested in terms of its predicted values of the compressibility factors, liquid fugacity coefficients, and isothermal enthalpy departures of pure compounds. 

Besides difference measures, it is frequently convenient to describe deviations from ideality by using ratio measures. In this section we present the ratio measures commonly employed to measure deviations from ideal-gas behavior the compressibility factor and the fugacity coefficient. 

This function calculates the compressibility factor and the % fugacity coefficient of the vapor of species 1 in a binary % mixture using the Peng Robinson EOS... 

Generalized charts are applicable 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, compressibility factors, liquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibility factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

PI 1.5 Start with the defining equations for the fugacity / and the fugacity coefficient equations (11.36), (11.37), and (11.38), along with the relationships given in Table 11.1, and show that 4> is related to the compressibility factor z by equation (11.44)... 

Fugacity coefficients (and therefore fugadties) are evaluated by this equation from PVT data or from an equation of state. For example, when the compressibility factor is given by Eq. (3.31), we have... 

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). 

In eqs 2 and 3, V is the molar volume, z is the compressibility factor, n is the total number of moles in the system, and ni is the number of moles of component i. Equations 2 and 3 show that the fugacity coefficient their derivatives with respect to the number of moles of solute are known. While near the critical point the fluctuations are important and an EOS involving them should be used, we neglect for the time being their effect. 

Suppose that n /fl > I, as would occur, for example, as the result of a dissociation reaction undergone by a nominally pore chemical species. Then, according to (1.3-42), the apparent compressibility factor is greater than urtiiy. On the other hand, suppose thel n ln < I, as would occur, for example, if a nominally pure substance underwent association. Then, by ([, 3-42), the apparent compressibility factor is less than unity. In both cases—dissociation and association of a nominally pane substance at low pressure—the apparent fugacity coefficient is also different from the expected value of unity. 

Alternatively if compressibility factor charts are available, these Z factors may be used to compute the fugacity of pure component i by use of the following equation which is readily obtained by commencing with Eqs. (14-12) and (14-26)... 

Although only compressibility factor calculations are used as an example in the explanation of the method, other properties can be predicted equally well. Because of the temperature and density dependence of the diameters and shape factors needed to relate them to critical constants it is best to determine separate values of them for each component. Three basic dimensionless properties should be determined. These are the ones best suited to the use of the HSE method with an equation of state in terms of temperature and density. These are the compressibility factor, z the internal energy deviation (U — V)/RT and a dimensionless fugacity ratio, ln(f/pRT). All other desired properties can be obtained from them. The ln(f/pRT) and z are calculated similarly. The computation scheme is outlined as shown in Table III. 

A new pressure-explicit equation of state suitable for calculating gas and liquid properties of nonpolar compounds was proposed. In its development, the conditions at the critical point and the Maxwell relationship at saturation were met, and PVT data of carbon dioxide and Pitzers table were used as guides for evaluating the values of the parameters. Furthermore, the parameters were generalized. Therefore, for pure compounds, only Tc, Pc, and o> were required for the calculation. The proposed equation successfully predicted the compressibility factors, the liquid fugacity coefficients, and the enthalpy departures for several arbitrarily chosen pure compounds. 

Table 1. Compression factor, fugacity coefficient, and residual thermodynamic functions of real fluid Refrigerant 500...

In the present investigation, the compression factor, fugacity coefficient, and residual thermodynamic functions of the real fluid R-500 have been calculated using the BACK equation of state. For this purpose, the experimental data, i.e., critical constants, saturated liquid density, saturation vapor pressure, and the PVT data have been utilized. 

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