Thermodynamics fugacity coefficient

The fugacity coefficient can be found from the equation of state using the thermodynamic relation (Beattie, 1949) ... 

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. 

Thermodynamic consistency tests for binary vapor-liquid equilibria at low pressures have been described by many authors a good discussion is given in the monograph by Van Ness (VI). Extension of these methods to isothermal high-pressure equilibria presents two difficulties first, it is necessary to have experimental data for the density of the liquid mixture along the saturation line, and second, since the ideal gas law is not valid, it is necessary to calculate vapor-phase fugacity coefficients either from volumetric data for... 

For more comprehensive calculations of the fugacity coefficients in mixtures, see J. M. Prausnitz, R. N. Lichtenthaler, and E. G. de Azevedo. Modular Thermodynamics of Fluid Phase Equilibria, Prentice Hall. Englewood Cliffs. N.J., 19S6. Chapter 5. 

DIPA) and methyldiethanolamine (MDEA) have also been employed. Earlier, Atwood et al. (J 5) proposed a thermodynamic model for the equilibria in I S+alkanol-amine+H20 systems. The central feature of this model is the use of mean ionic activity coefficient. The activity coefficients of all ionic species are assumed to be equal and to be a function only of ionic strengths. Klyamer and Kolesnikova ( 1j[) utilized this model for correlation of equilibria in C02+alkanol-amine+H O systems and Klyamer et al. (J 7) extended it to the H2S+C02+alkanolamine+H20 system. The model is restricted to low pressures as the fugacity coefficients are assumed unity and it has been found that the predictions are inaccurate in the four-component system since the activity coefficients are not equal when a number of different cations and anions are present. 

In the thermodynamic treatment of phase equilibria, auxiliary thermodynamic functions such as the fugacity coefficient and the activity coefficient are often used. These functions are... 

The thermodynamic reaction equilibrium constant K, is only a function of temperature. In Equation 4.18, m, the activity of the guest in the vapor phase, is equal to the fugacity of the pure component divided by that at the standard state, normally 1 atm. The fugacity of the pure vapor is a function of temperature and pressure, and may be determined through the use of a fugacity coefficient. The method also assumes that an, the activity of the hydrate, is essentially constant at a given temperature regardless of the other phases present. 

The algorithm used to equilibrate ice, COy-bHoO, and CH4 6H2O with the solution phase uses aspects of several of the above techniques. First, the model calculates the fugacity coefficients for CC>2(g) and CH4(g) using the approach outlined in Eqs. 3.36 to 3.48 and 3.72 to 3.74. Then the model calculates which of the phases - ice, C02-6H20, or CH4-6H20 - is thermodynamically most stable by selecting the phase that minimizes the activity of water (aw). The reaction,... 

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. 

The fugacity coefficient < >2 is calculated by using a thermodynamic model. In this work the SRK (Soave) and Peng Robinson (PR) Equations of State were considered. 

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. 

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). 

The fugacity coefficient 0 is generally calculated from an equation of state. However, many equations of state require a knowledge of the critical parameters of the solute, which may not always be available. Nevertheless, solubilities can be correlated, and sometimes extrapolated, using this approach. The addition of more solutes poses few problems from a thermodynamic viewpoint, as long as the appropriate solid-state fugacity is used in the calculations. This type of approach may also be used to study... 

The calculation of fugacity coefficients and the use of generalized charts are discussed in the standard thermodynamics texts. If the fugacity coefficients are known then in the nonideal case we find that... 

These are C equations, corresponding to the C components. The distribution coefficients are functions of the temperature, pressure, and liquid and vapor compositions. Equation 2.9 is based on the thermodynamic condition that at phase equilibrium the fugacities of each component in the liquid phase and the vapor phase are equal. Referring to Section 1.3, the fugacities can be expressed in terms of fugacity coefficients as follows ... 

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