Fugacity coefficients, pure components

Here, is the fugacity coefficient of component i in the vapor, not to be confused with, which refers to the saturated pure component i at the same temperature. This result takes a much simpler form if pressure is relatively low. Then, the Poynting correction can be neglected and the fugacity coefficients maybe set to 1. With these simplifications, eq. rii.i2lbecomes... 

For such components, as the composition of the solution approaches that of the pure liquid, the fugacity becomes equal to the mole fraction multiplied by the standard-state fugacity. In this case,the standard-state fugacity for component i is the fugacity of pure liquid i at system temperature T. In many cases all the components in a liquid mixture are condensable and Equation (13) is therefore used for all components in this case, since all components are treated alike, the normalization of activity coefficients is said to follow the symmetric convention. ... 

In some cases, the temperature of the system may be larger than the critical temperature of one (or more) of the components, i.e., system temperature T may exceed T. . In that event, component i is a supercritical component, one that cannot exist as a pure liquid at temperature T. For this component, it is still possible to use symmetric normalization of the activity coefficient (y - 1 as x - 1) provided that some method of extrapolation is used to evaluate the standard-state fugacity which, in this case, is the fugacity of pure liquid i at system temperature T. For highly supercritical components (T Tj,.), such extrapolation is extremely arbitrary as a result, we have no assurance that when experimental data are reduced, the activity coefficient tends to obey the necessary boundary condition 1... 

When i = J, all equations reduce to the appropriate values for a pure species. When i j, these equations define a set of interaction parameters having no physical significance. For a mixture, values of By and dBjj/dT from Eqs. (4-212) and (4-213) are substituted into Eqs. (4-183) and (4-185) to provide values of the mixture second virial coefficient B and its temperature derivative. Values of and for the mixture are then given by Eqs. (4-193) and (4-194), and values of In i for the component fugacity coefficients are given by Eq. (4-196). 

The chemical literature is rich with empirical equations of state and every year new ones are added to the already large list. Every equation of state contains a certain number of constants which depend on the nature of the gas and which must be evaluated by reduction of experimental data. Since volumetric data for pure components are much more plentiful than for mixtures, it is necessary to estimate mixture properties by relating the constants of a mixture to those for the pure components in that mixture. In most cases, these relations, commonly known as mixing rules, are arbitrary because the empirical constants lack precise physical significance. Unfortunately, the fugacity coefficients are often very sensitive to the mixing rules used. 

If we adopt as the standard state for gaseous components the state of pure perfect gas at P = 1 bar and T = 298.15 K = f% = 1) and neglect for simphcity the fugacity coefficients, equation 5.304 combined with equation 5.297 gives... 

For the evaluation of the solubility it is necessary to know the pure component properties and to use an equation-of-state model for the evaluation of the fugacity coefficients. In general, two problems arise ... 

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 fugacity coefficient ratio J can be estimated by assuming that the Lewis and Randall rule11 applies, at least approximately, for the mixture, so that each component has the same fugacity coefficient that it would have if it were a pure gas at the same total pressure. The Principle of Corresponding States can then be used to compare the fugacity coefficients of the three components. At p = 60 atm (61 bar) and in the temperature range from 900 to 1600 K, the reduced temperatures and pressures for the components of the equilibrium... 

The physical property monitors of ASPEN provide very complete flexibility in computing physical properties. Quite often a user may need to compute a property in one area of a process with high accuracy, which is expensive in computer time, and then compromise the accuracy in another area, in order to save computer time. In ASPEN, the user can do this by specifying the method or "property route", as it is called. The property route is the detailed specification of how to calculate one of the ten major properties for a given vapor, liquid, or solid phase of a pure component or mixture. Properties that can be calculated are enthalpy, entropy, free energy, molar volume, equilibrium ratio, fugacity coefficient, viscosity, thermal conductivity, diffusion coefficient, and thermal conductivity. 

When the vapor phase is ideal, the Kt are independent of the vapor composition. In such a case, the procedure for bubble-point determination is to (1) guess a temperature (2) calculate the K, which equal Yiff/P, where yt is the activity coefficient of the ith component in the liquid phase, f is the fugacity of pure liquid i at system temperature and pressure, and P is the system pressure and (3) check if the preceding bubble-point equation is satisfied. If it is not, repeat the procedure with a different guess. 

It is interesting to note that the vapor and liquid compositions are usually different for ideal mixtures. We can see this from Eq. (6.6), since different pure component vapor pressures are rarely equal at the same temperature. This picture changes when nonideal mixtures are considered. As we see from Eq. (6.55, the vapor and liquid mole fractions can become equal when the fugacity and activity coefficients alter the pressure ratio enough to cause the K value to become unity. We then have an azeotrope. 

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