Noncondensable

It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

The boundary between condensable and noncondensable components is somewhat arbitrary, especially because it depends on the range of temperatures where calculations are made. In this monograph we consider only common volatile gases (e.g. N2,... 

However, if the liquid solution contains a noncondensable component, the normalization shown in Equation (13) cannot be applied to that component since a pure, supercritical liquid is a physical impossibility. Sometimes it is convenient to introduce the concept of a pure, hypothetical supercritical liquid and to evaluate its properties by extrapolation provided that the component in question is not excessively above its critical temperature, this concept is useful, as discussed later. We refer to those hypothetical liquids as condensable components whenever they follow the convention of Equation (13). However, for a highly supercritical component (e.g., H2 or N2 at room temperature) the concept of a hypothetical liquid is of little use since the extrapolation of pure-liquid properties in this case is so excessive as to lose physical significance. 

For a noncondensable component, therefore, it is convenient to use a normalization different from that given by Equation (13) in its place we use... 

In a binary liquid solution containing one noncondensable and one condensable component, it is customary to refer to the first as the solute and to the second as the solvent. Equation (13) is used for the normalization of the solvent s activity coefficient but Equation (14) is used for the solute. Since the normalizations for the two components are not the same, they are said to follow the unsymmetric convention. The standard-state fugacity of the solvent is the fugacity of the pure liquid. The standard-state fugacity of the solute is Henry s constant. 

The use of Henry s constant for a standard-state fugacity means that the standard-state fugacity for a noncondensable component depends not only on the temperature but also on the nature of the solvent. It is this feature of the unsymmetric convention which is its greatest disadvantage. As a result of this disadvantage special care must be exercised in the use of the unsymmetric convention for multicomponent solutions, as discussed in Chapter 4. 

Standard-State Fugacity for a Noncondensable Component For a noncondensable component we write... 

Because of the approximation given by Equation (22), we obtain a convenient method for determining f for a noncondensable... 

The words "condensable" and "noncondensable" as used here are discussed in the footnote near Equation (13) of Chapter 2. 

As discussed in Chapter 2, for noncondensable components, the unsymmetric convention is used to normalize activity coefficients. For a noncondensable component i in a multicomponent mixture, we write the fugacity in the liquid phase... 

In subsequent discussion, therefore, we drop the superscript (P ) on H. Further, we designate a noncondensable component "solute" and a condensable component "solvent."... 

Figure 4-11. Activity coefficients for noncondensable solutes at infinite dilution.

Vapor-Liquid Equilibria for Mixtures Containing One or More Noncondensable Components... 

The critical temperature of methane is 191°K. At 25°C, therefore, the reduced temperature is 1.56. If the dividing line is taken at T/T = 1.8, methane should be considered condensable at temperatures below (about) 70°C and noncondensable at higher temperatures. However, in process design calculations, it is often inconvenient to switch from one method of normalization to the other. In this monograph, since we consider only equilibria at low or moderate pressures in the region 200-600°K, we elect to consider methane as a noncondensable component. 

Figure 13 presents results for a binary where one of the components is a supercritical, noncondensable component. Vapor-phase fugacity coefficients were calculated with the virial... 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

Isothermal Flash Calculations for Mixtures Containing Condensable and Noncondensable Components... 

Evaluation of the activity coefficients, (or y for noncondensable components),is implemented by the FORTRAN subroutine GAMMA, which finds simultaneously the coefficients for all components. This subroutine references subroutine TAUS to obtain the binary parameters, at system temperature. 

For liquid mixtures containing both condensable and noncondensable components. Equation (15) is applicable. However it is now convenient to rewrite that equation. Neglecting, as before, the last term in Equation (15), we obtain ... 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

Calculations for wide-boiling mixtures are a little more difficult to converge, especially for mixtures having very light or noncondensable components together with relatively nonvolatile components and lacking components of intermediate volatility. 

Flash calculations for these mixtures usually require four to eight iterations. Cases 5 and 6 in Table 1 have feeds of this type, including noncondensable components in Case 6. Within the limits of the thermodynamic framework used here, no case has been encountered where FLASH has required more than 12 iterations for satisfactory convergence. 

Appendix C-2 gives constants for the zero-pressure, pure-liquid, standard-state fugacity equation for condensable components and constants for the hypothetical liquid standard-state fugacity equation for noncondensable components... 

Appendix C-5 lists selected UNIQUAC binary parameters and characteristic binary parameters for noncondensable-condensable interactions for 150 binary pairs. For any binary pair, the parameters shown are believed to be the best now available. Parameters listed here were chosen from the more extensive lists in Appendix C-6 and C-7. A12 and A21 correspond to the UNIQUAC... 

The asterisk indicates a noncondensable component, and the parameters for these systems are those used in Equation (4-21) A12 =... 

Appendix C-7 gives interaction parameters for noncondensable components with condensable components. (These are also included in Appendix C-5). Binary data sources are given. 

Characteristic Binary Parameters for Noncondensable-Condensable Interactions... 

UNIQUAC Binary Parameters for Noncondensable Components with Condensable Components. Parameters Obtained from Vapor-Liquid Equilibrium Data in the Dilute Region... 

Data Sources for Binary Systems with a Condensable Component and a Noncondensable Component... 

An additional option allows the user to fit data for binary mixtures where one of the components is noncondensable. The mixture is treated as an ideal dilute solution. The solute... 

PURE calculates pure liquid standard-state fugacities at zero pressure, pure-component saturated liquid molar volume (cm /mole), and pure-component liquid standard-state fugacities at system pressure. Pure-component hypothetical liquid reference fugacities are calculated for noncondensable components. Liquid molar volumes for noncondensable components are taken as zero. 

Standard-state fugacities at zero pressure are evaluated using the Equation (A-2) for both condensable and noncondensable components. The Rackett Equation (B-2) is evaluated to determine the liquid molar volumes as a function of temperature. Standard-state fugacities at system temperature and pressure are given by the product of the standard-state fugacity at zero pressure and the Poynting correction shown in Equation (4-1). Double precision is advisable. 

VIP(I) Vector (length 20) of saturated liquid molar volumes (cm / mole) for condensable components for noncondensable components Vip(i) = 0 (I = 1,N). 

---