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2.8 Selecting an Appropriate Model 59

predictive Soave-Redlich-Kwong (PSRK) Model dilute to concentrated solutions, but only the model of Chen
and associates, which is a substantial modification of the
~~~ation-of-~tate models, such as S-R-K and P-R, describe
NRTL model (see Section 2.6), can handle mixed-solvent
mixtures of nonpolar and slightly polar compounds. Gibbs
systems, such as those containing water and alcohols.
free-energy activity-coefficient models are formulated for
subcritical nonpolar and polar compounds. When a mixture
contains both polar compounds and supercritical (light-gas) Polymer Solution Models
components (e.g., a mixture of hydrogen, carbon monoxide, Polymer processing often involves solutions of solvent,
methane, methyl acetate, and ethanol), neither method ap-
monomer, and an amorphous (noncrystalline) polymer, re-
plies. To estimate vapor-liquid phase equilibria for such quiring vapor-liquid and, sometimes, liquid-liquid phase-
mixtures, a number of more theoretically based mixing rules equilibria calculations, for which estimation of activity coef-
for use with the S-R-K and P-R equations of state have ficients of all components in the mixture is needed. In general,
been developed. In a different approach, Holderbaum and
the polymer is nonvolatile, but the solvent and monomer are
Gmehling [58] formulated a group-contribution equation of
volatile. When the solution is dilute in the polymer, activity-
state referred to as the predictive Soave-Redlich-Kwong coefficient methods of Section 2.6, such as the NRTL method,
(PSRK) model, which combines a modified S-R-K equation can be used. Of more interest are solutions with appreciable
of state with the UNIFAC model. To improve the ability of concentrations of polymer, for which the methods of Sections
the S-R-K equation to predict vapor pressure of polar com- 2.5 and 2.6 are inadequate. Consequently, special-purpose
pounds, they provide an improved temperature dependence empirical and theoretical models have been developed. One
for the pure-component parameter, a, in Table 2.5. To handle method, which is available in simulation programs, is the
mixtures of nonpolar, polar, and supercritical components,
modified NRTL model of Chen [64], which combines a mod-
they use a mixing rule for a, which includes the UNIFAC ification of the Flory-Huggins equation (12-65) for widely
model for handling nonideal effects more accurately. differing molecular size with the NRTL concept of local com-
Additional and revised pure-component and group interac-
position. Chen represents the polymer with segments. Thus,
tion parameters for use in the PSRK model are provided
solvent-solvent, solvent-segment, and segment-segment
by Fischer and Gmehling [59]. In particular, [58] and [59] binary interaction parameters are required, which are often
provide parameters for nine light gases (Ar, CO, C02, CH4, available from the literature and may be assumed indepen-
HZ, HzS, Nz, NH3, and 02) in addition to UNIFAC parame- dent of temperature, polymer chain length, and polymer con-
ters for 50 groups.
centration, malung the model quite flexible.
Electrolyte Solution Models
2.8 SELECTING AN APPROPRIATE MODEL
Solutions of weak and/or strong electrolytes are common in
chemical processes. For example, sour water, found in many The three previous sections of this chapter have discussed
petroleum plants, may consist of solvent (water) and five the more widely used models for estimating fugacities,
dissolved gases: CO, COz, CH4, H2S, and NH3. The apparent activity coefficients, and K-values for components in mix-
composition of the solution is based on these six molecules. tures. These models and others are included in computer-
However, because of dissociation, which in this case is aided, process-simulation programs. To solve a particular
weak, the true composition of the aqueous solution includes separations problem, it is necessary to select an appropriate
ionic as well as molecular species. For sour water, the ionic model. This section presents recommendations for making
species present at chemical equilibrium include H+, OH-, at least a preliminary selection.
HC03-, C03=, HS-, S=, NH~+, and NH2COO-, with the The selection procedure includes a few models not cov-
total numbers of positive and negative ions subject to elec- ered in this chapter, but for which a literature reference is
troneutrality. For example, while the apparent concentration given. The procedure begins by characterizing the mixture
of NH4 in the solution might be 2.46 moles per kg of water, by chemical types present: Light gases (LG), Hydrocarbons
when dissociation is taken into account, the molality is only (HC), Polar organic compounds (PC), and Aqueous solu-
0.97, with NH~+ having a molality of 1.49. All eight ionic tions (A), with or without Electrolytes (E).
species are nonvolatile, while all six molecular species If the mixture is (A) with no (PC), then if electrolytes
are volatile to some extent. Accurate calculations of vapor- are present, select the modified NRTL equation. Otherwise,
liquid equilibrium for multicomponent electrolyte solutions select a special model, such as one for sour water (contain-
must consider both chemical and physical equilibrium, both ing NH3, H2S, C02, etc.) or aqueous amine solutions.
of which involve liquid-phase activity coefficients. If the mixture contains (HC), with or without (LG), cover-
A number of models have been developed for predicting ing a wide boiling range, choose the corresponding-states
activity coefficients in multicomponent systems of elec- method of Lee-Kesler-Plocker [8,65]. If the boiling range of
trolytes. Of particular note are the models of Pitzer [60] and a mixture of (HC) is not wide boiling, the selection depends
Chen and associates [61, 62, and 631, both of which are in- on the pressure and temperature. For all temperatures and
cluded in simulation programs. Both models can handle pressures, the Peng-Robinson equation is suitable. For