Prediction from pure-component

Pure-component vapor pressures can be used for predicting solu-bihties for systems in which RaoiilFs law is valid. For such systems Pa = Pa a, where p° is the pure-component vapor pressure of the solute andp is its partial pressure. Extreme care should be exercised when attempting to use pure-component vapor pressures to predict gas-absorption behavior. Both liquid-phase and vapor-phase nonidealities can cause significant deviations from the behavior predicted from pure-component vapor pressures in combination with Raoult s law. Vapor-pressure data are available in Sec. 3 for a variety of materials. 

When two similarly structured anionic surfactants adsorb on minerals, the mixed admicelle approximately obeys ideal solution theory (jUL - Below the CMC, the total adsorption at any total surfactant concentration is intermediate between the pure component adsorption levels. Adsorption of each surfactant component in these systems can be easily predicted from pure component adsorption isotherms by combining ideal solution theory with an empirical correspond ng states theory approach (Z3). ... 

A review is presented of techniques for the correlation and prediction of vapor-liquid equilibrium data in systems consisting of two volatile components and a salt dissolved in the liquid phase, and for the testing of such data for thermodynamic consistency. The complex interactions comprising salt effect in systems which in effect consist of a concentrated electrolyte in a mixed solvent composed of two liquid components, one or both of which may be polar, are discussed. The difficulties inherent in their characterization and quantitative treatment are described. Attempts to correlate, predict, and test data for thermodynamic consistency in such systems are reviewed under the following headings correlation at fixed liquid composition, extension to entire liquid composition range, prediction from pure-component properties, use of correlations based on the Gibbs-Duhem equation, and the recent special binary approach. 

Figure 4. Three-phase equilibrium LtL2V in the system carbon dioxide-water-1-propanol at 333 K and 13.1 MPa exp., this work — Calculated with Peng-Robinson EOS using Panagiotopoulos and Reid mixing rule, left side prediction from pure component and binary data alone, right side interaction parameters fitted to ternary three-phase equilibria at temperatures between 303 and 333 K...

Rates of binary O2/N2 diffusion in CMS s were also reported by Chen et al. (1994). It was found that the cross-term diffusivities. Ay, are quite significant, hence the diffusion rates cannot be predicted by approximating the system as pure component diffusion. A simple kinetic theory is derived in Chapter 3 for predicting binary (or mixture) diffusion from pure-component diffusivities (Chen and Yang, 1992). The concentration dependence of the pure component diffusivities are needed for this prediction. Figure 5.26 compares the rates predicted by the kinetic model with experimental data. Also shown are results predicted from pure component diffusivities. It is clear that pure component diffusivities cannot be used for predicting rates for binary diffusion. A statistical theory by MacElroy et al. (1997) has also been used to predict binary diffusion in CMS s with satisfactory results. 

Figure 5.26. Counter-diffusion (ieft) and co-diffusion (right) of O2/N2 in Bergbau Forschung CMS at 27°C (Chen et ai., 1994 Chen, 1994, with permission). Symbols are experimental data points solid lines are prediction by simple kinetic theory for mixture diffusion (Chen and Yang, 1992, and Chapter 3) dashed lines are prediction from pure component diffusivities.

Over the years, various other theories and models have been proposed for predicting salt effect in vapor-liquid equilibrium, including ones based on hydration, internal pressure, electrostatic interaction, and van der Waals forces. These have been reviewed in detail by Long and McDevit (25), Prausnitz and Targovnik (31), Furter (7), Johnson and Furter (8), and Furter and Cook (I). Although the electrostatic theory as modified for mixed solvents has had limited success, no single theory has yet been able to account for or to predict salt effect on equilibrium vapor composition from pure-component properties alone. 

The macroscopic properties such as mechanical behavior of block copolymers or polymer blends depend directly on the relative concentrations of different constituents and their meso-structures. How to predict the exact macroscopic properties of polymer blends or block copolymers with meso-phase separation structures from pure component properties remains a big challenge. Some theoretical efforts have been explored. For example, Buxton et al. found that the deformations and fractures of polymer blends can be described by the... 

When the gas or vapor feed stream contains a component that is highly soluble in the polymer membrane and causes plasticization, then the selectivity as defined by Equation 4.6 will depend on the partial pressure or the amount of the plasticizing component sorbed into the membrane. Furthermore, pure-gas permeation measurements are generally not a good indicator of the separation performance, and mixed-gas permeation measurements will be needed [21-23]. Often, the mixed-gas selectivity is less than predicted from pure-gas measurements [8] however, the opposite has been observed [24], Competitive sorption effects can also compromise the prediction of mixed-gas behavior from pure-gas measurements [25], For gas pairs where each component is less condensable than C02, like 02/N2, it is generally safe to conclude that the selectivity characteristics can be accurately judged from pure-gas permeabilities at all reasonable pressures. When the gas pair involves a component more condensable than C02, plasticization is likely to be a factor and pure-gas data may not adequately reflect mixed-gas selectivity. When C02 is a component, the situation depends on the partial pressures and the nature of the polymer. 

Since the type of solutions encountered in extractive distillation involve mixtures of polar compounds or polar with nonpolar ones, the solutions are usually nonideal, and predicting the phase equilibrium from pure component data only is practically impossible. Theoretical and experimental studies through the years, however, have established certain trends which are used to search for and screen potential solvents. 

The variation of total and partial amount of ethane adsorbed as a function of composition at 270 kPa for a meUiane-ethane mixture is shown in Fig. 1. Two models, Langmuir for mixtures using Innes and Rowley correlation [2] and lAST [3] are used to predict the data from pure component isotherms. Both the models do reasonably well in predicting both the partial and total amount adsorbed. The pure component methane and ethane isotherms fix the end points of total amount adsorbed. The partial amount of ethane is also restricted between its pure component value and zero. The two models simply predict the curves in between the end points fixed by these thermocfynamic restrictions. 

For biomaterials that are thermally unstable and decompose before reaching the critical temperature, several estimation techniques are available. We have used the Lydersen group contributions method ( ). Other techniques available for predicting critical properties have been reviewed and evaluated by Spencer and Daubert ( ) and Brunner and Hederer Qfi). It is also possible to determine the EOS parameters from readily measurable data such as vapor pressure, and liquid molar volume instead of critical properties (11). We used the Lydersen method to get pure component parameters because the vapor compositions we obtained were in closer agreement with experiment than those we got from pure component parameters derived by Brunner s method. The critical properties we used for the systems we studied are summarized in Table II. 

Mixing rules are relations used to calculate mean values for the parameters of an equation of state from pure component values and mixture composition. Note that the accuracy of predictions for pure component properties is a necessary but not sufficient condition for the accuracy for mixture properties. Equally important is the type of mixing rules, as well as the quality of the interaction parameters used in these relations. 

Transport in OSN membranes occurs by mechanisms similar to those in membranes used for aqueous separations. Most theoretical analyses rely on either irreversible thermodynamics, the pore-flow model and the extended Nemst-Planck equation, or the solution-diffusion model [135]. To account for coupling between solute and solvent transport (i.e., convective mass transfer effects), the Stefan-Maxwell equations commonly are used. The solution-diffusion model appears to provide a better description of mixed-solvent transport and allow prediction of mixture transport rates from pure component measurements [136]. Experimental transport measurements may depend significantly on membrane preconditioning due to strong solvent-membrane interactions that lead to swelling or solvent phase separation in the membrane pore structure [137]. 

Among the theories of predicting mixed-gas adsorption equilibria from pure component adsorption isotherms, the ideal adsorbed solution theory (IAST) [14] has become the standard and often serves as a benchmark for the purpose of comparison by other models. IA ST is a thermodynamically rigorous theory based on the mixing of individual components at constant spreading pressure to form an ideal solution. It has the advantages that (1) no mixture data are required and (2) the theory is independent of the actual model of physical adsorption. 

However, some arbitrary assumptions such as the energy distribution and energy matching do exist in the HEL model. Meanwhile, the performance of the HEL model depends on the LUD parameters derived from pure component data. When the quality of pure component data is not good or there are too few data points, it is possible that the energy parameters (especially e, niin nd e max) derived from the LUD equation are meaningless or inconsistent between different species. In this case, the model prediction from the HEL model must be treated with care. 

The ideal adsorbed solution (IAS) theory of Myers and Prausnitz (1965) was the first major theory for predicting mixed gas adsorption from pure component isotherms, and it remains the most widely accepted. There have been approximately a dozen other theories that have been discussed in Yang (1987) however, they are not repeated here. 

A simple kinetic-theory derivation was made by Chen and Yang (1992) for predicting binary and multicomponent diffusivities from pure component diffu-... 

Chen, Y.D. Yang, R.T., and Sun, L.M., Further work on predicting multicomponent diffusivities from pure-component diffusivities for surface diffusion and diffusion in zeolites. Chem. Eng. Sci., 48(15). 2815-2816... 

The modern cubic equations of state provide reliable predictions for pure-component thermodynamic properties at conditions where the substance is a gas, liquid or supercritical. Walas and Valderrama provided a thorough evaluation and recommendations on the use of cubic equation of state for primary and derivative properties. Vapour pressures for non-polar and slightly polar fluids can be calculated precisely from any of the modem cubic equations of state presented above (Soave-Redlich-Kwong, Peng-Robinson or Patel-Teja). The use of a complex funetion for a (such as those proposed by Twu and co-workers ) results in a significant improvement in uncertainty of the predicted values. For associating fluids (such as water and alcohols), a higher-order equation of state with explicit account for association, such as either the Elliott-Suresh-Donohue or CPA equations of state, are preferred. For saturated liquid volumes, a three-parameter cubic equation of state (such as Patel-Teja) should be used, whereas for saturated vapour volumes any modern cubic equation of state can be used. 

In the study eorrducted by Chen and Yang, the diffusivities of binary rrrixtures were measured using the laboratory fabricated CMSM and the results were compared with the authors own kinetic theory developed for the prediction of birrary diffusivities from pure component diffusivities. 

Chen and Yang [9] prepared a large, crack-free carbon molecular sieve membrane (CMSM) supported on a macroporous substrate by coating a layer of PFA followed by controlled pyrolysis. Diffusion of binary mixtures was measured and the results were compared with the kinetic theory for predicting binary dififusivities from pure component dififusivities. Good agreement was obtained between theoretical predictions and experimental data for binary diffusion, as shown in Chap. 2. 

Ideal Adsorbed Solution Theory. Perhaps the most successful approach to the prediction of multicomponent equiUbria from single-component isotherm data is ideal adsorbed solution theory (14). In essence, the theory is based on the assumption that the adsorbed phase is thermodynamically ideal in the sense that the equiUbrium pressure for each component is simply the product of its mole fraction in the adsorbed phase and the equihbrium pressure for the pure component at the same spreadingpressure. The theoretical basis for this assumption and the details of the calculations required to predict the mixture isotherm are given in standard texts on adsorption (7) as well as in the original paper (14). Whereas the theory has been shown to work well for several systems, notably for mixtures of hydrocarbons on carbon adsorbents, there are a number of systems which do not obey this model. Azeotrope formation and selectivity reversal, which are observed quite commonly in real systems, ate not consistent with an ideal adsorbed... 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

Vapor pressure is the most important of the basic thermodynamic properties affec ting liquids and vapors. The vapor pressure is the pressure exerted by a pure component at equilibrium at any temperature when both liquid and vapor phases exist and thus extends from a minimum at the triple point temperature to a maximum at the critical temperature, the critical pressure. This section briefly reviews methods for both correlating vapor pressure data and for predicting vapor pressure of pure compounds. Except at very high total pressures (above about 10 MPa), there is no effect of total pressure on vapor pressure. If such an effect is present, a correction, the Poynting correction, can be applied. The pressure exerted above a solid-vapor mixture may also be called vapor pressure but is normallv only available as experimental data for common compounds that sublime. 

---