Pure component parameters

Chemical Thermodynamics for Process Simulation, First Edition, liirgen Gitiehling, Barbel Kolbe, Michael Kleiber, and (urgen Rarey. 

The required critical data Tc and Pc are given in the Table General data for selected compounds . 

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Pure-component parameters required in Equations (16) through (23) are... 

Pure component parameters for 92 components, and as many binary interaction parameters as have been established, are cited in Appendix C. These parameters can be loaded from formated cards, or other input file containing card images, by subroutine PARIN. 

To recapitulate, the Flory version of the Prigogine free-volume or corresponding-states polymer solution theory requires three pure-component parameters (p, v, T ) for each component of the solution and one binary parameter (p ) for each pair of components. 

Another type of ternary electrolyte system consists of two solvents and one salt, such as methanol-water-NaBr. Vapor-liquid equilibrium of such mixed solvent electrolyte systems has never been studied with a thermodynamic model that takes into account the presence of salts explicitly. However, it should be recognized that the interaction parameters of solvent-salt binary systems are functions of the mixed solvent dielectric constant since the ion-molecular electrostatic interaction energies, gma and gmc, depend on the reciprocal of the dielectric constant of the solvent (Robinson and Stokes, (13)). Pure component parameters, such as gmm and gca, are not functions of dielectric constant. Results of data correlation on vapor-liquid equilibrium of methanol-water-NaBr and methanol-water-LiCl at 298.15°K are shown in Tables 9 and 10. 

The evaluation of the sublimation pressure is a problem since most of the compounds to be extracted with the supercritical fluids exhibit sublimation pressures of the order of 10 14 bar, and as a consequence these data cannot be determined experimentally. The sublimation pressure is thus usually estimated by empirical correlations, which are often developed only for hydrocarbon compounds. In the correlation of solubility data this problem can be solved empirically by considering the pure component parameters as fitting-parameters. Better results are obviously obtained [61], but the physical significance of the numerical values of the parameters obtained is doubtful. For example, different pure component properties can be obtained for the same solute using solubility data for different binary mixtures. 

Determination of pure component parameters. In order to use the EOS to model real substances one needs to obtain pure component below its critical point, a technique suggested by Joffe et al. (18) was used. This involves the matching of chemical potentials of each component in the liquid and the vapour phases at the vapour pressure of the substance. Also, the actual and predicted saturated liquid densities were matched. The set of equations so obtained was solved by the use of a standard Newton s method to yield the pure component parameters. Values of exl and v for ethanol and water at several temperatures are shown in Table 1. In this calculation vH and z were set to 9.75 x 10"6 m3 mole"1 and 10, respectively (1 ). The capability of the lattice EOS to fit pure component VLE was found to be quite insensitive to variations in z (6[Pg.90]

For a supercritical fluid (SCF) component, the pure component parameters were obtained by fitting P-v data on isotherms (300-380K). Preliminary data for these substances suggest that although the computed v is a weak function of temperature, exl is a constant within regression error. 

Table 1 Pure Component parameters for ethanol and water at several temperatures ( z-10, v -9.75 x 10"6 m3mole 1)...

In order to test the applicability of the model to polymer-SCF systems, a hypothetical system of CC>2 and a monodisperse -mer with a monomeric unit molecular weight of 100 was simulated. Pure component parameters for the polymer, polystyrene, were obtained from Panayiotou and Vera (16). Constant values of kj< were used for the polymer system, where the degree of polymerization, , varied between 1 and 7. It was assumed that all chains had the same e, and v scaled as the molecular weight of the chain. Figure 5 shows the results of the predicted mole fraction of the -mer in the SCF phase. 

Equations 2 and 3 are called the van der Waals mixing rules. In these equations, a j t and b j j (i j) are parameters corresponding to pure component ti) while ay and by (i j) are called the uni ike-interaction parameters. It is customary to relate the uni ike-interaction parameters to the pure-component parameters by the following expressions ... 

To estimate the pure component parameters, we used the technique of Panagiotopoulos and Kumar (11). The technique provides parameters that exactly reproduce the vapor pressure and liquid density of a subcritical component. Table II presents the pure component parameters that were used. For the supercritical components, the usual acentric factor correlation was utilized. 

Although equations of state based on statistical mechanics, like the Perturbed Hard Chain and Chain of Rotators equations of state are good at predicting phase equilibria at conditions far from the critical point of mixtures, a critical evaluation of six of these type of equations of state showed that they are rather inaccurate in the mixture critical region[3]. Satisfactory correlation of the data is obtained with a Peng Robinson equation of state using two interaction parameters per binary as proposed by Shibata and Sandler[4], The correlations of Huang[5] were used for the pure component parameters. 

Table 2C.1 Pure component parameters for equation of state calculations.

In addition to pure component parameters, mixture calculations require the estimation of the unlike-pair interaction parameters. These were obtained in this study using the Lorenz-Berthelot rules ... 

Figure 2. Gibbs-ensemble Monte Carlo results for a system with pure component parameters corresponding to acetone and carbon dioxide at T - 313 K, with varying 6, ...

Simulations of ternary systems were performed using the pure component parameters in Table I and the cross parameters for the systems acetone/ CO2 and water/C02 determined previously (fi j - 1 and 0.81 respectively). Because of expected difficulties similar to the ones mentioned for the water/C02 system, no attempt was made to simulate the system acetone/water near room temperature. Thus, we set the acetone/water interaction parameters to the values from the Lorenz-Berthelot rules with fi j-l. Direct simulations of ternary phase equilibria have not been previously reported to the best of our knowledge. 

For simple mixtures, the parameters a and b are related to the pure component parameters and composition through the following mixing rules ... 

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. 

Mixtures Both liquid and vapor densities can be estimated using pure-component CS and EoS methods by treating the fluid as a pseudo-pure component with effective parameters calculated from the pure-component parameters and using ad hoc mixing rules. 

These interaction parameters are used in place of the corresponding pure-component parameters to determine the B,j values. 

A number of methods based on regular solution theory also are available. Only pure-component parameters are needed to make estimates, so they may be applied when UNIFAC group-interaction parameters are not available. The Hansen solubility parameter model divides the Hildebrand solubility parameter into three parts to obtain parameters 8d, 5p, and 5 accounting for nonpolar (dispersion), polar, and hydrogenbonding effects [Hansen,/. Paint Technot, 39, pp. 104-117 (1967)]) An activity coefficient may be estimated by using an equation of the form... 

Table I Mobility and solubility contributions to the permeability and selectivity of typical glassy polymers at 35°C for a 20 atm pressure of both components based on pure component parameters.

Table 3.1.1. Pure component parameters for PRSV equation of state...

The following conibining rules are frequently used to obtain the cross coefficients atj and bij from the corresponding pure component parameters ... 

THE UNIQUAC MODEL WILL REQUIRE PURE COMPONENT PARAMETERS R, Q, Q. ... 

IN ADDITION Kl2 PARAMETER OF THE WS MODEL IS FIT (other parameters such as alpha of the NRTL model, or UNIQUAC pure component parameters must be supplied by user.) "... 

FIGURE 16.10 Pressure-composition phase diagram for the system polydimethylsiloxane (PDMS) — -pen-tane with the SAFT equation of state. Using PDMS pure-component parameter sets, which reproduce the PDMS densities well, no acceptable reproduction of the binary equilibria is possible. (From Pfohl, O. et al., Fluid Phase Equilibria, submitted, 2001. With permission.)... 

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