Activity coefficient prediction

Figs. 5.5 and 5.6 show the deviation in the activity coefficients predicted by COSMOSPACE and the BGY model from those obtained directly from the MC simulations using an addition to our MC code, which allows us to evaluate the activity coefficients of the components. We see from these results that COSMOSPACE is in much better agreement with the MC simulations than the BGY model. We have not calculated the activity coefficients for the AD model since it is not a model for the excess Gibbs energy. 

Activity Coefficients Predicted by the Local Composition Model for Aqueous Solutions Used in Flue Gas Desulfurization... 

The goal of this research was to improve activity coefficient prediction, and hence, equilibrium calculations in flue gas desulfurization (FGD) processes of both low and high ionic strength. A data base and methods were developed to use the local composition model by Chen et al. (MIT/Aspen Technology). The model was used to predict solubilities in various multicomponent systems for gypsum, magnesium sulfite, calcium sulfite, calcium carbonate, and magnesium carbonate SCU vapor pressure over sulfite/ bisulfite solutions and, C02 vapor pressure over car-bonate/bicarbonate solutions. 

The BMREP and SDM currently use the Davies technique for activity coefficient prediction. The Davies technique is a combination of the extended Debye-Huckel equation (6) and the Davies equation (7). The Davies technique (and hence both equilibrium models) is accurate up to ionic strengths of 0.2 molal and may be used for practical calculations up to ionic strengths of 1 molal (8). Ion-pair equilibria are incorporated for species that associate (e.g., 1-2 and 2-2 electrolytes). The activity coefficients (y ) are calculated as a simple function of ionic strength (I) and are represented as ... 

The LCM is a semi-theoretical model with a minimum number of adjustable parameters and is based on the Non-Random Two Liquid (NRTL) model for nonelectrolytes (20). The LCM does not have the inherent drawbacks of virial-expansion type equations as the modified Pitzer, and it proved to be more accurate than the Bromley method. Some advantages of the LCM are that the binary parameters are well defined, have weak temperature dependence, and can be regressed from various thermodynamic data sources. Additionally, the LCM does not require ion-pair equilibria to correct for activity coefficient prediction at higher ionic strengths. Thus, the LCM avoids defining, and ultimately solving, ion-pair activity coefficients and equilibrium expressions necessary in the Davies technique. Overall, the LCM appears to be the most suitable activity coefficient technique for aqueous solutions used in FGD hence, a data base and methods to use the LCM were developed. 

Figure 1 demonstrates the necessity of ion-pair equilibria to insure an accurate activity coefficient prediction in the low concentration range (0-0.2 molal) for salts that associate. 

A data base of necessary binary parameters and equilibrium constants for activity coefficient prediction by the LCM is presented. The LCM has proven to be accurate from 0-6 molal ionic strength for typical FGD aqueous solutions. In general, the LCM is slightly less accurate than the Davies technique for 0-1 molal ionic strength. The advantages of the LCM over the current Davies technique are clearly seen when predicting over the entire concentration range. 

Bastos, J.C., Soares, M.E., Medina, A.G. Infinite dilution activity coefficients predicted by UNIFAC group contribution. Ind. Eng. Chem. Res. 1988,27 1269-1277. 

How Well Does the Debye-Huckel Theoretical Expression for Activity Coefficients Predict Experimental Values ... 

According to the phase rule, a three-component, two-phase system has three degrees of freedom. Thus, by specifying the temperature, pressure, and concentration of one component in one phase, the state of the system is defined. The component concentration in one phase defines one point on the equilibrium curve, and this point marks one end of a tie line. The other end is determined thermodynamically either from experimental data or on the basis of liquid activity coefficient predictions methods. 

In binary mixtures the Van Laar equations allow the component activity coefficient predictions at any composition by interpolation from... 

The Peng-Robinson-Stryjek-Vera (PRSV) eos with the incorporation of UNIFAC activity-coefficient predicts well experimental data of numerons mixtnres, including ethanol-water mixtnres at 150-350°C and acetone-with mixtnres at 100-250°C. 

The PR eos has been modified by Stryjek and Vera to extend to polar substances that do not follow the three-parameter principle of corresponding states. The modified eos is fitted to the vapor pressure of polar substances with additional substance-specific parameters. The PRSV equation has been described in Equation (4.163) et seq. The free-energy-matched mixture eos parameters are given in Equations (4.436) and (4.438) the fugacity coefficients are given in Equation (4.439). PRSV eos using the UNIEAC activity coefficient predicts the vie data for both ethanol/water mixtures at 423-623°K and acetone/water mixtures at 373-523°K from low to high pressure. 

It is clear from this figure that, for this simple system, the UNIFAC predictions are good— much better than the regular solution predictions of Fig. 9 6-l. Although the UNIFAC predictions for all systems are not always as good as for the benzene-2,2,4-trimethyl pentane system, UNIFAC with its recent improvements is the best activity coefficient prediction method currently available. ... 

Activity coefficients predicted by the D-H equation decrease monotonically with solute concentration. Measured activity coefficients typically decrease at first, but then increase at higher concentrations. This indicates that the simple coulombic model used by the D-H theory is inadequate in more concentrated solutions, which is not surprising. There have been many theoretical attempts to model the additional interactions that occur at high concentrations. Detailed summaries are given by Friedman (1962) and Helgeson et al. (1981), and a brief summary is in Nordstrom and Munoz (1994). Two of these are the B method and ion hydration method, but they are rather similar in effect, in that they add a more or less linear positive term to the right side of Equation (15.22). 

A rigorous test of multicomponent solution activity coefficient prediction methods is the calculation of the mutual solubilities of salts and the calculation of salt solubilities in aqueous electrolyte solutions. The salt solubilities are affected by the solution composition. In order to calculate the saturation molalities, the activity coefficients must be adequately predicted. 

This test of activity coefficient prediction methods is also recommended due to the wealth of good experimental solubility data available. 

From earlier discussions, it was found that this free energy difference represents a difference in screened and unscreened partial molar Helmholtz free energies. Thus, the activity coefficient can be seen to result from the partial molar free energy, which is due to the screening of the counter ion atmosphere surrounding each ion in any real solution. This definition is consistent with the view that the activity coefficient predicts electrostatic screening in real solutions or the difference between real and ideal solution properties. 

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