Liquid solutions activity-coefficient models

The non-random two-liquid segment activity coefficient model is a recent development of Chen and Song at Aspen Technology, Inc., [1], It is derived from the polymer NRTL model of Chen [26], which in turn is developed from the original NRTL model of Renon and Prausznitz [27]. The NRTL-SAC model is proposed in support of pharmaceutical and fine chemicals process and product design, for the qualitative tasks of solvent selection and the first approximation of phase equilibrium behavior in vapour liquid and liquid systems, where dissolved or solid phase pharmaceutical solutes are present. The application of NRTL-SAC is demonstrated here with a case study on the active pharmaceutical intermediate Cimetidine, and the design of a suitable crystallization process. 

Liquid-State Activity-Coefficient Models. If the conditions of the unit operation are far from the critical region of the mixture or that of the major conponent and if experimental data are available for the phase equilibrium of interest (VLE or LEE), then a liquid-state activity-coefficient model is a reasonable choice. Activity coefficients (y,) correct for deviations of the liquid phase from ideal solution behavior, as shown in Equation fl3.ll. 

Selection of appropriate thermodynamic model for the simulation of COj or SO2 in gas absorbers using water as a solvent is very important. Nonrandom two liquids (NRTL) activity coefficient model is chosen to explain the nonideal phase behavior of a liquid mixture between H2O and SO2. Henry s law option is also selected for the calculation of noncondensable supercritical gases such as Hj, CO, CO2, CH4, and Nj in a liquid mixture. In this example, NRTL was selected. Double click on NRTL01, the thermodynamic data modification window pops up. Click on Enter Data, vapor liquid equilibria (VLE) /(-values window pops up, and then click on Henry s law Enter Data as shown in Figure 7.3. Check use Henry s law for VLE of solute components. 

Any convenient model for liquid phase activity coefficients can be used. In the absence of any data, the ideal solution model can permit adequate design. 

Activity coefficient models offer an alternative approach to equations of state for the calculation of fugacities in liquid solutions (Prausnitz ct al. 1986 Tas-sios, 1993). These models are also mechanistic and contain adjustable parameters to enhance their correlational ability. The parameters are estimated by matching the thermodynamic model to available equilibrium data. In this chapter, vve consider the estimation of parameters in activity coefficient models for electrolyte and non-electrolyte solutions. 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

Experimental vapor-liquid-equilibrium data for benzene(l)/n-heptane(2) system at 80°C (176°F) are given in Table 1.8. Calculate the vapor compositions in equilibrium with the corresponding liquid compositions, using the Scatchard-Hildebrand regular-solution model for the liquid-phase activity coefficient, and compare the calculated results with the experimentally determined composition. Ignore the nonideality in the vapor phase. Also calculate the solubility parameters for benzene and n-heptane using heat-of-vaporization data. 

We focus on the thermodynamic models that deal with the liquid mixtures in this chapter. From the two categories of activity coefficient models, the correlative one is not very useful for solubility prediction and solvent screening purposes. The main reason for this is the lack of experimental data for the binary interaction parameters of the solute-solvent, solute-antisolvent, and solvent-antisolvent systems. As an example, the activity coefficient from... 

The activity coefficient models mentioned above depend on the overall space-averaged composition of the solution. On the other hand the range of intermolecular forces acting in an ordinary liquid mixture is rather short and is limited to a few molecular diameters. Consequently, it has been proposed that one use a local composition around the molecules that could be different from the overall composition of the solution. A thorough analysis of the local composition concept can be found... 

Kontogeorgis, G. M., Fredenslund, A., Economou, I. G., and Tassios, D. P., 1994a. Equations of state and activity coefficient models for vapor-liquid equilibria of polymer solutions. AIChEJ., 40 1711-1727. 

It was reported by Dixon and Johnston (56) that up to a moderate pressure, the liquid phase activity coefficient of the solid component 73 could be obtained by any activity coefficient model or, more conveniently, from the regular solution theory, as... 

Next, one frequently would like to be able to make some assessment of the accuracy of a set of experimental vapor-liquid or activity coefficient measurements. Basic thermodynamic theory (as opposed to the solution modeling of Chapter 9) provides no means of predicting the values of liquid-phase activity coefficients to which the experimental results could be compared. Also, since the liquid solution models discussed in Chapter 9 only approximate real solution behavior, any discrepancy between these models and experiment is undoubtedly more a reflection of the inadequacy of the model than a test of the experimental results. 

The question of evaluating the liquid-phase activity coefficient of the solute species still remains. Although experimental data for y would be preferable, such data may not be available. Consequently, various liquid solution models and correlations are used. If the regular solution model is used, we have... 

The thermodynamic factor is evaluated for liquid mixtures from activity coefficient models. For a regular solution, for example,... 

It is observed frommFigure 7 that, first,Pthe value of r icu is not unity and, second, that there exists a partial cancellation of the composition dependence in the liquid phase activity coefficient product by that found in the solid solution. The second observation suggests that the liquid and solid solution model selection process should be insensitive with respect to liquidus and solidus data alone. Indeed, the assumption of ideal solution behavior in both phases closely predicts the correct distribution coefficient, yet experimental measurements of the solution thermochemical properties clearly indicate moderate negative deviations from ideal behavior. 

The coefficients a,y, and c,y are binary interaction parameters specific to components / and j. A list of binary interaction parameters and Antoine coefficients for systems prominently featured systems in the book are given in Appendix B. Evidently, modeling nonideal systems can be rather laborious and computationally intensive, but the solution strategy is exactly the same to the one outlined for ideal solutions in Equation 1.7, and simply incorporating the activity coefficients. Activity coefficient models can account for azeotropes, that is, where vapor and liquid compositions are equal, while neither Raoult s law nor the constant volatility model is able to. Examples of binary nonideal systems modeled with the NRTL equation are shown in Figure 1.6. 

All other liquid components are present in dilute solutions in water, which require an appropriate activity coefficient model for the dilute component. Here the UNIFAC/UNIQUAC model [197] is selected, where the activity coefficient is calculated as the sum of a combinatorial part and a residual part. The residual part uses fitted binary parameters valid for the components present in the liquid mixture. If no binary parameters are available - which is often the case in syngas preparation - the UNIFAC method may be used to calculate the residual part. 

Kontogeorgis, G.M., Saraiva, A., Fredenslund, Aa., and Tassios, D.P., 1995. Prediction of liquid-liquid equilibrium for binary polymer solutions with simple activity coefficient models. Ind. Eng. Chem. Res., 34 1823. 

Activity-coefficient models, however, can only be used to calculate liquid-state fugacities and enthalpies of mixing. These models provide algebraic equations for the activity coefficient (y,) as a function of composition and temperature. Because the activity coefficient is merely a correction factor for the ideal-solution model (essentially Raoult s Law), it cannot be used for supercritical or noncondensable components. (Modifications of these models for these types of systems have been developed, but they are not recommended for the process simulator user without consultation with a thermodynamics expert.)... 

Using ePC-SAFT, liquid densities, vapour pressures [directly obtained by Eq. (16) not included in the parameter estimation], and solute activity coefficients (MIAC) are modelled whereas only activity coefficients will be presented for MSA-NRTL as this quantity is the only one that can be obtained by a G -model. Any deviations from experimental data will be given by absolute relative deviations (ARD) ... 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

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