Activity coefficient local composition

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

The local compostion model is developed as a symmetric model, based on pure solvent and hypothetical pure completely-dissociated liquid electrolyte. This model is then normalized by infinite dilution activity coefficients in order to obtain an unsymmetric local composition model. Finally the unsymmetric Debye-Huckel and local composition expressions are added to yield the excess Gibbs energy expression proposed in this study. 

A wide variety of data for mean ionic activity coefficients, osmotic coefficients, vapor pressure depression, and vapor-liquid equilibrium of binary and ternary electrolyte systems have been correlated successfully by the local composition model. Some results are shown in Table 1 to Table 10 and Figure 3 to Figure 7. In each case, the chemical equilibrium between the species has been ignored. That is, complete dissociation of strong electrolytes has been assumed. This assumption is not required by the local composition model but has been made here in order to simplify the systems treated. 

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. 

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 local composition model (LCM) is an excess Gibbs energy model for electrolyte systems from which activity coefficients can be derived. Chen and co-workers (17-19) presented the original LCM activity coefficient equations for binary and multicomponent systems. The LCM equations were subsequently modified (1, 2) and used in the ASPEN process simulator (Aspen Technology Inc.) as a means of handling chemical processes with electrolytes. The LCM activity coefficient equations are explicit functions, and require computational methods. Due to length and complexity, only the salient features of the LCM equations will be reviewed in this paper. The Aspen Plus Electrolyte Manual (1) and Taylor (21) present the final form of the LCM binary and multicomponent equations used in this work. 

It should be noted that distribution coefficients Ki comprise both fugacities in the gas phase and activity coefficients in the liquid phase. These coefficients are determined by the three-parametric Electrolyte-NRTL method. The latter is based on the local composition concept and satisfactorily represents physical interactions of this multicomponent electrolyte system [46]. 

A rate equation in terms of the local composition of reacting fluid in contact with the surface of the cata-lytically active material may be called the "intrinsic rate equation, the coefficients in this equation are "intrinsic rate coefficients. The local concentrations of reactants and products at the catalytic surface in general cannot be observed and have to be inferred from the observable composition at the boundary of a larger system, the observed rate of reaction and the kinetics... 

Modern theoretical developments in the molecular thermodynamics of liquid-solution behavior are based on the concept of local composition. Within a liquid solution, local compositions, different from the overall mixture composition, are presumed to account for the short-range order and nonrandom molecular orientations that result from differences in molecular size and intermolecular forces. The concept was introduced by G. M. Wilson in 1964 with the publication of a model of solution behavior since known as the Wilson equation. The success of this equation in the correlation of VLE data prompted the development of alternative local-composition models, most notably the NRTL (Non-Random-Two Liquid) equation of Renon and Prausnitz and the UNIQUAC (UNIversal QUAsi-Chemical) equation of Abrams and Prausnitz. A further significant development, based on the UNIQUAC equation, is the UNIFAC method,tt in which activity coefficients are calculated from contributions of the various groups making up the molecules of a solution. 

We can estimate the activity coefficients by using the excess Gibbs energy models. Based on the local composition concept, the Wilson, NRTL, and UNIQUAC models for excess Gibbs energy provide relations for activity coefficient... 

Since the degree of coupling is directly proportional to the product Q (D/k)in, the error level of the predictions of q is mainly related to the reported error levels of Q values. The polynomial fits to the thermal conductivity, mass diifusivity, and heat of transport for the alkanes in chloroform and in carbon tetrachloride are given in Tables C1-C6 in Appendix C. The thermal conductivity for the hexane-carbon tetrachloride mixture has been predicted by the local composition model NRTL. The various activity coefficient models with the data given in DECHEMA series may be used to estimate the thermodynamic factors. However, it should be noted that the thermodynamic factors obtained from various molecular models as well as from two sets of parameters of the same model might be different. 

Wilson (1964) modified the Flory-Huggins theory to account for the local composition affects caused by the differences in intermolecular forces. From these considerations the following expressions for the activity coefficients are derived. 

Renon and Prausnitz (8) proposed another equation, based also on the local mole fraction concept, which would avoid this limitation and could be applied to partially miscible mixtures. The relationship between activity coefficient and liquid phase composition is given by the equation... 

Equations 19 and 20 coupled with expressions for the local compositions and for the activity coefficients at infinite dilution allowed the evaluation of the correlation volume and the unlike interaction energy parameter at infinite dilution. ... 

The correlation volume and the energy of interaction between two unlike molecules in the systems HFB—B were calculated as for the binary aqueous solutions of alcohols and hydrocarbons, using eqs 19—20 and expressions for the local compositions and activity coefficients at infinite dilution. It should be however emphasized that the calculation procedure is not very accurate when the activity coefficients at infinite dilution are close to unity. For the system HFB (1)—B (2) at 40 °C, =... 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

The concentrations of the components in the vicinity of any molecule are usually called local compositions (LCs). According to the LC concept, the composition in the vicinity of any molecule differs from the overall composition. If a binary mixture is composed of components 1 and 2 with overall mole fractions x and xi, respectively, four LCs can be defined local mole fractions of components 1 and 2 near a central molecule 1 (xii and X2 ) and local mole fractions of components 1 and 2 near a central molecule 2 x 2 and X22). Many attempts have been made to express LC in terms of the bulk compositions and some intermolecular interaction parameters. " Wilson was the first to suggest expressions for the local mole fractions and to derive on their basis expressions for the activity coefficients of binary mixtures. Since then, many expressions for LC were suggested, and the LC concept proved to be a very effective... 

The Electrolyte NRTL model " and the Extended UNIQUAC model" are examples of activity coefficient models derived by combining a Debye-Hiickel term with a local composition model. Equation of state models with electrostatic terms for... 

Wilson then derived Eq. (39) based on the local composition theory. Eqs. (40) and (41) for the activity coefficient result from Eq. (39). 

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... 

Concentration-dependent activity coefficients can be accommodated with relative ease by an added term (e.g., [see Helfferich, 1962a Brooke and Rees, 1968] and variations in diffusivities are easily included in numerical calculations (Helfferich and Petruzzelli, 1985 Hwang and Helfferich, 1986). In both instances, however, a fair amount of additional experimental information is required to establish the dependence on composition. Electro-osmotic solvent transfer and particle-size variations are more difficult to deal with, and no readily manageable models have been developed to date. A subtle difficulty here is that, as a rule, there is not only a variation in equilibrium solvent content with conversion to another ionic form, but that the transient local solvent content is a result of dynamics (electro-osmosis) and so not accessible by thermodynamic considerations (Helfferich, 1962b). Theories based on the Stefan-Maxwell equations or other forms of (hcrniodyiiainics of ir-... 

Since 1980 polymer thermodynamics has been developed considerably and, to date, models are available that are suitable for at least satisfactory calculations of VLE and, qualitatively, also for LLE. Some of these methods are models for the activity coefficient, which are modifications of the FH equation. These modifications use a similar to FH but better combinatorial/free-volume expression and a local-composition-type energetic term such as those found in the UNIQUAC and UNIFAC models. Models like the UNIFAC-FV and the Entropic-FV are discussed in Section 16.4. 

We will consider only one additional activity coefficient equation here, the UNI-QUAC (universal quasichemical) model of Abrams and Prausnitz. This model, based on statistical mechanical theory, allows local compositions to result from both the size and energy differences between the molecules in the mixture. The result is the expression... 

The Wilson equation can be extended to immiscible liquid systems by multiplying the right-hand side of (5-41) by a third binary-pair constant evaluated from experimental data. However, for multicomponent systems of three or more species, the third binary-pair constants must be the same for all constituent binary pairs. Furthermore, as shown by Hiranuma, representation of ternary systems involving only one partially miscible binary pair can be extremely sensitive to the third binary-pair Wilson constant. For these reasons, application of the Wilson equation to liquid-liquid systems has not been widespread. Rather, the success of the Wilson equation for prediction of activity coefficients for miscible liquid systems greatly stimulated further development of the local composition concept in an effort to obtain more universal expressions for liquid-phase activity coefficients. 

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