Local composition model

The local-composition models have hmited flexibility in the fitting of data, but they are adequate for most engineering purposes. Moreover, they are implicitly generalizable to multicomponent systems without the introduction of any parameters beyond those required to describe the constituent binaiy systems. For example, the Wilson equation for multicomponent systems is written ... 

Follow the four-step procedure for the composite model of bonding. Use localized bonds and hybrid orbitals to describe the bonding framework and the inner atom lone pairs. Next, analyze the system, paying particular attention to resonance structures or conjugated double bonds. Finally, make sure the bonding inventory accounts for all the valence electrons and all the valence orbitals. 

A simple composite model of slow motions and molecular reorientations is the so-called slowly relaxing local structure model by Freed.156,157 This... 

Chen, C.-C.., 1993, A Segment Based Local Composition Model for the Gibbs Energy of Polymer solutions. Fluid Phase Equilibria, 83, 301. 

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. 

The local composition model makes it possible to study electrolyte thermodynamics over a wide range of compositions. 

It should be noted that the local composition model is not consistent with the commonly accepted solvation theory. According to the solvation theory, ionic species are completely solvated by solvent molecules. In other words, the local mole fraction of solvent molecules around a central ion is unity. This becomes unrealistic when applied to high concentration electrolyte systems since the number of solvent molecules will be insufficient to completely solvate ions. With the local composition model, all ions are, effectively, completely surrounded by solvent molecules in dilute electrolyte systems and only partially surrounded by solvent molecules in high concentration electrolyte systems. Therefore, the local composition model is believed to be closer to the physical reality than the solvation theory. 

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. 

For the industrially important class of mixed solvent, electrolyte systems, the Pitzer equation is not useful because its parameters are unknown functions of solvent composition. A local composition model is developed for these systems which assumes that the excess Gibbs free energy is the sum of two contributions, one resulting from long-range forces between ions and the other from short-range forces between all species. 

The microductile/compliant layer concept stems from the early work on composite models containing spherical particles and oriented fibers (Broutman and Agarwal, 1974) in that the stress around the inclusions are functions of the shear modulus and Poisson ratio of the interlayer. A photoelastic study (Marom and Arridge, 1976) has proven that the stress concentration in the radial and transverse directions when subjected to transverse loading was substantially reduced when there was a soft interlayer introduced at the fiber-matrix interface. The soft/ductile interlayer allowed the fiber to distribute the local stresses acting on the fibers more evenly, which, in turn, enhanced the energy absorption capability of the composite (Shelton and Marks, 1988). 

Grunbauer, H.J.M., deMeere.A.L.J., andvanRooij, H.H. Local composition models in pharmaceutical chemistry. III. Prediction of drug solubility in binary aqueous mixturtefe, J. Pharm., 32, 187198,... 

Wu et al., [88] compared several local composition models with LMC simulations for lattice mixtures. The models tested included UNIQUAC, the AD model for lattice fluids of Aranovich and Donohue [89], and the Born-Green-Yvon (BGY) model of Lipson [90]. 

Chen CC, Evans LB. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE J 1986 32 444-459. 

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. 

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. 

Chen, C-C, et al., A Local Composition Model for the Excess Gibbs Energy of Multicomponent Aqueous Systems, AlChE Annual Meeting, San Francisco, 1984. 

C.-C. Chen, H. I. Britt, J. F. Boston, et ah, Local compositions model for excess Gibbs energy of electrolyte systems. Part I Single solvent, single completely dissociated electrolyte systems, AIChE J., 1982, 28, 588-596. 

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. 

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. 

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