Gibbs Energy Model

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. 

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... 

MoUerup, J. A note on excess Gibbs energy models, equations of state and the local composition concept. Fluid Phase Equilib. 1981, 7, 121-138. 

ENTER EXCESS GIBBS ENERGY MODEL PARAMETERS. THEY ARE ... 

Michelsen, M. L., 1990a. A method for incorporating excess Gibbs energy models in equations of state. Fluid Phase Eq 60 47—58. 

A more realistic approach attempts to describe each equilibrium in terms of its thermodynamic equilibrium constant, molar volumes of specific aggregates, and a heat of reaction to estimate the chemical contribution to excess enthalpy Hchem- The first two parameters contribute to the excess Gibbs energy model. 

The molecular-level assumption underlying the Redlich-Kister expansion is that completely random mixtures are formed, that is, that the ratio of species 1 to species 2 molecules in the vicinity of any molecule is, on the average, the same as the ratio of their mole fractions. A different class of excess Gibbs energy models can be formulated by assuming that the ratio of species 1 to species 2 molecules surrounding any molecule also depends on the differences in size and energies of interaction of the chosen molecule with species 1 and species 2. Thus, around each molecule there is a local composition that is different from the bulk composition. From this picture, the several binary mixture models have been developed. 

COMBINED EQUATION-OF-STATE AND EXCESS GIBBS ENERGY MODEL... 

Combined Equation-of-State and Excess Gibbs Energy Model 463... 

Activity coefficient (or excess Gibbs energy) models... 

The excess Gibbs energy models for binary mixtures discussed in Sec. 9.5 can be extended to multicomponent mixtures. For example, the Wohl expansion of Eq. 9.5-8 can be extended to ternary mixtures ... 

However, before we proceed with the discussion, it is useful to consider the range of validity of the activity coefficient (y -activity coefficient (or excess Gibbs energy) models can be used for liquid mixtures of all species. This description generally does not include density, and therefore will not give a good description of an expanded liquid, which occurs near the vapor-liquid critical point of a mixture. Also, when two different models are used—for example, an activity coefficient model for the liquid phase and an equation-of-state model for the... 

Cotnbined Ec iuition-of-State and Exce.ss Gibbs Energy Model 462... 

By consequence, the test of phase splitting consists of checking if the excess Gibbs energy model satisfies somewhere the condition (6.104). Then, the immiscibility range... 

Chen, C.-C., C.P. Bokis, and P. Mathias, Segment-based Excess Gibbs Energy Model for Aqueous Organic Electrolytes, AIChE J., 47(11), 2593-2602 (2001). 

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