Abrams and Prausnitz

The UNIQUAC equation developed by Abrams and Prausnitz is usually preferred to the NRTL equation in the computer aided design of separation processes. It is suitable for miscible and immiscible systems, and so can be used for vapour-liquid and liquid-liquid systems. As with the Wilson and NRTL equations, the equilibrium compositions for a multicomponent mixture can be predicted from experimental data for the binary pairs that comprise the mixture. Also, in the absence of experimental data for the binary pairs, the coefficients for use in the UNIQUAC equation can be predicted by a group contribution method UNIFAC, described below. 

Here y,1 and y,2 are the corresponding activity coefficients of component i in phase 1 and 2, Xj1, and x,2 are the mole fraction of components i in the system and in phase 1 and 2 respectively. The interaction parameters between methylcyclohexane, methanol and ethyl benzene are used to estimate the activity coefficients from the UNIQUAC groups. Eqs. (1) and (2) are solved for the mole fraction (x) of component i in the two liquid phase.The UNIQUAC model (universal quasi -chemical model) is given by Abrams and prausnitz [8] as... 

The methods most generally used for the calculation of activity coefficients at intermediate pressures are the Wilson (1964) and UNIQUAC (Abrams and Prausnitz, 1975) equations. Wilson s equation was used by Sato et al. (1985) to predict the composition of fhe condensate gas stripped from a packed bed fermenter at 30°C, whilst Beck and Bauer (1989) used the UNIQUAC equation, with temperature-dependent parameters given by Kolbe and Gmehling (1985), for their model of an anaerobic gas-solid fluidized bed fermenter at 36°C. In this case it was necessary to go beyond the temperature range of fhe source data down to 16°C in order to predict the composition of the fluidizing gas leaving the condenser. 

The UNIFAC (Unified quasi chemical theory of liquid mixtures Functional-group Activity Coefficients) group-contribution method for the prediction of activity coefficients in non-electrolyte liquid mixtures was first introduced by Fredenslund et al. (1975). It is based on the Unified Quasi Chemical theory of liquid mixtures (UNIQUAC) (Abrams and Prausnitz, 1975), which is a statistical mechanical treatment derived from the quasi chemical lattice model (Guggenheim, 1952). UNIFAC has been extended to polymer solutions by Oishi and Prausnitz (1978) who added a free volume contribution term (UNIFAC-FV) taken from the polymer equation-of-state of Flory (1970). 

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. 

Lichtenthaler et al. (55) determined interaction parameters for 22 solutes in poly(dimethyl siloxane) to test several expressions of the combinatorial entropy of mixing [Eq. (7)]. The magnitude of the interaction parameter is indeed directly dependent on the evaluation of the combinatorial contribution. The combinatorial contribution was computed following both the Flory-Huggins approximation and the multiple-connected-site model recently developed by Lichtenthaler, Abrams and Prausnitz (56). This model, which retains the Flory-Huggins term, also corrects for the bulkiness of the components of the mixture. Interaction parameters were computed through both approximations, showing the sensitivity of the results to the model chosen. 

There are many other equations, which have been proposed, that do not result from Wohl s method. Two of the most popular equations are the Wilson and the universal quasi-chemical theory (UNIQUAC) by Abrams and Prausnitz.These equations are based on the concept of local composition models, which was proposed by Wilson in his paper. It is presumed in a solution that there are local compositions that differ... 

The UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts, the combinatorial part and a part describing the inter-molecular forces. The sizes and shapes of the molecule determine the combinatorial part and are thus dependent on the compositions and require only pure component data. As the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. The UNIQUAC equations are about as simple for multicomponent solutions as for binary solutions. Parameters for the UNIQUAC equations can be found by Gmehling, Onken, and Arlt. ... 

The UNIQUAC equation (Abrams and Prausnitz, 1975) is based on the two-liquid model in which the excess Gibbs energy is assumed to result from differences in molecular sizes and structures and from the energy of interaction between the molecules. 

Lattice theories [37] enable one to consider nonspecific physical forces (e.g., molecular dipole moments, induction effects, and London dispersion forces) and have been applied successfully to model nonideality in a wide range of mixtmes. Guggenheim [43] was the first to develop a quasichemical theory using lattice models. Wilson [44], Renon and Prausnitz [45], Abrams and Prausnitz [46], and Vera et al. [47] modified it for nomandom mixtures. Panayiotou and Vera... 

The UN1QUAC equation (Abrams and Prausnitz, Anderson and Prausnitz.4 Maurer and Prausnitz5) provides en example of a two-parameter local-composition equation of great flexibility. In itsorigioal form, it is written... 

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... 

UNIQUAC stands for UNIversal QUAsi-Chemical model, and has been developed by Abrams and Prausnitz (1978). Unlike Wilson and NRTL, where loeal volume fraction is used, in UNIQUAC the primary variable is the local surface area fraction O j. Each molecule is characterised by two structural parameters r, the relative number of segments of the molecule (volume parameter) and q, the relative surface area (surface parameter). Values of these parameters have been obtained in some cases by statistical mechanics. There is also a special form of UNIQUAC for systems containing alcohols, where a third surface parameter q can increase significantly the accuracy (Prausnitz et al., 1980). 

In an attempt to place calculations of liquid-phase activity coefficients on a simpler, yet more theoretical basis, Abrams and Prausnitz used statistical mechanics to derive a new expression for excess free energy. Their model, called UNIQUAC (universal qua si-chemical), generalizes a previous analysis by Guggenheim and extends it to mixtures of molecules that differ appreciably in size and shape. As in the Wilson and NRTL equations, local concentrations are used. However, rather than local volume fractions or local mole fractions, UNIQUAC uses the local area fraction 0,j as the primary concentration variable. 

Abrams and Prausnitz found that for vapor-liquid systems, the UNIQUAC equation is as accurate as the Wilson equation. However, an important advantage of the UNIQUAC equation lies in its applicability to liquid-liquid systems, as discussed in Section 5.8. Abrams and Prausnitz also give a one-parameter form of the UNIQUAC equation. The methods previously described can be used to determine UNIQUAC parameters from infinite-dilution activity coefficients or from azeotropic or other single-point data. 

Example 5.9. Solve Example 5.8 by the UNIQUAC equation using values of binary interaction constants given by Abrams and Prausnitz. ... 

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