UNIQUAC

UNIQUAC (short for "UN"iversal "QUA"si"C"hemical) is an activitycoefficient model in which the activity coefficients, γ, of the components in achemical mixture can be related through their molar fraction,x_i [Abrams D.S., Prausnitz J.M., "StatisticalThermodynamics of Liquid Mixtures: A New Expression for the Excess GibbsEnergy of Partly or Completely Miscible Systems", AIChE J., 21(1), 116-128,1975] .

Equations

In UNIQUAC the activity coefficients of the i^th component of a twocomponent mixture are modelled, with the intermolecular forces are described by aresidual and combinatorial parts.

$ln\; ;\; gamma\_i\; =\; gamma^C\_i;+;gamma^R\_i$

Combinatorial component

The combinatorial component γ^C is calculated exclusively from thepure chemical parameters, using the relative Van der Waals volumes r_i andsurface areas q_i of the pure chemicals.

$ln\; ;\; gamma\_i^C\; =\; 1\; -\; V\_i\; +\; ln\; ;\; V\_i\; -\; 5\; q\_i\; left(\; 1\; -\; frac\{V\_i\}\{F\_i\}\; +ln\; frac\{Vi\}\{Fi\}\; ight)$

With the volume fraction per mixture mole fraction, V_i, for the i^thcomponent given by:

$V\_i\; =\; frac\{r\_i\}\{sum\_j\; r\_j\; x\_j\}$

And the surface area fraction per mixture molar fraction, F_i, for thei^th component given by:

$F\_i\; =\; frac\{q\_i\}\{sum\_j\; q\_j\; x\_j\}$

Residual

The residual term contains an empirical parameter, which is derived fromexperimental, or occasionally estimated, activity coefficients.

$ln\; ;\; gamma\_i^R\; =\; q\_i\; left(\; 1\; -\; ln\; ;\; frac\{sum\_j\; q\_j\; x\_j\; au\_\{ji\}\; \}\{\; sum\_j\; q\_j\; x\_j\}\; -\; sum\_j\; \{frac\{q\_j\; x\_j\; au\_\{ij\{sum\_k\; q\_k\; x\_k\; au\_\{kj\}\; ight)$

with

$au\_\{ij\}\; =\; e^\{-Delta\; u\_\{ij\}/\{RT$

Δu_ij [J/mol] is the estimated binary parameter between two components,i and j.

Uses

Activity coefficients can be used to predict simple phase equilibria(vapour-liquid, liquid-liquid, solid-liquid), or to estimate other importantthermodynamic parameters. Models such as UNIQUAC allow for the calculation ofchemical mixtures that are commonly used in process simulation. This can beachieved by interpolation from only a few known parameters, without requiringexperimental data from all desired points.

Parameters

UNIQUAC requires two basic underlying parameters.
#Relative surface and volume fractions are chemical constants, which must be known for all chemicals.
#An empirical parameter between components that describes the intermolecular behaviour. This parameter must be known for all binary pairs in the mixture. In a quaternary mixture there are six such parameters (1-2,1-3,1-4,2-3,2-4,3-4) and the number rapidly increases with additional chemical components. The empirical parameters are derived from experimental activity coefficients, or from phase diagrams, from which the activity coefficients themselves can be calculated. An alternative is to obtain activity coefficients with a method such as UNIFAC, and the UNIFAC parameters can then be simplified by fitting to obtain the UNIQUAC parameters. This method allows for the more rapid calculation of activity coefficients, rather than direct usage of the more complex method.

Newer Developments

UNIQUAC has been extended by several research groups. Some selected derivativesare:
*UNIFAC : A method which permits the volume, surface and in particular,the binary interaction parameters to be estimated. This eliminates the use of experimental data to calculate the UNIQUAC parameters.
*Extensions for the estimation of activity coefficients for electrolytic mixturesWisniewska-Goclowska B., Malanowski S.K., "A new modification of the UNIQUAC equation including temperature dependent parameters", Fluid Phase Equilib., 180, 103-113, 2001] .
*Extensions for better describing the temperature dependence of activity coefficients

See also

*Chemical equilibrium
*Chemical thermodynamics
*Fugacity

References