Non-random two-liquid model
It is frequently applied in the field of chemical engineering to calculate phase equilibria.
The concept of NRTL is based on the hypothesis of Wilson, who stated that the local concentration around a molecule in most mixtures is different from the bulk concentration.
The energy difference also introduces a non-randomness at the local molecular level.
These local-composition models are not thermodynamically consistent for a one-fluid model for a real mixture due to the assumption that the local composition around molecule i is independent of the local composition around molecule j.
[4] Models, which have consistency between bulk and the local molecular concentrations around different types of molecules are COSMO-RS, and COSMOSPACE.
Like Wilson (1964), Renon & Prausnitz (1968) began with local composition theory,[5] but instead of using the Flory–Huggins volumetric expression as Wilson did, they assumed local compositions followed with a new "non-randomness" parameter α.
The excess Gibbs free energy was then determined to be Unlike Wilson's equation, this can predict partially miscible mixtures.
However, the cross term, like Wohl's expansion, is more suitable for
, and experimental data is not always sufficiently plentiful to yield three meaningful values, so later attempts to extend Wilson's equation to partial miscibility (or to extend Guggenheim's quasichemical theory for nonrandom mixtures to Wilson's different-sized molecules) eventually yielded variants like UNIQUAC.
For a liquid, in which the local distribution is random around the center molecule, the parameter
In that case, the equations reduce to the one-parameter Margules activity model: In practice,
The high value reflects the ordered structure caused by hydrogen bonds.
In some cases, a better phase equilibria description is obtained by setting
In general, NRTL offers more flexibility in the description of phase equilibria than other activity models due to the extra non-randomness parameters.
However, in practice this flexibility is reduced in order to avoid wrong equilibrium description outside the range of regressed data.
This situation occurs for molecules of equal size but of different polarities.
It also shows, since three parameters are available, that multiple sets of solutions are possible.
The extended Antoine equation format: Here the logarithmic and linear terms are mainly used in the description of liquid-liquid equilibria (miscibility gap).
The other format is a second-order polynomial format: The NRTL parameters are fitted to activity coefficients that have been derived from experimentally determined phase equilibrium data (vapor–liquid, liquid–liquid, solid–liquid) as well as from heats of mixing.
Other options are direct experimental work and predicted activity coefficients with UNIFAC and similar models.
Noteworthy is that for the same mixture several NRTL parameter sets might exist.
The NRTL parameter set to use depends on the kind of phase equilibrium (i.e. solid–liquid (SL), liquid–liquid (LL), vapor–liquid (VL)).
In the case of the description of a vapor–liquid equilibria it is necessary to know which saturated vapor pressure of the pure components was used and whether the gas phase was treated as an ideal or a real gas.
Accurate saturated vapor pressure values are important in the determination or the description of an azeotrope.
Determination of NRTL parameters from regression of LLE and VLE experimental data is a challenging problem because it involves solving isoactivity or isofugacity equations which are highly non-linear.
In addition, parameters obtained from LLE of VLE may not always represent the experimental behaviour expected.
[9][10][11] For this reason it is necessary to confirm the thermodynamic consistency of the obtained parameters in the whole range of compositions (including binary subsystems, experimental and calculated tie-lines, calculated plait point location (by using Hessian matrix), etc.)
by using a phase stability test such as, the Free Gibss Energy minor tangent criteria .
[12][13][14] NRTL binary interaction parameters have been published in the Dechema data series and are provided by NIST and DDBST.
There also exist machine-learning approaches that are able to predict NRTL parameters by using the SMILES notation for molecules as input.
