Non-random two-liquid model

The non-random two-liquid model (short NRTL equation) is an activity coefficient model that correlates the activity coefficients γ i {displaystyle gamma _{i}} of a compound with its mole fractions x i {displaystyle x_{i}} in the liquid phase concerned. 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 that the local concentration around a molecule is different from the bulk concentration. This difference is due to a difference between the interaction energy of the central molecule with the molecules of its own kind U i i {displaystyle U_{ii}} and that with the molecules of the other kind U i j {displaystyle U_{ij}} . The energy difference also introduces a non-randomness at the local molecular level. The NRTL model belongs to the so-called local-composition models. Other models of this type are the Wilson model, the UNIQUAC model, and the group contribution model UNIFAC. 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. This assumption is not true, as was shown by Flemr in 1976. However, they are consistent if a hypothetical two-liquid model is used. The non-random two-liquid model (short NRTL equation) is an activity coefficient model that correlates the activity coefficients γ i {displaystyle gamma _{i}} of a compound with its mole fractions x i {displaystyle x_{i}} in the liquid phase concerned. 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 that the local concentration around a molecule is different from the bulk concentration. This difference is due to a difference between the interaction energy of the central molecule with the molecules of its own kind U i i {displaystyle U_{ii}} and that with the molecules of the other kind U i j {displaystyle U_{ij}} . The energy difference also introduces a non-randomness at the local molecular level. The NRTL model belongs to the so-called local-composition models. Other models of this type are the Wilson model, the UNIQUAC model, and the group contribution model UNIFAC. 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. This assumption is not true, as was shown by Flemr in 1976. However, they are consistent if a hypothetical two-liquid model is used. For a binary mixture the following function are used: { ln ⁡   γ 1 = x 2 2 [ τ 21 ( G 21 x 1 + x 2 G 21 ) 2 + τ 12 G 12 ( x 2 + x 1 G 12 ) 2 ] ln ⁡   γ 2 = x 1 2 [ τ 12 ( G 12 x 2 + x 1 G 12 ) 2 + τ 21 G 21 ( x 1 + x 2 G 21 ) 2 ] {displaystyle left{{egin{matrix}ln gamma _{1}=x_{2}^{2}left\\ln gamma _{2}=x_{1}^{2}leftend{matrix}} ight.}