The Nonrandom two-liquid model (NRTL) is an activity coefficient model used to calculate the Gibbs free energy of a non-ideal system. It defines the activity coefficient $\gamma_i$ as a function of the molar composition $x_i$. This model has been used in chemical engineering applications and has been used in a wide variety of mixtures calculating vapour-liquid and liquid-liquid equilibria ^[1] . The NRTL equation of a binary system is as follows:

\[ln \gamma_1 = x_2^2[\tau_{2 1} (\dfrac{G_{2 1}}{x_1 + x_2 G_{2 1}})^2+\dfrac{\tau_{1 2} G_{1 2}}{(x_2 + x_1 G_{1 2})^2}]\]

where

\[G_{1 2} = e^{-\alpha_{1 2}\tau_{1 2}} \\ G_{2 1} = e^{-\alpha_{2 1}\tau_{2 1}} \\ \tau_{1 2} = \dfrac{(g_{1 2} - g_{2 2})}{RT} \\ \tau_{2 1} = \dfrac{(g_{2 1} - g_{1 1})}{RT}\]

In the NRTL model the $R$ is the universal gas constant, $T$ is the temperature at equilibrium, $G$ is a dimensionless interaction parameter, that depends on a the specific component interaction energy parameter $g$ and a non-randomness factor $\alpha$. The two energy parameters $(g_{1 2} - g_{2 2})$ and $(g_{2 1} - g_{1 1})$ are adjustable values obtained by the regression of experimental data. $\alpha_{1 2}$ and $\alpha_{2 1}$ are the two adjustable non-randomness parameters. Experimental data for a large number of systems show that they range from $0.20$ to $0.47$. It is sometimes chosen casually as it has no physical correlation ^[2].

The equation for a multicomponent system is as follows:

\[ln \gamma_i = \dfrac{\sum_{j=1}^C {\tau_{j i} G_{j i} x_{j}} }{ \sum_{j=1}^C {G_{j i} x_{j}} } + \sum_{j=1}^C \dfrac{x_j G_{i j}}{\sum_{k=1}^C { x_k G_{k j}}}(\tau_{i j} - \dfrac{\sum_{k=1}^C {x_k \tau_{k j} G_{k j}}}{\sum_{k=1}^C {x_k G_{k j}}})\]