Problems and limitations in the calculation of liquid-liquid equilibrium

Model calculations of the liquid-liquid equilibria encounter several considerable serious difficulties due to the relatively complicated requirements that must be met in the equilibrium state. These requirements can prevent a solution from being obtained or lead to false solutions. In this paper, we investigate the possibility that the numerical procedure aimed at looking for concentrations of coexisting phases in an isothermal binary system will fall into a trivial solution or end up with a solution lacking the physical sense. The model system is generated on the basis of the NRTL equation. We propose the modified Equal Area Rule (EAR) algorithm to overcome some of these difficulties. The advantages of the EAR over the traditional approach are shown and discussed for binary systems. Using this method, we determined a range of the NRTL parameters leading to different kinds of immiscibility regions in the liquid-liquid equilibrium (LLE). The shape of the objective function during the fitting of the NRTL parameters to the LLE experimental data was determined and discussed. This has a potentially strong impact on the convergence of the optimization algorithm.