A new simulation method using an extended phase-stability and phase-splitting algorithm has been programmed, and new three-phase regions are identified in published azeotropic distillation examples.If phase splitting is ignored, then an erroneous composition profile can be produced. The modern thermodynamic models UNIFAC-VLE, UNIFAC-LLE, modified UNIFAC, UNIQUAC, NRTL, ASOG, and modified ASOG have been investigated in the simulation model. The sensitivity of the selection of thermodynamic model on temperature and composition profiles has been studied for a wide range of systems. The changes in the number of theoretical stages required for the separation is dependent on the choice of thermodynamic model. A worked example of ethanol dehydration with 2,2,4-trimethylpentane shows the importance of reflux ratio, feed plate location, and number of stages on the separation. Multiple solutions for azeotropic distillation columns reported in the literature can be rationalized by the inclusion of a phase-splitting algorithm in the simulation model.