A calculation procedure has been developed for the simulation of a heterogeneous azeotropic distillation column which does not require prior specification of the number of stages with two liquid phases present. The complete Napthali-Sandholm matrix method for column simulation was combined with the modified (Larsen et al.) UNIFAC method for predicting vapour-liquid-liquid equilibrium data. The Pham and Doherty phase stability test was applied to determine the presence of two liquid phases. The predictions of ternary azeotrope compositions and temperature, for the ethanol-water-benzene and isopropanol-water-toluene systems, are very accurate. Predictions of liquid compositions in the heterogeneous region are not as accurate, but are of acceptable accuracy for design. There is considerable sensitivity to initial values supplied for these predictions. The prediction of column performance over a range of conditions demonstrated considerable flexibility in the developed programme. Experimental data are required to improve the accuracy of parameter values, and to provide a basis for testing column performance prediction accuracy.