Thermodynamic approach to heat integration of processes involving separation of multicomponent mixtures is described. An integrability criterion based on geometrical presentation of distillation columns in temperature-enthalpy flow rate diagram was tested by rigorous simulation of distillation columns. The integrability criterion for distillation columns sequence was defined as the minimum sum of products of intracolumn temperatures and their heat flow rates (Min-criterion). Distillation columns sequences were studied according to their profitability in heat integration. Energy-pinch analysis was used for the synthesis of the best heat integrated distillation system. The representation using extended grand composite curve was demonstrated to be a very convenient one for understanding and evaluating, the heat integration. The selection of possible distillation columns sequences using rising values of the integrability criterion gave a very good approximation towards the best sequence of heat integrated distillation columns when compared to their total annual cost. Their estimation using rigorous models of distillation columns was shown to be better than using short cut models. The method allows alternative distillation sequences to be evaluated using rigorous calculations, prior to column design. The method is demonstrated with three five- and six-components example problems.