Separation of azeotropic mixtures receives special attention for their impact on various significant industrial processes. Because of the non-ideal behaviour of these mixtures, it is impossible to separate them by conventional distillation. Instead of a single distillation unit, a system of multiple operations is to be employed. Heterogeneous azeotropic distillation (HAD) is an example of this kind of systems, where entrainers are applied to modify the behaviour of the mixture. The selection of the best separation system is a key objective during the synthesis of the process network. However, synthesis of HAD is especially difficult because of the complex interaction between its continuous and discrete features. Therefore, traditional separation network synthesis tools are incapable of solving this problem. In this work, the properties of the ternary vapor-liquid-liquid equilibrium diagram are exploited for systematically identifying plausible operating units that perform the separation of the azeotrope. Subsequently, energy consumption of the entire network is estimated through rigorous simulation. The P-graph framework is employed to represent the system’s structure. Additionally, its combinatorial algorithms generate a rigorous superstructure for the synthesis problem, and the set of n-best designs that minimize energy consumption. The method is illustrated by synthesizing the dehydration of furfural through HAD. The results demonstrate that it constitutes a valuable tool for the designer by being effective in the systematic identification and assessment of HAD alternatives.