In this work, several energy-saving designs of an industrial 1,4-dioxane dehydration process with small amounts of triethylamine (TEA) impurity were compared. The original process contains a preconcentrator column to remove TEA and two other columns operated at different pressures by pressure-swing distillation to separate the remaining azeotrope-containing mixture. To save on the operating costs of this process, two alternative designs were investigated. The first combines the condenser of a high-pressure column with the reboiler of a low-pressure column. The second design uses a completely different method for this separation by heterogeneous azeotropic distillation. This second design can further be thermally coupled into a dividing-wall column with only one column shell. It was found that significant savings in the operating costs (49.09%) and in the total annual cost (43.31%) can be realized by using this second design as compared to the original process. The proposed method uses the light impurity as an entrainer, so no foreign component is added into the system. The operation and control of the proposed design were also studied. An overall conventional tray-temperature control strategy was proposed to maintain high-purity product streams despite disturbances in feed composition and throughput.