From the view of thermodynamic insight, a new concept (ROE: F-E,F-Eope/F-E,F-pref), the ratio of the entrainer flow rate (F-E) needed for reaching given relative volatility at operating pressure (P-ope) to reference pressure (Pref), is firstly proposed to quantitatively determine the search space of operating pressure of the extractive column in a homogeneous extractive distillation (ED) process for the separation of binary minimum azeotrope with heavy entrainer. This novel concept is illustrated by the extractive distillation of tetrahydrofuran-water minimum boiling point mixture with an entrainer dimethyl sulfoxide. Six process designs under different pressures are obtained by a two-step optimization procedure and compared from the economic view based on total annual cost (TAC). Furthermore, three double-effect heat integration (DEHI) processes, are employed under atmospheric and a reduced pressure for the first time to further improve the energy efficiency and investigate the effect of pressures on the studied ED process. The final results of case study demonstrate the optimal heat integration approach with a suitable low pressure is the most economic one among the three DEHI processes. The TAC of the best proposed design exhibits a 20.3% reduction than that at atmosphere pressure. The proposed pressure selection rule and optimization process are helpful for reducing the TAC of the ED process. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.