Methanol is an important industrial chemical, and its synthesis and purification units are among the most widely used processes in the field of energy. The two-column separation unit of methanol has been analyzed from the thermodynamic and energy points of view in the present study. The simulation has been done by Aspen Hysys V11 and the SRK equation has been regarded as the most appropriate equation of state (EOS) for this simulation with the mean relative error (MRE) of 2 %. Then, the design of the heat exchanger network (HEN) has been calculated using the Aspen Energy Analyzer V11. Both distillation towers have been analyzed using pinch technology. As a result, the amount of hot and cold utilities used has been LP=1.482×〖10〗^8, MP=1.57×〖10〗^4, and Air =1.423×〖10〗^8, respectively. Besides, the total heating and cooling target of the process has been 1.482×〖10〗^8 and 1.423×〖10〗^8, accordingly. Then, the 〖∆T〗_min (minimum allowable temperature difference between hot and cold currents) and its effect on the annual cost have been investigated. The optimum value 〖∆T〗_min is determined to have better-operating conditions and to meet the design of the HEN economically. Reducing 〖∆T〗_min increases operating costs and reduces energy costs.