Thermal separation processes, such as distillation, play a pivotal role in the chemical and petrochemical sectors, constituting a substantial portion of the industrial energy consumption. Consequently, owing to their huge application scales, these processes contribute significantly to greenhouse gas (GHG) emissions. Decarbonizing distillation units could mitigate carbon emissions substantially. Heat Pumps (HP), that recycle lower quality heat from the condenser to the reboiler by electric work present a unique opportunity to electrify distillation systems. In this research we try to answer the following question in the context of multi-component distillation – Do HPs actually reduce the effective fuel consumption or just merely shift the fuel demand from chemical industry to the power plant? If they do, what strategies consume minimum energy? To address these inquiries, we construct various simplified surrogate and shortcut models designed to effectively encapsulate the fundamental physics of the system. These models are integrated into a superstructure-based Mixed-Integer Nonlinear Programming (MINLP) formulation, which is amenable to global optimization algorithms aimed at minimizing the effective fuel consumption of the system. Moreover, through the examination of a toy 4-component alcohol separation example, we demonstrate how HPs can notably reduce carbon emissions, even when the consumed electricity is generated by burning fossil fuels.