Diabatic distillation is a separation process in which heat is transferred on the trays inside the column as opposed to classical adiabatic columns where heat is only supplied to the reboiler and extracted from the condenser. Such diabatic columns dramatically reduce the exergy needed to perform the separation. One implementation, particularly suitable for retrofitting applications, uses a single heating fluid circulating in series from one tray to the next below the feed tray and a single cooling fluid circulating in series above the feed tray. The optimal design of these sequential heat exchangers, minimizing the overall rate of entropy production in the separation process, is a difficult optimization problem because traditional algorithms for optimization invariably get stuck. However, an algorithm based on physical intuition for adjusting the temperature profile can find the optimum. The resulting column operation is compared to the optimal operation with independent heat transfer to each tray (the completely controlled diabatic column) and to a conventional adiabatic column. In the former comparison, we find how much exergy is lost by circulating a fluid in series rather than using independently adjustable heat exchanges. In the latter, we find the possible savings available by retrofitting. The comparisons show that most of the potential exergy savings can be captured by diabatization using heat exchangers in series. The potential impact of this technology on the chemical and process industry is enormous because distillation is the single largest energy degrading unit operation worldwide.