The second law optimal state of a diabatic binary tray distillation column

A new numerical procedure to minimize the entropy production in diabatic tray distillation columns has been developed. The method was based on a least square regression of the entropy production at each tray. A diabatic column is a column with heat exchangers on all trays. The method was demonstrated on a distillation column separating propylene from propane. The entropy production included contributions from the heat transfer in the heat exchangers and the mass and heat transfer between liquid and vapor inside the distillation column. It was minimized for a number of binary tray distillation columns with fixed heat transfer area, number of trays, and feed stream temperature and composition. For the first time, the areas of heat exchange were used as variables in the optimization. An analytical result is that the entropy production due to heat transfer is proportional to the area of each heat exchanger in the optimal state. For many distillation columns, this is equivalent to a constant driving force for heat transfer. The entropy production was reduced with up to 30% in the cases with large heat transfer area and many trays. In large process facilities, this reduction would ideally lead to 1-2 GWh of saved exergy per year. The most important variable in obtaining these reductions is the total heat transfer area. The investigation was done with a perspective to later include the column as a part in an optimization of a larger process. We found that the entropy production of the column behaved almost as a quadratic function when the composition of the feed stream changed. This means that the feed composition is a natural, easy variable for a second law optimization when the distillation column is a part of a process. The entropy production was insensitive to variations in the feed temperature.