Distribution of heat exchange in optimum diabatic distillation columns

We improved our model for minimization of entropy production rate in diabatic tray distillation. The entropy production rate had contributions from heat and mass transfer on the trays and from heat exchangers connected to the trays. The areas of the heat exchangers were not used as free variables, but calculated from four different area distribution rules. The total heat exchange area and its distribution over the column had a significant effect on the entropy production rate in the system. In the limit of infinitely large forces, the results of an adiabatic column were obtained, as expected. As the forces became smaller, the distribution of the area became more important. The area distribution rule with constant average force in each heat exchanger had the lowest entropy production rate of the rules used. Possible consequences for column design were discussed, and a sketch with the characteristics of an optimum distillation column was presented. Two minimization algorithms were used with similar outcome; the Matlab function fmincon being the fastest.