Comparing both solutions several observations can be made. First both solutions are close together. The reboiler duty calculated with the new approach is smaller, but only by 0.29%. The difference in the reboiler duties is larger than the difference between both solutions calculated with and without additional inequalities (see Table ). The purity demands are slightly violated in the solution with the Aspen Plus R simulation. The largest violation in the solution calculated with the new approach is in the order of 10 -16 . In the new approach the purity demands can be calculated as a linear constraint on the optimization variables. These linear constraints are respected by the sqp-algorithm up to a numerical precision. The situation is different using a simulation software together with an external optimizer. The concentrations are outputs of the simulation and their dependency to the optimization variables is highly nonlinear. The largest difference in the solutions can be observed for the split ratios. This means that in this example the solution is not very sensitive to changes in the split ratios, which is known from literature Halvorsen and Skogestad 2001. 2.23 • 10 -8 x T o /(mol/mol) 0.0500 0.0501 x pX /(mol/mol) 0.9500 0.9499