On the effort of approaching pure components and azeotropes in distillation

In most distillation problems, the desired products are located at the singular points of the vapor liquid equilibrium, i.e. pure components or azeotropes. The effort to approach these points depends on the specified purity of the product and tends to infinity as the composition approaches that of a pure component or azeotrope. In the present work, a method to quantify this effort in terms of equilibrium stages is given. It is shown that there is a constant lower bound on the number of stages required to decrease the impurity delta of the product by a certain factor b. Further, it is shown that this lower bound is proportional to the logarithm of c. The results of the method are valid for ideal and non ideal systems of any number of components. The information is obtained from the eigenvalues and eigenvectors of the singular points, no process simulations are needed. We propose adding key figures derived from the eigenvalues to distillation line/residue curve diagrams to immediately grasp the effort upon approaching the singular points.