Difficulties associated with the optimisation of distillation column models by non-linear programming are considered. The paper presents a systematic procedure to enable these difficulties to be overcome and proposes a particular formulation of the distillation column model. A certain limiting case of the column model is examined, that of infinite reflux or zero feed. This limiting case considerably simplifies the model and provides a system of non-linear equations that is readily solved. The solution of this problem gives useful information about the purity that can be achieved in the general case and the number of plates needed to attain a given level of purity. The limiting problem provides starting values for the solution of the general column and suggests a homotopy that can be followed if difficulties arise in obtaining convergence. To obtain a stable form of the limiting case requires the general column model to be formulated in a certain way, which to our knowledge has not previously been considered. The ideas have been successfully tested on various multi-column flowsheets involving distillation columns with heat integration.