If the feed contains micro-components and reflux ratio is extremely high, distillation problems sometimes become impossible to solve because micro-components behave in a complicated manner. The acetic acid purification problem is an example of these problems. No conventional single algorithm could solve this problem. It can be solved by a combination algorithm : to make a favorable initial profile, the successive iteration algorithm precedes the Newton-Raphson one. A detailed consideration of convergence is given in the text.
A novel column profile of micro-components is observed : it shows three extremes in column concentration of formic acid, and two extremes for water, which we had never seen. Failure of the single algorithm comes from this novel type of profile.