Polynomial interpolations introduced into the classical model to describe the state functions along the column length and to include discontinuities (feed plate, side withdrawal plate), allowed to reduce the order of the original model and to shorten simulation time by a factor of about 15-50. Esterification of AcOH with EtOH with sulfuric acid as catalyst was used as a model process run in a 20 bubble-cap plate glass column, circle divide 0.075 m, and theoretical calculations were compared with experimental data. Consistency was satisfactory, differences were quantitative, not qualitative, in nature. The algorithms were found to be useful in design practice and in on-line process control.