Calculation of parametric sensitivity in binary batch distillation

Abstract

This paper provides a comprehensive analysis of parametric sensitivity of batch distillation operations to perturbations in the feed composition. Three column arrangements are considered: batch rectifiers, batch strippers and total-reflux columns. The perturbation dynamics is parameterized in such a way as to allow the analytical calculation of the sensitivity function in the whole composition range, for both sharp and non-sharp separations. This makes it possible to determine a priori which operating conditions and system parameters favor sensitivity of the nominal state variable profiles, and to calculate to which extent parametric sensitivity is exhibited by a certain batch distillation operation. For conventional batch rectifiers, it is shown that there exists a limiting value r top of the reflux ratio above which there is a ‘sensitive’ operating region characterized by a linear increase of the sensitivity function with respect to the concentration of the heavy component in the reboiler; the higher the reflux ratio, the wider this sensitive operating region. For operations with r< r top, the sensitivity function is independent of the reflux ratio. For batch strippers, it is found that sensitive and non-sensitive operating regions are located somewhat symmetrically with respect to the case of batch rectifiers. However, the sensitivity function profiles are not symmetrical to those exhibited by regular batch columns. Finally, for columns operated at total reflux with a ‘balanced feed’, it is shown that if the feed is ‘very’ light or ‘very’ heavy, the transient behavior of the bottom composition sensitivity function is either always increasing or always decreasing. The parametc sensitivity in total-reflux operations appears higher than the one exhibited in finite-reflux-ratio operations.