(140e) Determination of Minimum Vapor Flow Rate Regions for Petlyuk System Using a Simple Pre-Fractionator Model
Short cut methods are useful to calculate some limiting operating conditions for the design of simple or complex distillation systems. For the particular case of minimum reflux conditions, it has been shown that the point of minimum vapor flow rate (Vmin) for pre-fractionator arrangements and for the fully thermally coupled distillation column (or Petlyuk system) it is not unique, but there is a flat region that is a function of the distribution of the middle component in the pre-fractionator.
Using Underwood's equations, Christiansen and Skogestad (1997) developed analytical expressions for pre-fractionator arrangements to predict the two distributions of the middle component of a ternary mixture that limit the flat region of Vmin; such points have been identified as the preferred separation and the balanced columns condition. To develop those expressions they assumed sharp splits, the pre-fractionator feed as saturated liquid, the upper feed to the main column as saturated vapor, and the lower feed to the main column as saturated liquid. They point out that, since the Petlyuk column shows a strong similarity with the prefrationator arrangement, the results could be applied to the Peltyuk system as well.
This work presents the calculations of the flat Vmin region for Petlyuk columns using an extension of Underwood's equations. The interconnecting flows are represented by equivalent net feed streams with adjusted thermal conditions, which are calculated from the work by Glinos and Malone (1985). With this simplification we reduce the Petlyuk structure to a pre-fractionator arrangement, modified only by the assumption on thermal conditions.
Calculations for the flat regions for fifteen ternary mixtures with different values of the Ease of Separation Index (ESI, equal to the ratio of relative volatilities of A and B with respect to B and C, with A being the most volatile component) are presented. Some of the assumptions, such as thermal conditions of the pseudo-streams and non-sharp separations, limited the development of an analytical expression. However, we show that the extension of Underwoodxs equation is straightforward. We found that the point for the preferred separation in the prefractionator was always close to the value predicted by Christiansen and Skogestad, but that the value of the balanced columns condition depended strongly on the pseudo-streams thermal conditions, especially when ESI is different from 1 and the feed concentration of the intermediate component is low.
Christiansen, A.C., Skogestad, S., ?Energy Savings in Complex Distillation Arrangements: Importance of Using the Preferred Separation?, AIChE Annual Meeting, Los Angeles, paper 199d, (1997). Glinos, K., and M.F. Malone, ?Minimum Vapor Flows in a Distillation Column with a Sidestream Stripper,? Ind. Eng. Chem. Process Des. Dev., 24, 1087 (1985).