Batch distillation processes rely on dynamic models. Over the last three decades rigorous algorithms have been developed for different types of Batch Distillation Columns (BC), including Reactive Batch Columns, but there is still a lack of understanding about Dividing Wall Batch Reactive Distillation Columns (DWBC). In fact, no rigorous model has been reported for their solution. Reactive Batch Distillation Columns (RBDC), as Continuous Distillation Columns (CDC), are characterized by high energy consumption. An innovative solution to overcome this problem is the use of Dividing Wall Columns (DWC). The Petlyuk configuration, consisting of two coupled distillation columns [1], evolved into a more practical application by adding a vertical wall that splits the column into two separate sections. Thanks to this flexibility, DWC has found great appeal in the chemical process industry as it can separate more components in a single distillation unit thus achieving cost savings by requiring single columns instead of two and by a decrease in operation costs using a single condenser and reboiler. In fact, the use of DWC in Continuous Distillation Columns can save up to 30% in capital investment and up to 40% in operating costs [2].

In this study a model and solution strategies are proposed for the optimization of a Dividing Wall Batch and Semi-Batch Reactive Distillation Column. A profit maximization involving methanol esterification reaction for the production of methyl acetate (as the main product) is proposed. In order to determine the potential benefits, such like energy savings and reduction of batch time we propose a dynamic rigorous model that involves tray-by-tray calculations when a dividing wall and side feeds are added to the batch column for the time varying profiles. We also investigate how the distillate product composition varies when different reaction zones and different positions of the dividing wall are included in the model. The optimization variables, considered to achieve a given product specification, are batch time, vapor flowrate and reflux ratio as the control variable. The dynamic optimization problem is converted into an NLP problem by using the oriented equation method proposed by Biegler [3], finite elements and collocation points implemented in GAMS (General Algebraic Modeling System, 24.2.2). The Control Vector Parametization approach proposed by Pantelides [4,5] is solved by using gPROMS (general PROcess Modeling System, 2004) which makes use of Succesive Quadratic Programming (SQP) method.

** ****References**

** **[1] Slavinskii D. M. Petlyuk F. B., Platonov V. M. Thermodynamically optimal method for separating multicomponente mixtures. *Int. Chemical Engineering*, pages 555–561, 1965.

[2] Draghiciu L. Isopescu R.,Woinaroschy A. Energy reduction in a divided wall distillation. *Rev. Chim.*, 59:812–815, 2008.

[3] Biegler L. T. Solution of dynamic optimization problems by succesive quadratic programming and orthogonal collocation. *Comput. Chem. Eng.*, 8:243–248, 1984.

[4] Pantelides C. C. Vassiliadis V. S., Sargent R. W. H. Solution of a class of multistage dynamic optimization problems. Part I - Algorithmic framework. *Ind. Eng. Chem. Res.*, 33:2115–2123, 1994.

[5] Pantelides C. C. Vassiliadis V. S., Sargent R. W. H. Solution of a class of multistage dynamic optimization problems. Part II - Problems with path constraints. *Ind. Eng. Chem. Res.*, 33:2123–2133, 1994.

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