Equation-Oriented Optimization of Processes with Dividing-Wall Columns
Richard Pattison, Akash Gupta, and Michael Baldea
McKetta Department of Chemical Engineering
The University of Texas at Austin, 1 University Station C0400, Austin, TX 78712
Distillation is one of the largest energy consumers in chemical and petrochemical processes, and typically the primary focus for improving energy efficiency and profitability. Complex column configurations, like Petlyuk (thermally coupled) columns (Figure 1, left), can substantially reduce energy use. Dividing-wall columns (DWCs) (Figure 1, right) follow the same principle as the Petlyuk configuration, but utilize a single-shell construction with a wall that partitions the stages in the middle of the column .
Figure 1: Left: Petlyuk column Right: Dividing-wall column
In spite of the potential economic and environmental benefits, the adoption of DWCs in industry has been slow, owing partially to the lack of a transparent and systematic method for optimal design of processes with DWCs. DWCs have more degrees of freedom than conventional distillation columns, and selecting the number stages, the feed and side draw stages, and the location of the dividing wall requires the solution of a highly nonlinear, nonconvex mixed-integer nonlinear program (MINLP).
Previous results relied on shortcut models to approximate the number of stages in each distillation cascade, thus formulating the design optimization as an NLP [2-4]. However, such approximations become inaccurate when the process mixture exhibits non-ideal behavior. On the other hand, detailed models that employ discrete decisions for activation/deactivation of stages in a column [5-7] have been employed, often reporting that initializing and solving the resulting MINLP are highly challenging tasks.
In this work, we propose a novel approach for equation-oriented modeling, simulation and optimization of DWCs and associated flowsheets. We begin with configuring distillation systems as an interconnection of units including: the reboiler, condenser, feed tray, side draw tray, and stage cascades with a variable number of stages. Specifically, a DWC has at least six stage cascades, corresponding to the stages above and below the dividing wall sections, and, within the divided section, two cascades each above and below the feed point, and above and below the side draw point. We rely on our previous results  to formulate the model of each distillation stage in a pseudo-transient fashion, as the combination of a mixing step and an equilibrium step that are connected via a tear stream. The formulation strategy improves the flowsheet convergence properties by decoupling the flash calculations between adjacent stages. The number of stages in each cascade is determined by defining (continuous) tray bypass efficiencies  to activate/deactivate stages. The proposed developments result in a pseudo-transient stage cascade model, which we demonstrate to be equivalent, at steady-state, with the conventional Material Energy Summation and Hydraulics (MESH) model of a distillation stage.
Subsequently, we show that the proposed pseudo-transient model has desirable initialization and convergence properties, and incorporate it in our previously developed pseudo-transient process flowsheet modeling and optimization framework .
We demonstrate the efficacy of the proposed DWC model and optimization framework on an extensive case study, focusing on the intensification of the dimethyl ether production process. Specifically, we demonstrate that the conventional two column design can be replaced with a new flowsheet structure, comprising a single DWC, which has lower capital and operating costs.
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