(165b) Equation-Oriented Optimization of Processes with Dividing-Wall Columns

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

email: mbaldea@che.utexas.edu

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 [1].

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 [9] 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 [8] 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 [9].

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.

References

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