(534e) A State-Space-Based Mixed Integer Dynamic Optimization Formulation for Batch Distillation Process Synthesis

Batch
distillation is widely used in fine chemical and pharmaceutical industries for
the purification or recovery of high value-added products. The transient nature
of the batch distillation process provides great flexibilities in both various
operating policies and alternative complex configurations. Such unique
characteristics can help further explore the economic potential and process
efficiency through the optimal synthesis of batch distillation process.
However, the dynamic behavior and complicated economical
trade-offs make a huge challenge for the synthesis problem.

Over the past decades, the optimal design and operation
of batch distillation have received significant attentions (Logsdon,
Diwekar and Biegler, 1990; Mujtaba and Macchietto, 1996; Sharif, Shah and
Pantelides, 1998; Low and Sørensen, 2003).  The previous works have provided some general insights on the comparative
performances of various batch distillation systems and indicated that the
interdependent design and operating control variables should be optimized
simultaneously. Furthermore, different configuration of
batch distillation column was also taken into account as an optimization parameter with the method of a
disjunctive model consisting a given set of equipment modules and the
corresponding logical relationships provided by the design context (Oldenburg, Marquardt and Leineweber, 2004; Low
and Sørensen, 2005). With the development of
manufacture and control in chemical industry, more efficient and energy saving
techniques are applied in batch distillation process. As a result, the number
of possible batch distillation column configurations and complex operating
strategies proposed in the literature continue to increase, such as the side
withdrawals, thermally linked streams or other complex designs. So there is an
urgent need to propose a completed superstructure of batch distillation system
that encompasses all possible configurations and operating strategies to reduce
the energy consumption and capital investment, and eventually achieve the
profit maximization. The incompletion of the superstructure may preclude a
series of design alternatives, where the optimal solution may actually lies.

In this work, an improved superstructure based on state
space representation (Bagajewicz and Manousiouthakis, 1992), a framework that
takes all streams splitting and mixing possibilities into consideration, is
proposed for the synthesis of batch distillation process. The state space based
superstructure has been successfully used for the synthesis of continuous
distillation process to reduce both the utility and capital costs (Zou et al.,
2012), and we take the unique characteristics of batch distillation process (dynamic
behavior and tray-vessel configuration) into
account to develop the superstructure. To be specific, the superstructure of
batch distillation system is viewed as a system of two interconnected parts
(see Figure 1). One is referred to as the distribution network (DN), in which
all mixers, splitters and the connections between them are embedded. The other
is the so-called process operator (PO), which is further divided into two kinds
of equilibrium stages, i.e. the vessels and the trays,
with intermediate condenser and/or reboiler. From the superstructure we can see
that the initial feed stream can be charged into arbitrary number of vessels
according to its property, such as the number of components and each
composition in the feed stream. Then the streams out of the vessel(s) are
delivered to DN for distribution to arbitrary trays for further mass and heat
exchanges, and similarly, the trays are fully connected to each other and also
have opportunities to distribute streams to arbitrary vessels through DN.
Finally, when the required purities are satisfied, each product can be
collected in certain vessel or withdrawn from certain tray.

Based on the analysis above, all possible configurations
of batch distillation, not only three typical structures (regular,
inverse, multivessel columns), but also more complex designs (like thermal
links, side withdrawals, etc) are merged into the superstructure. Considering the Mass
balance, Equilibrium relation, Summation check and Heat balances (MESH) for
each of equilibrium stage, all mixers and splitters, the overall synthesis
problem can be formulated as a mixed integer dynamic optimization (MIDO), where
the sales revenue, operating costs (including costs of cold and hot utilities)
and equipment cost (including costs of distillation columns and heat
exchangers) can be all considered to maximize the overall profitability.
Therefore under this framework, the design variables (the number and the
connecting relations of vessels and trays) and the operating control
variables (the flow rate of each stream) are optimized simultaneously, and then
an optimal batch distillation process for a given separation duty is achieved.

In addition, because the batch distillation is a dynamic
process, the separation difficulty also varies with the processing time,
especially for multicomponent separation duty. Under the proposed framework,
not only the operation strategy (liquid/vapor ratio on each equilibrium stage)
, but also the corresponding structure of the batch distillation system (the
number and the connecting relations of vessels and trays) can be both optimally
changed in different time intervals instead of fixing vapor load and the batch
distillation column configuration on total time horizon.
Thus, in every time interval, the operation strategy and the corresponding
structure of batch distillation column can be matched perfectly to avoid
compromising the operation strategy due to the limit of the fixed column
configuration during the conceptual design period. Hence the batch distillation
process is optimized both on time and space dimensions.

In summary, since (1) with the mechanism of arbitrary
split and/or mix of any streams, as well as the arbitrary connections between
any vessels and trays, all possible operating strategies and batch distillation
column configurations are embedded in the completed superstructure, and (2)
both operating strategy and column configuration can be simultaneously
optimized in each time interval. So it is reasonable to expect that a more
efficient batch distillation process can be achieved for the specific
separation duty. From the comparison analysis of the example results, not only dramatic
energy savings but also significant capital investment reduction has been brought in our
novel conceptual designs. Both binary and multicomponent separation case
studies are presented to illustrate the validity and advantages of the proposed
approach.

References

1.      Logsdon JS, Diwekar UM, Biegler LT. On
the simultaneous optimal design and operation of batch distillation columns. Transactions of IChemE. 1990; 68:
434-444.

2.      Mujtaba
IM, Macchietto S. Simultaneous optimization of design and operation of
multicomponent batch distillation column-single and multiple separation duties. J of Process Control. 1996; 6: 27-36.

3.      Sharif
M, Shah N, Pantelides CC. On the design of multicomponent batch distillation
columns. Comp & Chem Eng. 1998;
S22: 69-76.

4.      Low
KH, Sørensen E. Simultaneous optimal design and operation of multivessel batch
distillation. AIChE J. 2003; 49:
2564-2576.

5.      Oldenburg
J, Marquardt W, Heinz D, Leineweber DB. Mixed-logic dynamic optimization
applied to batch distillation process design. AIChE J. 2003; 49: 2900-2917.

6.      Low
KH,
Sørensen
E. Simultaneous optimal configuration, design and operation of batch
distillation. AIChE J. 2005; 51:
1700-1713.

7.     
Bagajewicz M, Manousiouthakis
V. Mass/heat-exchange network representation of distillation networks. AIChE J 1992; 38: 1769-1800.

8.     
Zou X, Cui YH,
Dong HG, Wang JQ, Grossmann IE. Optimal design of complex distillation system
for multicomponent zeotropic separations.
Chem Eng Sci. 2012; 75: 133-143.

Figure
1. The improved state-space superstructure of batch distillation system