(304b) A Novel MILP Approach to the Synthesis of Thermally Coupled Distillation Sequences

Caballero, J. A., University of Alicante
Grossmann, I. E., Carnegie Mellon University

Novel MILP Approach to the Synthesis of Thermally Coupled Distillation

A. Caballero*; Ignacio E. Grossmann**

of Chemical Engineering. University of Alicante. Ap. Correos 99. 03080
Alicante. Spain

Department of Chemical Engineering. Carnegie
Mellon University. Pittsburgh, PA. USA.


The distillation is still the most
widely used separation technique in the
chemical industry. It
handles more than 90% of separations and purifications and this trend seems unlikely to
change in the near future. The
capital investment for these distillation systems was estimated in 8x109
US$ [1]. Using data by Mix et al [2], Soave & Feliu [3] calculated that distillation accounts
about the 3% of the total US energy consumption which is equivalent to 2.87x1018
J (2.87 million TJ) a year or to a power consumption of 91 GW or 54 million
tons of crude oil.

A renew interest
in Thermally Coupled Distillation (TCD) appeared in, say the last 15-20 years,
due the important potential savings in energy: typical values around 10% to 40%
(in some cases even larger) has been reported [4-9] when compared with conventional
distillation sequences. An although the TCD can only be implemented in mixtures
involving the separation of at least three components the reader can have an
idea of the impact just looking at the numbers presented in the first

The design of TCD sequences is much more
complex than conventional distillation (each column with a condenser and a
reboiler) by at least two reasons. First, the number of alternatives is much
larger and second when we introduce a thermal couple we are introducing also
two thermodynamically equivalent configurations (TEC) [10-12],. Therefore, the number of alternatives
rapidly increases (i.e. in a five component mixture there are 203 basic
configurations, more than 8000 if we consider internal heat exchangers and more
than 2·105 if we take into account TEC). In order to avoid the
degeneracy created by TEC it is convenient to use a task based approach instead
of a column based approach. ?All TEC shares the same sequence of separation

As noted by Andrecovich and Westerberg [13] in
the 80's of last century, when we consider conventional separation sequences,
we can, a priori, optimize each possible column of the sequence, and then use a
MILP approach to extract the optimal sequence. But, when we deal with non-sharp
separations we cannot know a priori the distribution of no-key components and
therefore we must simultaneously optimize the columns and the sequence which
produces a non-convex MINLP even with shortcut methods [4, 5, 14]. However,
taking into account the following two facts, it is possible to develop a
strategy that allows decoupling the column and sequence optimization in TCD

Any distillation
sequence of zeotropic mixtures have a structure without recycles (A thermal
couple can be simulated with an equivalent system without recycles).

In TCD sequences the
flows of some column sections are not in the optimal operation conditions
because they must be modified in order to accomplish with the mass balance. But,
the introduction of heat exchangers allows decoupling these sections and avoids
the necessity of a simultaneous optimization.

It is possible then generating a tree of possible separation tasks as

1.     First we consider, and optimize, all the
initial separation tasks (those that have the initial mixture as feed).

2.     For each of the products (distillate and
bottoms of each column) we generate all the possible separations. At this point
we consider that mixtures of the same components with different concentrations
or different thermal states are different -explicitly takes into account the
possibility of a heat exchanger or a thermal couple-.

3.     Following recursively this approach we can
optimize all possible separation tasks and, implicitly, generate a tree that
includes all the separation tasks.

The number of possible separation tasks is
large, but much smaller than the number of sequences. Using the Underwood-Fenske
shortcut method the complete tree for a 5 component mixture can be generated in
around 4-5 seconds of CPU time.

The final step consists of extracting the
optimal separation sequence. However this is not straightforward. The simple
connectivity, like in conventional columns, does not assure a feasible basic

It is necessary to include logical relationships
accomplish with these task (a comprehensive description of these logical
relationships can be found in the work by Caballero & Grossmann [5].

b)    For some internal mixtures, there are more than one possible
separation task that depends on their origin (which separation task generate
it) and the thermal state (include or not a heat exchanger or a thermal
couple). Therefore it is necessary to include a set of logical relationships to
assure the feasibility and relates the tree of separations with the feasible

Divided Wall Columns (DWC) are explicitly included.
A DWC is generated by a subsystem of three fully thermally coupled tasks [15] and some logical relationships added to
avoid only feasible configurations.

all the data of all the separation tasks is calculated when each of the
individual columns are calculated, the resulting problem is a MILP in where we
select the best feasible sequence of tasks (i.e. the sequence with minimum
Total Annualized Cost). Calculate the excess of defect of heat (or vapor flows)
in the connectivity of each individual task and estimate the extra cost


As an example considers a mixture of 5
hydrocarbons (all relevant data and main results are showed in Table 1).

The optimal solution includes a DWC and a
set of small heat exchangers in the final products that appears as a
consequence of the differences in the flows in the different column sections
?See Figure 1-. Alternatively it is possible to remove all these heat
exchangers by adjusting the flows in the implied column sections. The net
result will be an increase in the heats of reboiler (associated with product E)
and condenser (product A) approximately in the same quantity of the heat
removed in the intermediate products. This could have two opposite effects. In
one side we remove three heat exchangers, but at the same time we lose the
possibility of using utilities at intermediate temperatures.

1. Sequence of separation tasks and a possible arrangement in actual columns.

Table 1.
Data and results for example 1.


Feed composition (mol fraction)




(A)- Benzene


Total Flow

100 kmol/h

(B)- Toluene



1 atm

(C)- Ethylbencene


Steam cost

5.02 $/GJ

(D)- Styrene


Cold water cost

0.19 $/GJ

(E)- α-methyl styrene


(8000 h/year)

Capital charge factor 0.18 (9% interest ; 8 years)

Optimal sequence

ABC/DE -  ABC/CD -  AB/BC ? A/B ? B/C ? C/D ? D/E


Condensers:   ABC; A; B

Reboilers:       C; D; E

Vessels cost (k$)


Tray cost (k$)


Heat Exchangers cost (k$)


Total Investment (k$)


Total utilities cost (k$/year)


TAC ( (k$/year)


Model Statistics


CPU time (s)


Nº equations


Nº continuous variables


Binary variables




The authors wish to
acknowledge support from the Spanish Ministry of Science and Innovation under
project (CTQ2009-14420-C02).


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15.          Caballero, J.A. and I.E.
Grossmann, Logic-Sequential Approach to the Synthesis of Complex Thermally
Coupled Distillation Systems
, in Computer Aided Chemical Engineering,
M.C.G. E.N. Pistikopoulos and A.C. Kokossis, Editors. 2011, Elsevier. p.

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