Assuming a predetermined reactor combination and changing its parameters to maximize
the desired performance objective is known as Super-structure approach. The terminology ‘Super
Structure’ is apt because this structure includes all conceivable structures by setting some of its
parameters to zero or some suitable value. (For example PFR with recycle is a super-structure
that can produce a PFR by setting the recycle ratio to zero, and a CSTR by increasing the recycle
ratio to an arbitrarily large value). This method is successfully applied since 1967 (Horn and
Tsai, 1967; Jackson, 1968; Ravimohan, 1971). However Chitra and Govind (1985) applied it
first time to arrive at optimal reactor networks for complex reactions. The super-structure they
used was PFR with a recycle from an intermediate point.
A PFR with recycle can approach both PMR and PFR performances. This fact was used
to propose a network of 5 such reactors in series. Further, they provided for temperature change
at the inlet of each reactor so that non-isothermal reactor operation can also be realized. With
this scheme, they found solutions for isothermal van de Vusse reaction (PMR followed by PFR)
and Denbigh reaction (PFR followed by PMR). The non-isothermal network was used for van de
Vusse reaction and naphthalene oxidation, and resulted in complex reactor networks involving
up to five reactors. Achenie and Biegler (1990) also used similar Recycle Reactors and employed
variational calculus for optimization.
Kokossis and Floudas (1989) formulated a network of 4 PMRs and 4 PFRs with each
PFR represented by 20 PMRs in series. This approximation of a PFR with a series of PMRs is
similar to the well-known ‘Tanks-in-Series’ model (Levenspiel, 1962). The resultant
optimization problem contained up to 3044 variables and 3066 constraints. It was then solved
using Mixed Integer Non-Linear Programming (MINLP) package called OREAN. Formulation
of such large sized optimization problems using super structure and its subsequent reduction
through programming to the optimal network has been reported around the same time in many
process synthesis tasks aimed at arriving at the optimal flowsheet configuration. Development in
computers and computational speeds offered impetus to this progress. Nevertheless, such
techniques cannot conclusively assert that the solution that is found subsequently is a global
optimum and not merely a local optimum.
Schweiger and Floudas (1999) noticed that very often the optimum reactor network
consists of one PFR and one PMR. They proposed a network of Cross Flow Reactor (CFR) and
PMR (Fig 2.1), which can mimic any combination of these two reactors. The resultant
optimization problem contained less than 100 variables and 100 constraints. They solved the
system of equations using MINOPT and CHEMKIN packages and achieved or even improved
the results obtained by Kokossis and Floudas (1989). It only proved that any superstructure
based optimization approach is prone to getting stalled at a local optimum. At least, it is
impossible to say with full confidence that what is achieved is indeed a global optimum. This is
generally the price to pay when optimization is unaided by some structural and analytical insight
into the physical system.

Cordero et al. (1997) suggested the use of stochastic optimization technique: Simulated
Annealing, to determine the optimum reactor configuration. The information on reactor network
is coded in a modified incidence matrix. Several candidate configurations are progressively
changed till an optimum is found. Using this method, they have analyzed parallel reactions (A →
B, A → C) and van de Vusse reaction. Mehta and Kokossis (1998 and 2000) also used Simulated
Annealing for nonisothermal reactor network optimization.
It seems that the Super Structure Approach always comes out with some answer usually
within 10% of what could later on be obtained by alternative and/or more rigorous methods.
However, as Schweiger and Floudas (1999) note, there is no guarantee of the obtained solution
being Global. They obtained multiple local solutions by using different starting points at random.
Moreover the approach is evolving with time as different reactor configurations are tried.