Page 456 - Design and Operation of Heat Exchangers and their Networks

Optimal control process of heat exchanger networks 439

find which heat exchanger areas should be increased to make a design suffi-
ciently flexible. Grossmann et al. (1983) established the optimization strategies
for flexible chemical process, which were emphasized on two major areas:
optimal design with a fixed degree of flexibility and design with optimal
degree of flexibility. Saboo and Morari (1985) proposed a resilience index
to characterize the largest total uncertainty, which a HEN can tolerate while
remaining feasible. Kotjabasakis and Linnhoff (1986) introduced a procedure
for the design of flexible HENs, which was aimed at establishing the trade-off
between energy, capital, and flexibility. Picon Nunez and Polley (1995)
developed an approach to solve the flexibility problems of heat recovery net-
works by the use of network simulation and suggested the modification strat-
egies and steps. Picon Nunez and Polley (2000) also incorporated a
consideration of operability into the design of multistream heat exchangers
(MHE). The operability characteristics of MHEs are considered satisfying if
the steady-state response to disturbances of specified magnitude are within
acceptable bounds. Roetzel and Luo (2001) proposed a set of sensitivity
matrices of one-dimensional MHEs when study their flexibility, which were
applied to determine the regulations of mass flow rates of fluids in MHEs. Of
all these works, the efforts of Papalexandri and Pistikopoulos (1994a,b) to
incorporate flexibility and controllability considerations simultaneously in
the synthesis and retrofit design of HEN are the most systematic works. They
gave a systematic framework for the synthesis of cost optimal heat exchanger
networks that satisfy a set of controllability criteria. Based on a hyperstructure
network representation, dynamics are explored via the introduction of an
analytical model for dynamic gains and time delays in a heat exchanger net-
work. Input-output pairing criteria are explicitly included within a mixed-
integer nonlinear programming (MINLP) formulation for the synthesis of
HEN. Network configurations can be obtained featuring minimum total
annualized cost controllability characteristics, which may form the basis for
a successful control scheme.

9.2.1 Flexibility and structural controllability considerations

In the process of synthesis and retrofit design of HEN, the structural control-
lability targets can be expressed with different kinds of criteria. Papalexandri
and Pistikopoulos (1994a) defined the target as the total disturbance rejection
with respect to the specified controlled variables and disturbances.
To consider flexibility and structural controllability, we denote the set
of the uncertain variables of the network by u, the specified range of