Page 461 - Design and Operation of Heat Exchangers and their Networks

444 Design and operation of heat exchangers and their networks

manipulating input j shall be as small as possible compared with the response
time to any disturbance input k. This criterion is in fact for a feedforward
control; however, since it will yield a quick response of a controlled output
to the corresponding manipulating input, we can use it also for a feedback
control.

9.2.3 Minimal interaction requirements
An effective control structure also requires a minimal interaction among the
manipulating variables. We hope that a controlled variable i shall be more
sensitive to its pairing manipulating variable j and less sensitive to other
manipulating variables k (k6¼j). Papalexandri and Pistikopoulos (1994b)
further introduced a minimal interaction criterion into the synthesis model
as follows:

G ik G ij 1 m ij M 3 + α 3 0 8i, j,kk 6¼ jð Þ (9.33)
where i indicates a controlled output ϕ i , j indicates a pairing manipulating
input c j , k indicates a nonpairing manipulating input c k (k6¼j), and G ik is
the gain of the controlled output ϕ i to the manipulating input c k , which
is defined by

∂ϕ
i
G ik ¼ (9.34)

∂c k
The synthesis and retrofit design with controllability requirements can be
expressed by Eq. (9.30) with additional constraints (9.31)–(9.33).

9.3 Operation of heat exchanger networks
under uncertainty

A HEN is usually designed at given fixed operating conditions. However,
there may exist deviations of some inlet parameters of process streams.
A HEN designed with the methods described in the previous sections should
have a satisfied operability and controllability to shift between different
operation states, since they have already been considered in the synthesis/
retrofit process. In this section, we will discuss its online optimization or
the control between two steady states. To find methods for the operation
of HENs, Mathisen et al. (1992) investigated bypass selection for control
of HEN, without considering the utility consumption. Glemmestad et al.
(1997) proposed a method for optimal operation of HENs. Their method
uses steady-state optimization carried out online with regular time intervals.