Page 455 - Design and Operation of Heat Exchangers and their Networks

438 Design and operation of heat exchangers and their networks

the streams. But if all the target output temperatures are only required to
maintain within the limited ranges, there may exist infinite numbers of reg-
ulation solutions. Thus, the optimal solution can be determined, and the task
becomes an optimization problem.
(2) N M +N T >N U
For this case, if the deviations are within the feasible region of the HEN,
there will exist infinite large number of regulation solutions, with which
all the target output temperatures can be exactly maintained or can be
maintained within limited ranges. Therefore, the optimal set need to be
determined.
(3) N M +N T <N U
For this case, only some of the target output temperatures of N U process
streams can be exactly maintained even if the deviations are within the feasible
region,buttheremaystillexistinfinitenumberofregulationsolutionstomain-
tain all the target output temperatures of N U process streams within their lim-
ited ranges. Thus, the optimal regulation solution also needs to bedetermined.

9.1.2.2 Controllability analysis
A HEN is controllable when there are enough regulatable bypasses con-
nected with these N M +N T inlets; therefore, controllability should be con-
sidered in the synthesis stage instead of for an existing structure. How to
manipulate the bypass values within limited time is a task of control design.
Controllability includes two aspects: structural controllability and dynamic
controllability. The former is often expressed as criteria or index describing
relations between disturbances and controlled variables, and the latter is
expressed as criteria based on dynamics model of HEN.
From control theory, a system is controllable if there exists a control sig-
nal c(τ) such that the state of the system can be taken from any initial state x 0
to any desired final state x j in a finite time interval. Papalexandri and
Pistikopoulos (1994a) gave an explicit structural controllability criteria based
on a multiperiod hyperstructure network representation; they included their
criteria within a synthesis/retrofit mixed-integer nonlinear programming
model with total annualized cost as objective function.

9.2 Synthesis and retrofit design of flexible and
controllable heat exchanger networks

Since the mid 1980s several authors have investigated flexibility of HENs, for
example, Kotjabasakis and Linnhoff (1986) that introduced sensitivity tables to