Page 449 - Design and Operation of Heat Exchangers and their Networks

432 Design and operation of heat exchangers and their networks

9.1 Feasibility, flexibility, and controllability of heat
exchanger networks

9.1.1 Feasibility and flexibility
A well-designed HEN or multistream heat exchanger should be a flexible
one that is able to adapt to parameter deviations from nominal values and
remain flexible when the parameters vary within a prespecified range. There
is another word, feasibility, which is easily confounded with flexibility.
Feasibility analysis gives us the information on whether or not a HEN
can maintain the target temperatures after any possible disturbances within
a prespecified range. However, flexibility analysis will tell us how the oper-
ating cost changes over the specified range of uncertain parameters. Swaney
and Grossmann (1985a,b) proposed a quantitative index, which they called
“flexibility index” to measure the size of the parameter space over which
feasible steady-state operation of the plant could be obtained by proper reg-
ulation of controlling variables. Later, Roetzel and Luo (2002) defined a new
flexibility factor to quantitatively address the flexibility of a HEN.
Assume a HEN in a process, its thermal performance at the nominal
operation point is described by
hd, c N , u N Þ ¼ 0 (9.1)
ð
gd, c N , u N Þ 0 (9.2)
ð
where d is the vector of design variables and c N and u N are the vectors of
controlling variables and uncontrolled operation variables at the nominal
operation point, respectively. The set h contains the exit stream tempera-
tures to be maintained at given targets, and the set g contains the exit stream
temperatures to be limited in given regions. The total utility cost at the
nominal operation point is calculated according to
X X
ð
ð
C N ¼ f HU Q HU,N Þ + f CU Q CU,N Þ (9.3)
in which f HU and f CU are cost functions of corresponding hot and cold utility
requirements, respectively.
A HEN is feasible if for any deviations in uncontrolled operation vari-
ables, Δu¼u u N (u2R u ), there exists c2R c such that the constraints
h(d, c N , u N )¼0 and g(d, c N , u N ) 0 are satisfied. To specify the feasibility
of a HEN quantitatively, the flexibility index D introduced by Swaney and
Grossmann (1985a,b) is adopted, which is defined as

D dðÞ ¼ maxδ (9.4)