Page 458 - Design and Operation of Heat Exchangers and their Networks

Optimal control process of heat exchanger networks 441

The generic rank of M is determined by the following optimization
problem (Georgiou and Floudas, 1989):
m n
XX
max y ij (9.29)
i, j
i¼1 j¼1
m
X
s:t: y ij v i ¼ 0 ð i ¼ 1, 2, ⋯, nÞ
j¼1
n
X
ð
y ij w j 0 j ¼ 1, 2, ⋯, mÞ
i¼1
n
X
v i ¼ GR
i¼1
m
X
w j ¼ GR
j¼1
in which v i is a binary variable corresponding to a row and denoting whether
the row is active (when v i ¼1) or redundant (when v i ¼0), w j is a binary
variablecorrespondingtoacolumnanddenotingwhetherthecolumnisactive
(when w j ¼1)orredundant(when w j ¼0),and y ij isabinaryvariableindicating
that the variable of the jth column is an output variable of the ith row if y ij ¼1.
y ij is set to zero when the corresponding elements of M are zero.
The synthesis and retrofit problems can be equivalently written as
min TAC (9.30)
Δd,x,c

s:t: max min maxg j d, x, c, uð Þ 0
c
u2R u j2J g
s:t: hd, x, c, uÞ ¼ 0
ð
GR Mx, c, z, uފ AR Mx, c, z, uފ 1
ð
½
½
ð
9.2.2 Dynamics and control structure considerations
Dynamic controllability deals with the maintenance of the target output
parameters upon short-term deviations of inlet parameters or operation tran-
sitions from one operating point to another. The dynamic controllability
depends on dynamic characteristics of the HEN.
Papalexandri and Pistikopoulos (1994b) used a multiperiod hyperstruc-
ture to present structural, operational, and control alternatives in a HEN net-
work. The multiperiod hyperstructure for a stream k is shown in Fig. 9.2.