Page 471 - Design and Operation of Heat Exchangers and their Networks

454 Design and operation of heat exchangers and their networks

n X
ð
C k,min x, uÞ ¼ min a Q HU x, c b , c e , u τ k +1 Þ½ ð Š
c b 2R c b ,c e 2R c e
X o
+ b Q CU x, c b , c e , u τ k +1 Þ½ ð Š (9.53)
in which

u τ ðÞ,
_ τ τ k +1
u τ ðÞ ¼ (9.54)
ð
u τ k +1 Þ, τ > τ k +1
The time step τ k represents the control horizontal, 0¼τ 0 <τ 1 <τ 2
<…<τ k <τ k+1 . C k is the mean utility cost in the kth time interval [τ k ,
τ k+1 ], C k,min is the steady-state minimum utility cost under the optimal
controlling variables c b and c e against the disturbance u at τ k+1 , and C k,
max is the possible maximum utility cost in the time range of [τ k , ∞) due
to the disturbance expressed by Eq. (9.54).

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