Page 454 - Design and Operation of Heat Exchangers and their Networks

Optimal control process of heat exchanger networks 437

control variables are c 1 =0.4242kW/K, c 2 =0.2685kW/K, c 3 =0.7356kW/K,
c 4 =0.7594kW/K, and c 5 =0.9678kW/K.
The flexibility index can be obtained by solving Eq. (9.4), which yields
D=1. The worst operation condition lies at c min (u max ). By substituting the
utility cost at this point and that at the nominal operation point into
Eq. (9.6), the flexibility factor is obtained as F=0.2775. That means,
although the network is feasible, the utility cost at the worst operating
point would be 2.925 $/h, which is 260% higher than that at the
nominal operation point.

9.1.2 Operability and controllability analysis
In this book, operability considerations mainly deal with manipulation
methodology to maintain the target temperatures under uncertainties or
operation changes between different steady states so that the utility con-
sumption is minimized; therefore, it is closely linked to structural network
flexibility. Controllability is to deal with the maintaining target output
parameters upon short-term deviations of inlet parameters and stable and safe
transitions from one operating point to another.

9.1.2.1 Operability analysis
The operability analysis (Aguilera and Marchetti, 1998) is usually based on
the existing structural information. It can be also incorporated into the syn-
thesis/retrofit process. Consider a HEN with N streams exchanging heat in
it, there are N U (N U N) process streams need to be heated or cooled to
their target output temperatures. The supply temperatures and the mass flow
rates of process streams are considered as the inlet variables, and the prop-
erties of process streams are all taken as constants.
Suppose that there are N M +N T (N M +N T <2N) regulatable parame-
ters, in which N M represents mass flow rates and N T represents temperatures,
respectively. The remainders are unregulatable parameters, N U ¼2N
(N M +N T ). When some of them deviate from their design values, the
N M +N T inlet parameters (or some of them) are needed to be regulated
to maintain the target output temperatures. There will be three cases affect-
ing the operability of the system (Li et al., 2002):
(1) N M +N T ¼N U
For this case, there will exist only one set of regulation solution to exactly
maintain all the target output temperatures. Although some of the inlet tem-
peratures could be regulatable parameters, in practical processes, the inlet
flow rates are much easier to be regulated than the inlet temperatures of