Page 253 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchanger networks 243

According to the mass balance constraints, we have

_ C c,E1 ¼ _ C C1 _ C c,E2 _ C c,E3 , _ C c,E5 ¼ _ C C1 _ C c,E4
TAC is taken as the objective function
6 6
X X
TAC xðÞ ¼ 1200A 0:6 + 1200A 0:6 + 140Q HU,i + 1200A 0:6
E, j HU,i CU,i +10Q CU,i
j¼1 i¼1
in which the areas and heat loads of heaters and coolers are calculated by
Eqs. (6.30)–(6.35) according to the calculated exit stream temperatures of
the network (excluding utilities) for given x by means of the matrix method.
The variable vector x is optimized by the use of Excel solver. The upper
and lower bounds of the variables are set to be [1, 100] for the heat transfer
areas and [1, 10] for the thermal capacity rates, and their lower bounds are
used as the initial values for the optimization. Besides the upper and lower
_ _
bounds of the variables, two mass balance constraints C c,E1 0 and C c,E2
0 are given in the solver. The penalty factor φ¼1000 is used for Eqs. (6.32),
(6.33). By repeated use of the evolutionary solving method EA of the solver,
the design is optimized and converges to TAC¼570,777$/yr, which is very
close to the global optimization result, TAC¼570,764$/yr (see Example
6.1). The calculation results are listed in Table 6.1.

6.2.2 Nonlinear programming formulation

In the nonlinear programming (NLP) formulation, we express the task of
sizing a heat exchanger network as follows:
For given supply temperatures, upper and lower bound target tempera-
tures and thermal capacity rates of N process streams
_
t , t 00 , t , C i ð i ¼ 1, 2, …, NÞ
0
00
i ub,i lb,i
thermal capacity rates of hot and cold streams and overall heat transfer coef-
ficients of N E heat exchangers
_ _
C h, j , C c, j , k j ð j ¼ 1, 2, …N E Þ
inlet and outlet temperatures of N HU hot utilities and N CU cold utilities

t 0 , t 00 ð k ¼ 1, 2, …N HU Þ, t 0 , t 00 ð l ¼ 1, 2, …N CU Þ
HU,k HU,k CU,l CU,l
investment costs of process heat exchangers, heaters, and coolers

C E AðÞ, C E,HU,k AðÞ k ¼ 1, 2, …N HU Þ, C E,CU,l AðÞ l ¼ 1, 2, …N CU Þ
ð
ð