Sets

ðTs i,p−T<sup>t</sup>

8 >><

8

>>:

8 >><

>>:

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

ðTt j,p−T<sup>s</sup>

<sup>i</sup>,pÞFi,<sup>p</sup> <sup>¼</sup> ∑

106 Heat Exchangers– Design, Experiment and Simulation

<sup>j</sup>,pÞFj,<sup>p</sup> <sup>¼</sup> ∑

<sup>ð</sup>ti, <sup>k</sup>,p−ti, <sup>k</sup>þ1,pÞFi,<sup>p</sup> <sup>¼</sup> ∑

<sup>ð</sup>tj, <sup>k</sup>,p−tj, <sup>k</sup>þ1,pÞFj,<sup>p</sup> <sup>¼</sup> ∑

ti, <sup>k</sup>,p≥ti, <sup>k</sup>þ1,pi∈Hp∈P tj, <sup>k</sup>,p≥tj, <sup>k</sup>þ1,pj∈Cp∈P ( )

qi,j, <sup>k</sup>,p−Ωpzi,j, <sup>k</sup> ≤ 0 n o

LMTDi,j, <sup>k</sup>,<sup>p</sup> <sup>¼</sup> <sup>2</sup>

ti, <sup>k</sup>,p, tj, <sup>k</sup>,p, qi,j, <sup>k</sup>,p, dti,j, <sup>k</sup>,p≥0

zi,j, <sup>k</sup>∈f0, 1g

Nomenclature

CU Cold utility

HU Hot utility

k Stage boundaries

Indices

ti, <sup>k</sup>¼2,<sup>p</sup> <sup>¼</sup> <sup>T</sup><sup>s</sup>

tj,K−1,<sup>p</sup> <sup>¼</sup> <sup>T</sup><sup>s</sup>

k∈K ∑ j∈C

k∈K ∑ i∈H

<sup>i</sup>,pi∈Hp∈P

<sup>j</sup>,pj∈Cp∈P

dti,j, <sup>k</sup>,<sup>p</sup> ≥ ε k ∈ Ki ∈ Hj ∈ Cp ∈ P n o

> 3 �

HENS Heat-exchanger network synthesis

MILP Mixed integer linear programme

MINLP Mixed integer non-linear programme

NLP Non-linear programme

SWS Stage-wise superstructure

i Hot-process streams and hot utilities j Cold-process streams and cold utilities

p Index representing period of operation (p = 1,…NOP)

j∈C

i∈H

( ) assignment of superstructure

qi,j, <sup>k</sup>,pi∈Hp∈P

9 >>=

>>;

inlet temperatures

9 >>=

>>;

( ) exchanger approach

� � � � logarithmic mean

bound for approach temperature

ðdti,j, <sup>k</sup>,pÞþðdti,j, <sup>k</sup>þ1,pÞ 2

overal energy balances

stage energy balances

temperatures

temperature difference

9

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>=

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>;

(A1)

qi,j, <sup>k</sup>,pj∈Cp∈P

qi,j, <sup>k</sup>,pk∈Ki∈Hp∈P

qi,j, <sup>k</sup>,pk∈Kj∈Cp∈P

temperature feasibility

logical constraint for heat load

�1=2 þ 1 3

dti,j, <sup>k</sup>,<sup>p</sup> ≤ ti, <sup>k</sup>,p−tci,j, <sup>k</sup>,<sup>p</sup> þ φð1−zi,j, <sup>k</sup>Þk ∈ Ki∈ Hj ∈ Cp ∈ P dti,j, <sup>k</sup>þ1,<sup>p</sup> ≤ thi,j, <sup>k</sup>þ1,p−tj, <sup>k</sup>þ1,<sup>p</sup> þ φ ð1−zi,j, <sup>k</sup>Þ k ∈ Ki ∈ Hj ∈ Cp ∈ P

ðdti,j, <sup>k</sup>,pÞðdti,j, <sup>k</sup>þ1,pÞ

