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A New Nodes-Based Model for Optimization of Heat Exchanger Network Synthesis

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Abstract

Searching the global optimal value in heat exchanger network synthesis (HENS) becomes more difficult along with the increasing scale of cases. In structural optimization model, such as stage-wise superstructure, solution domain can be enlarged by adding the stages of network, which would involve multiple integer and continuous variables in optimization and result in a decreasing computational efficiency. Thus, a new nodes-based model with stream splits is proposed, which can promote the quality of result and decrease time consumption at the same time. The characteristic of this model is that it changes the matching mode of heat exchangers by setting the number of nodes on streams to quantify the positions of heat exchangers. The proposed nodes-based model has more flexibility in generating and eliminating the heat exchangers and strong ductility in exploring the solution domain. The random walk with compulsive evolution is modified for enhancing its searching ability and applying modified random walk algorithm with compulsive evolution (RWCE) into the new proposed model. The obtained results of Case 1, Case 2 and Case 3 are superior to those reported in the literature, which decreases 106 USD·a−1, 1253 USD·a−1, 23 444 USD·a−1, respectively, verifying the robust effectiveness of this new model in solving HENS problem.

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Abbreviations

A :

area cost of heat exchangers/m2

AMTD:

Arithmetic mean temperature difference

C A :

area cost coefficient/USD·a−1

C CU :

utility cost coefficient of cold utility/USD·a−1

C HU :

utility cost coefficient of hot utility/USD·a−1

F fix :

fixed capital cost/USD·a−1

F :

cost of a structure of HENS/USD·a−1

h :

coefficient of convective heat transfer kW·m−2·°C−1

it :

iteration step

LMTD:

logarithmic mean temperature difference

ΔL :

length of walk in evolution

MCp :

heat capacity of flow rate/kW·°C−1

Mn H :

serial number of hot node

Mn C :

serial number of cold node

N E :

number of optimization individuals

Nd H :

number of splitting group on each hot stream

Nd C :

number of splitting group on each cold stream

\(N{e_{{{\rm{N}}_{\rm{H}}}}}\) :

number of nodes on each hot stream.

\(N{e_{{{\rm{N}}_{\rm{C}}}}}\) :

number of nodes on each cold stream

Nf H :

number of nodes on each hot branch

Nf C :

number of nodes on each cold branch

N H :

number of hot stream

N C :

number of cold stream

NL :

mapping relation of two nodes

Nt H :

total number of nodes on hot streams

Nt C :

total number of nodes on cold streams

\(N{L_{M{n_{\rm{H}}}}}\) :

serial number of cold node which is pointed by MnH

\(N{L_{M{n_{\rm{C}}}}}\) :

serial number of hot node which is pointed by MnC

n :

number of heat exchangers in a structure

\({Q_{M{n_{\rm{H}}}}}\) :

heat load of hot node which serial number is MnH/kW

\({Q_{N{L_{M{n_{\rm{C}}}}}}}\) :

heat load of cold node which serial number is \(N{L_{M{n_{\rm{C}}}}}\) /kW

Q CU :

heat load of cold utility/kW

Q HU :

heat load of hot utility/kW

\(\overrightarrow {{Q_n}} \) :

each individual having n number heat exchangers

\(SP{H_{M{n_{\rm{H}}}}}\) :

split ratio of hot node which serial number is MnH

\(SP{C_{M{n_{\rm{C}}}}}\) :

split ratio of cold node which serial number is MnC

T :

temperature/°C

TAC:

total annual cost/USD·a−1

ΔT min :

the minimum temperature approach/°C

U :

coefficient of heat transfer/kW·m−2·°C−1

Z :

binary variable

α :

random value about deciding the direction of evolution

β :

area exponent random value about generating direction

γ :

of evolution

η :

random value of generating split ratio the difference of inlet temperature on hot

θ 1 :

stream and outlet temperature on cold stream in a single heat exchanger the difference of outlet temperature on

θ 2 :

hot stream and inlet temperature on cold stream in a single heat exchanger

κ :

random value about generating threshold value of split ratio

λ :

random value about deciding whether the heat load participates in evolution random value of generating serial number of nodes

δ :

probability of accepting imperfect structure

ω :

random value about generating threshold value of heat load

C:

cold stream

H:

hot stream

i :

the sequence number of hot stream

in:

inlet

j :

the sequence number of cold stream

out:

outlet

target:

target temperature

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Acknowledgements

We would like to thank the financial support in part from the National Natural Science Foundation of China (51176125), National Natural Science Foundation of China (21978171), Capacity Building Plan for some Non-military Universities and Colleges of Shanghai Scientific Committee (16060502600).

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Authors and Affiliations

  1. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Yue Xu, Ambonisye Kayange Heri, Yuan Xiao & Guomin Cui

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  1. Yue Xu
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  2. Ambonisye Kayange Heri
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  3. Yuan Xiao
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  4. Guomin Cui
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Correspondence to Guomin Cui.

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Xu, Y., Heri, A.K., Xiao, Y. et al. A New Nodes-Based Model for Optimization of Heat Exchanger Network Synthesis. J. Therm. Sci. 30, 451–464 (2021). https://doi.org/10.1007/s11630-020-1313-3

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