Optimization of Heat Recovery Networks for Energy Savings in Industrial Processes
Abstract
:1. Introduction
2. Problem Statement
3. Model Formulation
3.1. Overall Energy Balance for Process Streams
3.2. Energy Balance for Process Streams in Each Stage
3.3. Temperature Assignment and Feasibility Constraints
3.4. Utility Requirements and Latent Heat Balance
3.5. Feasibility of Latent Heat Exchange
3.6. Logical Constraints and Temperature Differences
3.7. Objective Function
4. Industrial Case Study
4.1. Preliminary Analysis
- No stream splitting is allowed;
- Any pair of hot and cold process streams has at most one match throughout the superstructure;
- The condenser, evaporator and reboiler streams each have at most one match with other process streams.
4.2. Analysis without Condensers, Evaporator and Reboilers
- No stream splitting is allowed (Equations (31) and (32));
- Any pair of hot and cold process streams has at most one match (Equation (33)).
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Nomenclature
Appendix A.1. Indices and Sets
process hot streams | |
process hot streams involving only sensible heat | |
process hot streams involving only latent heat | |
process hot streams involving both sensible and latent heat | |
process cold streams | |
process cold streams involving only sensible heat | |
process cold streams involving only latent heat | |
process cold streams involving both sensible and latent heat | |
temperature locations | |
stages |
Appendix A.2. Parameters
heat capacity of hot process stream i (J/g/°C) | |
heat capacity of cold process stream j (J/g/°C) | |
flowrate of hot process stream i (t/h) | |
flowrate of cold process stream j (t/h) | |
upper limit to the heat transfer from hot process stream i (kW) | |
upper limit to the heat transfer from hot process stream i to cold process stream | |
upper limit to the heat transfer to cold process stream j (kW) | |
outlet temperature of the cold utility (°C) | |
outlet temperature of the hot utility (°C) | |
inlet temperature of hot process stream i (°C) | |
outlet temperature of hot process stream i (°C) | |
inlet temperature of cold process stream j (°C) | |
outlet temperature of cold process stream j (°C) | |
phase change fraction of hot process stream i | |
phase change fraction of cold process stream j | |
minimum temperature difference for hot utility-process matches (°C) | |
minimum temperature difference for process-cold utility matches (°C) | |
minimum temperature difference for process-process matches (°C) | |
a sufficiently small value (°C) | |
latent heat of hot process stream i (J/g) | |
latent heat of cold process stream j (J/g) | |
a sufficiently large value (°C) |
Appendix A.3. Variables
cold utility requirement for hot process stream i (kW) | |
condensation heat load of hot process stream i in the cooler (kW) | |
heat transfer from hot process stream i to cold process stream j in stage k (kW) | |
condensation heat load of hot process stream i in stage k (kW) | |
evaporation heat load of cold process stream j in the heater (kW) | |
hot utility requirement for cold process stream j (kW) | |
evaporation heat load of cold process stream j in stage k (kW) | |
temperature of cold process stream j at temperature location k (°C) | |
binary indicating if the inlet temperature of hot process stream i at stage k is greater than or equal to the condensation temperature | |
binary indicating if the outlet temperature of cold process stream j at stage k is greater than or equal to the evaporation temperature | |
binary indicating if hot process stream i uses the cold utility | |
binary indicating if hot process stream i transfers heat to cold process stream j in stage k | |
binary indicating if cold process stream j uses the hot utility |
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Stream | Description | Flowrate (t/h) | Inlet Temperature (°C) | Outlet Temperature (°C) | Heat Capacity (J/g/°C) | Latent Heat (J/g) | Phase Change Fraction |
---|---|---|---|---|---|---|---|
H1 | Outlet recycle gas | 981 | 220 | 60 | 2.11 | - | 0 |
H2 | Recycled water | 1150 | 107.4 | 31 | 4.118 | - | 0 |
H3 | Recycled water | 37.1 | 116.1 | 35 | 4.118 | - | 0 |
H4 | Process condensate | 347 | 106.3 | 52 | 4.226 | - | 0 |
H5 | Process vapor | 17.4 | 124 | 124 | - | 2194.508 (at 124 °C) | 1 |
H6 | Process vapor | 7.8 | 171 | 139 | 1.925 | 2092 (at 171 °C) | 1 |
H7 | Absorbent | 354.1 | 45 | 33.1 | 4.163 | - | 0 |
H8 | MEG product | 48.5 | 138 | 60 | 2.761 | - | 0 |
H9 | DEG product | 5.1 | 123 | 38 | 2.552 | - | 0 |
H10 | Water vapor | 13.5 | 61 | 40 | 4.184 | 2397.432 (at 61 °C) | 1 |
H11 | Glycol vapor | 1.2 | 130 | 43 | 2.741 | 1125.496 (at 130 °C) | 1 |
H12 | Glycol vapor | 5.1 | 92 | 60 | 2.678 | 962.32 (at 92 °C) | 1 |
H13 | Glycol vapor | 10.9 | 147 | 120.5 | 2.72 | 627.6 (at 147 °C) | 1 |
H14 | Glycol vapor | 2.2 | 152 | 139 | 2.761 | 589.944 (at 152 °C) | 1 |
Stream | Description | Flowrate (t/h) | Inlet Temperature (°C) | Outlet Temperature (°C) | Heat Capacity (J/g/°C) | Latent Heat (J/g) | Phase Change Fraction |
---|---|---|---|---|---|---|---|
C1 | Inlet recycle gas | 981 | 45.5 | 192.5 | 1.979 | - | 0 |
C2 | Recycled water | 1189.2 | 45.8 | 102.4 | 4.118 | - | 0 |
C3 | EO solution | 400 | 44.8 | 146.3 | 4.079 | - | 0 |
C4 | Recycled water | 35.44 | 32 | 100 | 4.226 | - | 0 |
C5 | Process condensate | 30 | 30.7 | 90.1 | 4.226 | - | 0 |
C6 | Process condensate | 12 | 40 | 60 | 4.226 | - | 0 |
C7 | EG solution | 40.03 | 186.4 | 186.4 | - | 1966.48 (at 186.4 °C) | 1 |
C8 | Glycol mixture | 25.03 | 134 | 134 | - | 874.456 (at 134 °C) | 1 |
C9 | Glycol mixture | 341.2 | 163.3 | 170 | 2.954 | 782.408 (at 170 °C) | 0.2 |
C10 | Glycol mixture | 151.02 | 171.5 | 179.2 | 2.889 | - | 0 |
C11 | Glycol mixture | 283.221 | 167.5 | 172.1 | 2.933 | - | 0 |
C12 | Glycol mixture | 53.64 | 161.8 | 163.9 | 2.964 | - | 0 |
Stream | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | Cooling Water |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
H1 | 79,275 | 12,742 | |||||||||||
H2 | 64,257 | 36,253 | |||||||||||
H3 | 2829 | 615 | |||||||||||
H4 | 22,118 | ||||||||||||
H5 | 10,607 | ||||||||||||
H6 | 4534 | ||||||||||||
H7 | 4873 | ||||||||||||
H8 | 2092 | 810 | |||||||||||
H9 | 282 | 26 | |||||||||||
H10 | 9292 | ||||||||||||
H11 | 448 | ||||||||||||
H12 | 1493 | ||||||||||||
H13 | 2127 | ||||||||||||
H14 | 389 | ||||||||||||
180 °C steam | 8748 | 6080 | 93 | ||||||||||
213 °C steam | 21,866 | 16,707 | 933 | 1061 |
Stream | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | Cold Utility |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
H1 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 5 |
H2 | 10 | 3.39 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 2 |
H3 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 3 |
H4 | 10 | 10 | 7.2 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 5 |
H5 | 10 | 10 | 5 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 5 |
H6 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 5 |
H7 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 4 |
H8 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 15 |
H9 | 10 | 10 | 10 | 10 | 10 | 5 | 10 | 10 | 10 | 10 | 10 | 10 | 6 |
H10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
H11 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
H12 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 27 |
H13 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 89 |
H14 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 106 |
Hot utility | 10 | 10 | 33.7 | 10 | 10 | 10 | 21 | 42 | 33 | 28 | 17 | 15 | - |
Stream | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | Cooling Water |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
H1 | 46,223 | 12,374 | 482 | 10,151 | 6080 | 16,707 | |||||||
H2 | 75,135 | 25,374 | |||||||||||
H3 | 2346 | 98 | 999 | ||||||||||
H4 | 22,118 | ||||||||||||
H5 | 10,607 | ||||||||||||
H6 | 4508 | 27 | |||||||||||
H7 | 4873 | ||||||||||||
H8 | 908 | 1994 | |||||||||||
H9 | 282 | 26 | |||||||||||
H10 | 9292 | ||||||||||||
H11 | 344 | 103 | |||||||||||
H12 | 1493 | ||||||||||||
H13 | 1956 | 171 | |||||||||||
H14 | 379 | 10 | |||||||||||
180 °C steam | 26,209 | 93 | |||||||||||
213 °C steam | 11,715 | 933 | 1061 |
Stream | Description | Flowrate (t/h) | Inlet Temperature (°C) | Outlet Temperature (°C) | Heat Capacity (J/g/°C) | Latent Heat (J/g) | Phase Change Fraction |
---|---|---|---|---|---|---|---|
H1 | Outlet recycle gas | 981 | 222 | 60 | fH1(T) | - | 0 |
H2 | Recycled water | 1150 | 107.4 | 31 | 4.393 | - | 0 |
H3 | Recycled water | 37.1 | 116.14 | 35 | 4.393 | - | 0 |
H4 | Process condensate | 373.7 | 106.3 | 52 | 4.226 | - | 0 |
H5 | Process vapor | 18.74 | 124 | 124 | - | 2194.508 (at 124 °C) | 1 |
H6 | Process vapor | 8.4 | 171 | 139 | 1.925 | 2092 (at 171 °C) | 1 |
H7 | Absorbent | 354.1 | 45 | 33.1 | 4.163 | - | 0 |
H8 | MEG product | 48.5 | 138.2 | 60 | 2.761 | - | 0 |
H9 | DEG product | 5.1 | 123 | 38 | 2.552 | - | 0 |
C1 | Inlet recycle gas | 981 | 45.5 | 192.7 | fC1(T) | - | 0 |
C2 | Recycled water | 1189.2 | 45.8 | 102.38 | 4.155 | - | 0 |
C3 | EO solution | 400 | 44.8 | 146.3 | 4.393 | - | 0 |
C4 | Recycled water | 37.62 | 32 | 100 | 4.226 | - | 0 |
C5 | Process condensate | 30 | 30.7 | 90.1 | 4.226 | - | 0 |
C6 | Process condensate | 12 | 40 | 60 | 4.226 | - | 0 |
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Lee, J.-Y.; Chen, P.-Y. Optimization of Heat Recovery Networks for Energy Savings in Industrial Processes. Processes 2023, 11, 321. https://doi.org/10.3390/pr11020321
Lee J-Y, Chen P-Y. Optimization of Heat Recovery Networks for Energy Savings in Industrial Processes. Processes. 2023; 11(2):321. https://doi.org/10.3390/pr11020321
Chicago/Turabian StyleLee, Jui-Yuan, and Po-Yu Chen. 2023. "Optimization of Heat Recovery Networks for Energy Savings in Industrial Processes" Processes 11, no. 2: 321. https://doi.org/10.3390/pr11020321