Multi-Objective Optimization of the Basic and Regenerative ORC Integrated with Working Fluid Selection
Abstract
:1. Introduction
2. System Description
- The proposed system operates at a steady state;
- The maximum evaporation pressure is restricted below 90% of the working fluid critical pressure to ensure the safe operation of the ORC system;
- The ambient pressure and temperature are 101.3 kPa and 293.15 K, which is the reference state for the exergy analysis;
- The isentropic efficiencies of the expander and pump are assumed as 0.85;
- The heat exchangers are treated as externally adiabatic devices.
3. Mathematical Model
3.1. Thermodynamic Analysis
3.2. Thermo-Economic Analysis
3.3. Heat Exchanger Model
3.4. Working Fluid Selection and Multi-Objective Optimization with NSGA-II
3.4.1. Multi-Objective Optimization with NSGA-II
3.4.2. Decision-Making with TOPSIS
3.4.3. Working Fluid Selection Integrated with NSGA-II
4. Results and Discussion
4.1. Pareto Frontier Solutions of the BORC System
4.1.1. Pareto Frontier Solutions and Effect of Objectives on the Working Fluid Selection
4.1.2. Parametric Analysis of the Decision Variables
4.2. Pareto Frontier Solutions of the RORC System
4.2.1. Pareto Frontier Solutions
4.2.2. Parametric Analysis of the Decision Variables
5. Conclusions
- (1)
- The selection of working fluid and multi-objective optimization of the cycle parameters could be realized simultaneously by parameterizing pure working fluids into arrays of numbers. Several types of the working fluid, pure or mixed, are presented on the Pareto frontier;
- (2)
- The turbine inlet temperature is the most effective factor for both the BORC and RORC systems while the other four decision variable has quite limited influence on the objectives. The nonlinear relation between the exergy efficiency and the turbine inlet temperature is observed;
- (3)
- The decision variables mainly impose a reverse effect on the exergy efficiency and thermal efficiency while the exergy efficiency and LEC exhibit quite a weak conflict with each other. This makes the binary objective optimization tend to be a single objective optimization when the objectives are set as exergy efficiency and LEC;
- (4)
- The RORC with an IHE can provide higher thermal efficiency than ORC at the same exergy efficiency while the LEC of the RORC system also becomes higher because the bare module cost of buying one more heat exchange for the RORC is higher than the cost reduction contributed to the reduced heat transfer area;
- (5)
- The Pareto frontier solution is distributed in similar trends at different heat source temperatures. Under the heat source temperature of 423.15 K, the final obtained exergy efficiency and thermal efficiencies are 45.6% and 16.6% for BORC, and 38.6% and 20.7% for RORC, respectively.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Nomenclature
A | ) |
boiling number | |
cost ($) | |
capital recovery cost | |
diameter of the heat exchanger tube (m) | |
exergy (kw) | |
bare module factor | |
material factor | |
pressure factor | |
h | specific enthalpy (kJ/kg) |
K) | |
levelized energy cost ($/kWh) | |
mass flow rate (kg/s) | |
Nusselt number | |
pressure (kPa) | |
Prandtl number | |
energy (kW) | |
Reynolds number | |
specific entropy (kJ/kg K) | |
temperature (K) | |
operation hour (h) | |
W | power (kW) |
Greek Symbols | |
K) | |
Heat conductivity (W/m K) | |
efficiency | |
condensation temperature glide (K) | |
boiling process temperature glide (K) | |
) | |
Subscript | |
0 | environment, in equilibrium with the environment |
con | condensation, condenser |
eva | evaporator |
h | heatsource |
in | inlet |
net | Net |
o | outlet |
p | pinch point temperature difference |
pump | pump |
reg | regenerator |
s | isentropic |
sup | degree of superheat |
tur | turbine |
v | vapor |
wf | working fluid |
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Coefficient | Heat Exchanger | Pump | Expander |
---|---|---|---|
4.325 | 3.389 | 3.514 | |
−0.303 | 0.054 | 0.598 | |
0.163 | 0.154 | 0 | |
1.63 | 1.89 | ||
1.66 | 1.35 | ||
0.039 | −0.394 | ||
−0.113 | 0.396 | ||
0.082 | −0.002 | ||
1.35 | 1.55 | ||
1.5 |
Fluid 1 (Number) | Critical Temperature (K) | Critical Pressure (MPa) | Fluid 2 (Number) | Critical Temperature (K) | Critical Pressure (MPa) |
---|---|---|---|---|---|
hexane (1) | 507 | 3.03 | propyne (1) | 402 | 5.63 |
acetone (2) | 508 | 4.70 | isobutane (2) | 407 | 3.63 |
cyclopentane (3) | 511 | 4.57 | isobutene (3) | 418 | 4.01 |
heptane (4) | 540 | 2.74 | butene (4) | 419 | 4.00 |
isooctane (5) | 544 | 2.57 | butane (5) | 425 | 3.79 |
cyclohexane (6) | 553 | 4.08 | neopentane (6) | 433 | 3.19 |
benzene (7) | 562 | 4.91 | isopentane (7) | 460 | 3.37 |
octane (8) | 569 | 2.50 | Pentane (8) | 469 | 3.37 |
nonane (9) | 594 | 2.28 | isohexane (9) | 497 | 3.04 |
toluene (10) | 591 | 4.13 |
Item | Symbol | Unit | Range |
---|---|---|---|
Inlet temperature of the turbine | K | 373–453 | |
Superheat degree | K | 3–10 | |
PPTD in evaporator | K | 3–10 | |
PPTD in condenser | K | 3–10 | |
Fluid-1 | F1 | 1–10 | |
Fluid-2 | F2 | 1–9 | |
Mass fraction | 0–1 |
Selected Working Fluid | Concentration | Critical Temperature (K) | Condensation Temperature Glide (K) | |
---|---|---|---|---|
Figure 3a: | cyclopentane/isopentane | 0.07/0.93→0.13/0.87 | 464→467 | 0.8→1.45 |
cyclopentane/pentane | 0.08/0.92→0.21/0.79 | 473→479 | 0.25→0.69 | |
cyclopentane/isohexane | 0.8/0.2→1/0 | 509→511 | 0.3→0 | |
benzene | 1/0 | 562 | 0 | |
Figure 3b: | cyclopentane/isopentane | 0.03/0.97 | 462 | 0.35 |
Point | Exergy Efficiency | Thermal Efficiency | LEC ($/kWh) | (K) | (K) | (K) | (K) | Working Fluid | |
---|---|---|---|---|---|---|---|---|---|
Figure 3a: | A | 0.496 | 0.152 | 411 | 4.86 | 3.12 | 5.56 | cyclopentane/isopentane (0.07/0.93) | |
B | 0.456 | 0.166 | 424 | 4.97 | 3.12 | 6.30 | cyclopentane/pentane (0.17/0.83) | ||
C | 0.337 | 0.197 | 435 | 5.23 | 3.76 | 7.52 | benzene | ||
Figure 3b: | A | 0.504 | 0.0437 | 414 | 3.08 | 3.09 | 9.75 | cyclopentane/isopentane (0.03/0.97) | |
B | 0.492 | 0.0432 | 413 | 3.08 | 4.56 | 9.91 | cyclopentane/isopentane (0.03/0.97) | ||
C | 0.476 | 0.0429 | 413 | 3.11 | 6.41 | 9.88 | cyclopentane/isopentane (0.03/0.97) |
Point | Exergy Efficiency | Thermal Efficiency | LEC ($/kWh) | (K) | (K) | (K) | (K) | Working Fluid | |
---|---|---|---|---|---|---|---|---|---|
Figure 4a: | A | 0.406 | 0.122 | 381 | 4.21 | 3.17 | 6.58 | butane | |
B | 0.368 | 0.131 | 381 | 4.60 | 3.04 | 7.30 | cyclopentane/isohexane (0.83/0.17) | ||
C | 0.274 | 0.158 | 397 | 3.95 | 3.13 | 7.93 | benzene | ||
Figure 4b: | A | 0.415 | 0.0642 | 372 | 3.33 | 3.29 | 9.68 | isobutene | |
B | 0.399 | 0.0632 | 372 | 3.33 | 3.43 | 9.83 | isopentane | ||
C | 0.378 | 0.0625 | 371 | 3.35 | 5.34 | 9.88 | pentane |
Point | Exergy Efficiency | Thermal Efficiency | LEC ($/kWh) | (K) | (K) | (K) | (K) | Working Fluid | |
---|---|---|---|---|---|---|---|---|---|
Figure 5a: | A | 0.607 | 0.177 | 435 | 3.14 | 3.02 | 5.81 | cyclopentane/pentane (0.33/0.67) | |
B | 0.529 | 0.207 | 458 | 3.44 | 3.04 | 5.72 | cyclopentane/pentane (0.98/0.19) | ||
C | 0.414 | 0.225 | 470 | 3.68 | 3.77 | 5.71 | benzene | ||
Figure 5b: | A | 0.588 | 0.0336 | 442 | 3.42 | 3.16 | 8.11 | cyclopentane/pentane (0.52/0.48) | |
B | 0.577 | 0.0328 | 442 | 3.37 | 4.63 | 8.47 | cyclopentane/pentane (0.52/0.48) | ||
C | 0.536 | 0.0320 | 443 | 3.44 | 7.28 | 8.92 | cyclopentane/pentane (0.66/0.34) |
Point | Exergy Efficiency | Thermal Efficiency | LEC ($/kWh) | (K) | (K) | (K) | (K) | Working Fluid | |
---|---|---|---|---|---|---|---|---|---|
Figure 8a: | A | 0.485 | 0.180 | 415 | 4.97 | 3.60 | 7.37 | cyclopentane/isopentane (0.1/0.9) | |
B | 0.386 | 0.207 | 437 | 6.76 | 3.22 | 6.87 | hexane/isohexane (0.21/0.71) | ||
C | 0.286 | 0.223 | 447 | 7.62 | 3.62 | 5.30 | cyclohexane | ||
Figure 8b: | A | 0.499 | 0.0477 | 406 | 3.90 | 4.07 | 5.46 | cyclopentane/isopentane (0.03/0.97) | |
B | 0.484 | 0.0469 | 404 | 3.82 | 4.69 | 5.63 | cyclopentane/pentane (0.04/0.96) | ||
C | 0.462 | 0.0465 | 403 | 3.95 | 7.15 | 5.73 | cyclopentane/pentane (0.12/0.88) |
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Zhou, Y.; Ruan, J.; Hong, G.; Miao, Z. Multi-Objective Optimization of the Basic and Regenerative ORC Integrated with Working Fluid Selection. Entropy 2022, 24, 902. https://doi.org/10.3390/e24070902
Zhou Y, Ruan J, Hong G, Miao Z. Multi-Objective Optimization of the Basic and Regenerative ORC Integrated with Working Fluid Selection. Entropy. 2022; 24(7):902. https://doi.org/10.3390/e24070902
Chicago/Turabian StyleZhou, Yuhao, Jiongming Ruan, Guotong Hong, and Zheng Miao. 2022. "Multi-Objective Optimization of the Basic and Regenerative ORC Integrated with Working Fluid Selection" Entropy 24, no. 7: 902. https://doi.org/10.3390/e24070902