# Exergy-Based Multi-Objective Optimization of an Organic Rankine Cycle with a Zeotropic Mixture

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{2}recompression cycle combined with regenerative organic Rankine cycle using the zeotropic mixture as working fluid was reported in [18]. In [19], a complex thermo-economic–environmental optimization and advanced exergy analysis were applied for a dual-loop organic Rankine cycle (DORC) using zeotropic mixtures. The payback period was selected as an economic evaluation criteria and annual CO

_{2}emission reduction as an environmental evaluation criterion. Higher performance was observed for the mixtures as working fluid of ORC. Both criteria, payback period and annual CO

_{2}emission reduction, could not be linked to the exergy variables (therefore, [19] was not included in Figure 1).

## 2. System Description

## 3. System Modeling and Analysis

#### 3.1. Thermodynamic Modeling

- -
- Pumps$${\dot{W}}_{p,ORC}={\dot{m}}_{wf}\left({h}_{2}-{h}_{1}\right)$$$${\dot{W}}_{p,HTF}={\dot{m}}_{HTF}\left({h}_{10}-{h}_{9}\right)$$
- -
- Turbine$${\dot{W}}_{t}={\dot{m}}_{wf}\left({h}_{4}-{h}_{5}\right)$$
- -
- Heat exchangers

_{k}[25,26] and the logarithmic mean temperature difference method LMTD

_{k}.

#### 3.2. Exergy Analysis

#### 3.3. Exergoeconomic Analysis

#### 3.4. Exergoenvironmental Analysis

## 4. System Optimization

- -
- Exergy efficiency$${\mathrm{E}}_{sys}=\frac{{\dot{W}}_{net}}{{\dot{E}}_{exh,in}}=\frac{{\dot{W}}_{t}-\left({\dot{W}}_{P,ORC}+{\dot{W}}_{P,HTF}\right)}{{\dot{E}}_{exh,in}}$$
- -
- Cost per exergy unit of the power generated$${c}_{p,sys}=\frac{{\dot{C}}_{net}}{{\dot{W}}_{net}}=\frac{{c}_{P,t}{\dot{W}}_{net}}{{\dot{W}}_{net}}$$
- -
- Environmental impact of the power generated$${b}_{p,sys}=\frac{{\dot{B}}_{net}}{{\dot{W}}_{net}}=\frac{{b}_{P,t}{\dot{W}}_{net}}{{\dot{W}}_{net}}$$

## 5. Results and Discussion

#### 5.1. Parametric Study

#### 5.2. Optimization Results

## 6. Conclusions

- -
- The application of zeotropic mixtures as a working fluid for ORC led to an increase in exergetic, exergoeconomic, and exergoenvironmental performances compared to using their pure constituents;
- -
- The heat exchangers were the most important ORC system components based on the exergy, exergoeconomic, and exergoenvironmental points;
- -
- The mass fraction of working fluids within a zeotropic mixture, turbine inlet pressure, and heat transfer fluid temperature had a significant effect on the exergetic, exergoeconomic, and exergoenvironmental performance of the ORC system;
- -
- Cyclohexane/toluene (mass fraction 90/10) and benzene/toluene (mass fraction 90/10) are recommended as the optimal mixtures for the selected operating conditions;
- -
- The mixture of cyclohexane and toluene will be a better choice only if energetic and economic criterions are considered. However, the mixture benzene/toluene is a beneficial choice to fulfill the environmental criteria.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | area (m^{2}) |

$\dot{B}$ | environmental impact rate (Pts/h) |

b | environmental impact per unit of exergy (Pts/GJ) |

$\dot{C}$ | cost rate ($/h) |

c | cost per exergy unit ($/GJ) |

c_{p} | heat capacity (kJ/kg K) |

$\dot{E}$ | exergy rate (kW) |

h | specific enthalpy (kJ/kg) |

M | weight of equipment (kg) |

$\dot{m}$ | mass flow rate (kg/s) |

p | pressure (bar) |

Q | heat flow rate (kW) |

T | temperature (°C, K) |

U | overall heat transfer coefficient (W/m^{2} K) |

$\dot{W}$ | power (kW) |

$\dot{Y}$ | component-related environmental impact (Pts/h) |

$\dot{Z}$ | capital investment cost rate ($/h) |

Abbreviations | |

HTF | heat transfer fluid |

IHE | intermediate heat exchanger |

LMTD | logarithmic mean temperature difference |

MOPSO | multi-objective particle swarm optimizer |

ORC | organic Rankine cycle |

Subscripts | |

0 | reference state |

1,2,…,i | system state points |

con | condenser |

D | destruction |

dusp | desuperheater |

eva | evaporator |

exh | exhaust gas |

F | fuel |

in | inlet |

k | kth component |

out | outlet |

P | product |

p | pump |

pre | preheater |

sys | system |

t | turbine |

w | water |

wf | working fluid |

Greek letters | |

ε | exergy efficiency (%) |

ƞ | isentropic efficiency(%) |

$\rho $ | density (kg/m^{3}) |

$\omega $ | life cycle inventory associated with the production of 1 kg of material (mpts/kg) |

$\delta $ | thickness (m) |

$n$ | lifetime of the system (year) |

$\tau $ | annual plant operation with full capacity (h) |

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**Figure 5.**Variations of (

**a**) exergy efficiency, (

**b**) cost, and (

**c**) environmental impact with toluene mass fraction.

**Figure 6.**Variations in the (

**a**) exergy efficiency, (

**b**) cost, and (

**c**) environmental impact with turbine inlet pressure.

**Figure 7.**Variations in the (

**a**) exergy efficiency, (

**b**) cost, and (

**c**) environmental impact with heat transfer fluid temperature.

Component | Fuel | Product | Cost Balances and Auxiliary Equations | Environmental Balances and Auxiliary Equations |
---|---|---|---|---|

Turbine | ${\dot{E}}_{4}-{\dot{E}}_{5}$ | ${\dot{W}}_{t}$ | ${\dot{C}}_{4}+{\dot{Z}}_{t}={\dot{C}}_{5}+{\dot{C}}_{Wt}$ ${c}_{{\dot{W}}_{p}}={c}_{{\dot{W}}_{tur}}$ $Z=6000{\dot{W}}_{tur}^{0.7}$ | ${\dot{B}}_{4}+{\dot{Y}}_{t}={\dot{B}}_{5}+{\dot{B}}_{Wt}$ ${b}_{{\dot{W}}_{p}}={b}_{{\dot{W}}_{tur}}$ $\dot{Y}=\left(M\times {\omega}_{steel}\right)/\left(\tau \times n\right)$ |

Preheater | ${\dot{E}}_{8}-{\dot{E}}_{9}$ | ${\dot{E}}_{3}-{\dot{E}}_{2}$ | ${\dot{C}}_{2}+{\dot{C}}_{8}+{\dot{Z}}_{pre}={\dot{C}}_{3}+{\dot{C}}_{9}$ ${c}_{8}={c}_{9}$ $Z=\mathrm{10,000}+324{A}^{0.91}$ | ${\dot{B}}_{2}+{\dot{B}}_{8}+{\dot{Y}}_{pre}={\dot{B}}_{3}+{\dot{B}}_{9}$ ${b}_{8}={b}_{9}$ $\dot{Y}=({\rho}_{steel}\times \delta \times {\omega}_{steel}\times A)/\left(\tau \times n\right)$ |

Evaporator | ${\dot{E}}_{7}-{\dot{E}}_{8}$ | ${\dot{E}}_{4}-{\dot{E}}_{3}$ | ${\dot{C}}_{3}+{\dot{C}}_{7}+{\dot{Z}}_{eva}={\dot{C}}_{4}+{\dot{C}}_{8}$ ${c}_{7}={c}_{8}$ $Z=\mathrm{10,000}+324{A}^{0.91}$ | ${\dot{B}}_{3}+{\dot{B}}_{7}+{\dot{Y}}_{eva}={\dot{B}}_{4}+{\dot{B}}_{8}$ ${b}_{7}={b}_{8}$ $\dot{Y}=({\rho}_{steel}\times \delta \times {\omega}_{steel}\times A)/\left(\tau \times n\right)$ |

Desuperheater | ${\dot{E}}_{5}-{\dot{E}}_{6}$ | ${\dot{E}}_{13}-{\dot{E}}_{12}$ | ${\dot{C}}_{5}+{\dot{C}}_{12}+{\dot{Z}}_{desup}={\dot{C}}_{6}+{\dot{C}}_{13}$ ${c}_{5}={c}_{6}$ $Z=\mathrm{10,000}+324{A}^{0.91}$ | ${\dot{B}}_{5}+{\dot{B}}_{12}+{\dot{Y}}_{desup}={\dot{B}}_{6}+{\dot{B}}_{13}$ ${b}_{5}={b}_{6}$ $\dot{Y}=({\rho}_{steel}\times \delta \times {\omega}_{steel}\times A)/\left(\tau \times n\right)$ |

Condenser | ${\dot{E}}_{6}-{\dot{E}}_{1}$ | ${\dot{E}}_{12}-{\dot{E}}_{11}$ | ${\dot{C}}_{6}+{\dot{C}}_{11}+{\dot{Z}}_{con}={\dot{C}}_{1}+{\dot{C}}_{12}$ ${c}_{6}={c}_{1}{c}_{11}=0$ $Z=\mathrm{10,000}+324{A}^{0.91}$ | ${\dot{B}}_{6}+{\dot{B}}_{11}+{\dot{Y}}_{con}={\dot{B}}_{1}+{\dot{B}}_{12}$ ${b}_{6}={c}_{1}{b}_{11}=0$ $\dot{Y}=({\rho}_{steel}\times \delta \times {\omega}_{steel}\times A)/\left(\tau \times n\right)$ |

IHE | ${\dot{E}}_{exh,in}-{\dot{E}}_{exh,out}$ | ${\dot{E}}_{7}-{\dot{E}}_{10}$ | ${\dot{C}}_{exh,in}+{\dot{C}}_{10}+{\dot{Z}}_{IHE}={\dot{C}}_{exh,out}+{\dot{C}}_{7}$ ${c}_{exh,in}={c}_{exh,out}$ $Z=\mathrm{10,000}+324{A}^{0.91}$ | ${\dot{B}}_{exh,in}+{\dot{B}}_{10}+{\dot{Y}}_{IHE}={\dot{B}}_{exh,out}+{\dot{B}}_{7}$ ${b}_{exh,in}={b}_{exh,out}$ $\dot{Y}=({\rho}_{steel}\times \delta \times {\omega}_{steel}\times A)/\left(\tau \times n\right)$ |

Pump_{ORC} | ${\dot{W}}_{P,ORC}$ | ${\dot{E}}_{2}-{\dot{E}}_{1}$ | ${\dot{C}}_{1}+{\dot{C}}_{{\dot{W}}_{p}}+{\dot{Z}}_{p}={\dot{C}}_{2}$ ${c}_{{\dot{W}}_{p}}={c}_{{\dot{W}}_{t}}$ $Z=422{\dot{W}}_{p}^{0.71}\left[1.41+1.41\left(\frac{1-0.8}{1-{\mathsf{\u019e}}_{p}}\right)\right]$ | ${\dot{B}}_{1}+{\dot{B}}_{{\dot{W}}_{p}}+{\dot{Y}}_{p}={\dot{B}}_{2}$ ${b}_{{\dot{W}}_{p}}={b}_{{\dot{W}}_{t}}$ $\dot{Y}=\left(M\times {\omega}_{steel}\right)/\left(\tau \times n\right)$ |

Pump_{HTF} | ${\dot{W}}_{P,HTF}$ | ${\dot{E}}_{10}-{\dot{E}}_{9}$ | ${\dot{C}}_{9}+{\dot{C}}_{{\dot{W}}_{p,HTF}}+{\dot{Z}}_{p,HTF}={\dot{C}}_{10}$ ${c}_{{\dot{W}}_{p,HTF}}={c}_{{\dot{W}}_{t}}$ $Z=422{\dot{W}}_{p}^{0.71}\left[1.41+1.41\left(\frac{1-0.8}{1-{\mathsf{\u019e}}_{p}}\right)\right]$ | ${\dot{B}}_{9}+{\dot{B}}_{{\dot{W}}_{p,HTF}}+{\dot{Y}}_{p,HTF}={\dot{B}}_{10}$ ${b}_{{\dot{W}}_{p,HTF}}={b}_{{\dot{W}}_{t}}$ $\dot{Y}=\left(M\times {\omega}_{steel}\right)/\left(\tau \times n\right)$ |

Performances | Results of This Study | Results from [30] | |
---|---|---|---|

${T}_{con}=25$ °C R245fa/R600a (0.413/0.569) | ${\dot{W}}_{net}$ (kW) ${\mathsf{\u019e}}_{cycle}$ (%) | 36.10 11.11 | 36.73 11.12 |

${T}_{con}=30$ °C R245fa/R600a (0.437/0.563) | ${\dot{W}}_{net}$ (kW) ${\mathsf{\u019e}}_{cycle}$ (%) | 32.21 10.50 | 32.52 10.51 |

${T}_{con}=35$ °C R245fa/R600a (0.443/0.557) | ${\dot{W}}_{net}$ (kW) ${\mathsf{\u019e}}_{cycle}$ (%) | 28.62 9.90 | 28.92 9.91 |

**Table 3.**A summary of the major parameters for the simulation of ORC [12].

Parameter | Value |
---|---|

${T}_{0}$ (°C) | 25 |

${p}_{0}$ (bar) | 1.01 |

${\dot{m}}_{exh}$ (kg/s) | 48.34 |

${\dot{m}}_{HTF}$ (kg/s) | 25.00 |

${T}_{exh,in}$ (°C) | 350 |

${T}_{7}$ (°C) | 310 |

$\Delta {T}_{eva}$ (°C) | 20 |

${p}_{4}$ (bar) | 12.00 |

${p}_{1}$ (bar) | 1.02 |

${\mathsf{\u019e}}_{t}$ | 0.85 |

${\mathsf{\u019e}}_{p}$ | 0.70 |

Cyclohexane/Toluene (90%/10%) | Benzene/Toluene (90%/10%) | |||||||
---|---|---|---|---|---|---|---|---|

T (°C) | p (bar) | $\dot{\mathit{m}}$ (kg/s) | h (kJ/kg) | T (°C) | p (bar) | $\dot{\mathit{m}}$ (kg/s) | h (kJ/kg) | |

1 | 81.7 | 1.02 | 19.70 | −0.936 | 81.2 | 1.02 | 18.39 | −0.814 |

2 | 82.3 | 13.9 | 19.70 | 1.2849 | 81.7 | 12.39 | 18.39 | 0.9407 |

3 | 204.2 | 13.91 | 19.70 | 299.43 | 193.1 | 12.39 | 18.39 | 235.93 |

4 | 204.9 | 13.91 | 19.70 | 541.09 | 194.2 | 12.39 | 18.39 | 529.47 |

5 | 140.1 | 1.02 | 19.70 | 454.56 | 119.4 | 1.02 | 18.39 | 442.89 |

6 | 82.8 | 1.02 | 19.70 | 356.65 | 82.7 | 1.01 | 18.39 | 392.43 |

7 | 299.5 | - | 25 | 757.74 | 298.4 | - | 25 | 754.95 |

8 | 224.2 | - | 25 | 567.28 | 213.1 | - | 25 | 539.04 |

9 | 131.3 | - | 25 | 332.29 | 144.7 | - | 25 | 366.19 |

10 | 132.3 | - | 25 | 334.82 | 145.7 | - | 25 | 368.72 |

11 | 25.0 | 1.02 | 50.33 | 104.92 | 25.0 | 1.02 | 52.17 | 104.92 |

12 | 58.5 | 1.02 | 50.33 | 244.89 | 58.15 | 1.02 | 52.17 | 243.51 |

13 | 67.6 | 1.02 | 50.33 | 283.24 | 62.4 | 1.02 | 52.17 | 261.29 |

Parameters | Cyclohexane/ Toluene (90/10) | Benzene/ Toluene (90/10) | Cyclohexane [12] | Benzene [12] | Toluene [12] |
---|---|---|---|---|---|

p_{4} (bar) | 13.91 | 12.39 | 15.12 | 14.43 | 12.96 |

T_{7} (°C) | 299.5 | 298.4 | 296.8 | 297.1 | 310.0 |

ΔT_{eva} (°C) | 20.0 | 20.0 | 20.0 | 20.0 | 21.1 |

ΔT_{con} (°C) | 24.3 | 24.6 | 37.0 | 34.6 | 26.1 |

${\dot{E}}_{exh,in}$ (MW) | 5.799 | 5.799 | 5.799 | 5.799 | 5.799 |

${\dot{E}}_{exh,out}$ (MW) | 1.272 | 1.567 | 1.383 | 1.736 | 2.431 |

${\epsilon}_{sys}$ (%) | 27.5 | 25.9 | 27.1 | 25.6 | 18.0 |

c_{p,sys} ($/GJ) | 17.25 | 17.58 | 18.14 | 18.49 | 20.21 |

b_{p,sys} (mpts/GJ) | 136 | 130 | 148 | 144 | 160 |

Turbine | Preheater– Evaporator Assembly | Desuperheater–Condenser Assembly | Pump_{ORC} | Pump_{HTO} | IHE | |
---|---|---|---|---|---|---|

Cyclohexane/Toluene | ||||||

${\dot{E}}_{D}$ (kW) | 219.4 | 623.5 | 982.2 | 7.3 | 46.6 | 463.2 |

${\dot{C}}_{D}$ ($/h) | 2.37 | 4.45 | 10.62 | 0.46 | 2.89 | 2.39 |

$\dot{Z}$ ($/h) | 85.03 | 4.49 | 354.70 | 1.41 | 1.84 | 23.36 |

$\dot{Z}+{\dot{C}}_{D}$ ($/h) | 87.40 | 8.94 | 365.32 | 1.87 | 4.73 | 25.75 |

${\dot{B}}_{D}$ (mPts/h) | 93 | 213 | 418 | 4 | 23 | 139 |

$\dot{Y}$ (mPts/h) | 17 | 67 | 13,643 | 4 | 6 | 1358 |

$\dot{Y}+{\dot{B}}_{D}$ (mPts/h) | 110 | 280 | 14,061 | 8 | 28 | 1497 |

Benzene/Toluene | ||||||

${\dot{E}}_{D}$ (kW) | 216.4 | 684.6 | 876.0 | 5.4 | 45.1 | 435.6 |

${\dot{C}}_{D}$ ($/h) | 2.36 | 4.89 | 9.53 | 0.34 | 2.85 | 2.20 |

$\dot{Z}$ ($/h) | 81.09 | 3.95 | 224.41 | 1.14 | 1.84 | 21.40 |

$\dot{Z}+{\dot{C}}_{D}$ ($/h) | 83.45 | 8.84 | 233.94 | 1.48 | 4.69 | 23.60 |

${\dot{B}}_{D}$ (mPts/h) | 87 | 215 | 352 | 2 | 21 | 120 |

$\dot{Y}$ (mPts/h) | 15 | 53 | 8214 | 3 | 6 | 1164 |

$\dot{Y}+{\dot{B}}_{D}$ (mPts/h) | 102 | 268 | 8566 | 5 | 27 | 1284 |

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**MDPI and ACS Style**

Fergani, Z.; Morosuk, T.; Touil, D.
Exergy-Based Multi-Objective Optimization of an Organic Rankine Cycle with a Zeotropic Mixture. *Entropy* **2021**, *23*, 954.
https://doi.org/10.3390/e23080954

**AMA Style**

Fergani Z, Morosuk T, Touil D.
Exergy-Based Multi-Objective Optimization of an Organic Rankine Cycle with a Zeotropic Mixture. *Entropy*. 2021; 23(8):954.
https://doi.org/10.3390/e23080954

**Chicago/Turabian Style**

Fergani, Zineb, Tatiana Morosuk, and Djamel Touil.
2021. "Exergy-Based Multi-Objective Optimization of an Organic Rankine Cycle with a Zeotropic Mixture" *Entropy* 23, no. 8: 954.
https://doi.org/10.3390/e23080954