# Exergy and Exergoeconomic Analysis of a Cogeneration Hybrid Solar Organic Rankine Cycle with Ejector

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions coming from electricity generation. The maintenance cost required of the ejector refrigeration system (ERS) is meager [1]. Solar energy is the most abundant, vast, and inexhaustible source of energy for a clean environment. Researchers have started investigating the replacement of high-priced fossil fuels with alternative renewable energy sources such as wind, solar, and geothermal. As the supply of solar energy is highly compatible with the demand, the use and implementation of solar energy in air conditioning and refrigeration applications have gained more attention over the last decades.

## 2. System Overview and Description

## 3. Methods

#### 3.1. Energy Analysis

- Flow-through, the ejector, is 1-D, adiabatic, and steady;
- Isentropic flow through diffuser and nozzle;
- CPM ejectors are used because they generate higher condenser pressures than ejectors of CAM with similar COP and entrainment ratios;
- Generator pressure and temperature are 33 bar and 90 °C, respectively;
- Evaporator pressure and temperature are 4.5 bar and 12.45 °C, respectively;
- The throat diameter of the ejector is 0.000605 m.

#### 3.2. Exergy Analysis

_{0}is 298.15 K and pressure p

_{0}is 1.013 bar for the reference environment in this analysis.

_{k}is calculated by the rate of exergy of product and exergy of fuel

_{tot}

#### 3.3. Economic Analysis

_{L}) and the expenses of fuel and operation and maintenance costs (FC

_{L}) and (OMC

_{L}), respectively.

_{L}is the capital investment cost, which includes total capital recovery, preferred stock, return on investment for debt, income taxes, and other taxes and insurances. Expenses are mainly FC

_{L}and OMC

_{L}. The CC

_{L}is the levelized value of the total capital investment cost (TCI), which is composed of the fixed capital investment (FCI) plus the interest to be paid for the investment.

#### 3.4. Exergoeconomic Analysis

_{k}indicates the relative contribution of the exergy destruction cost rate and those associated with the CC

_{L}and OMC. This factor is used during the optimization to make decisions of whether to invest in a more efficient component to reduce the exergy destruction or to sacrifice efficiency to decrease the cost rate associated with the carrying charges.

## 4. Results and Discussion

^{2}), outlet temperature of collector = 111.1 °C, maximum storage capacity = 2000 kg, storage volume = 2 m

^{3}, storage pressure = 10 bar, average storage temperature = 110 °C, and direct normal irradiation (DNI) = 1100 W/m

^{2}.

^{3}USD. The levelized carrying charges (CCL) are 31.7 × 10

^{3}USD/year, and the levelized operation and maintenance costs (OMCL) are 9.9 × 10

^{3}USD/year. As expected, the highest BMC is of the solar field or collector and the storage tanks. The resulting levelized cost of electricity (LCOE) for the system being evaluated is 1.8 USD/kWh.

_{D,k}) and exergoeconomic factors (f

_{k}) were calculated.

_{k}+ Ċ

_{D,k}) for the components of the overall system, and Figure 9 shows the exergoeconomic factor of these components. High exergoeconomic factor values of a component suggest a decrease in the investment costs of that component regardless of its exergetic efficiency.

_{k}+ Ċ

_{D,k}) is for the solar field, followed by the condenser of the ERC and the condenser of the ORC. The exergoeconomic factor of the solar field is 21%, suggesting that the capital cost is a relatively much lower rate than the cost of exergy destruction. So, 79% of the total cost associated with the solar field is owing to its high thermodynamic inefficiency (high exergy destruction). The second cost-ineffective component in the system is found to be the condenser, and its exergoeconomic factor is observed to be 34%, which means that only 34% of the cost is owing to component capital cost and 66% of the cost is because of high exergy destruction. The third cost-ineffective component in the system is found to be the condenser of the ORC, and its exergoeconomic factor is obtained to be approximately 58%, which means that only 58% of the cost is owing to component capital cost and 42% of the cost is owing to high exergy destruction.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$\dot{C}$ | cost rate [USD (h)^{−1}] |

COP | coefficient of performance [-] |

$\dot{E}$ | exergy rate [W] |

f | exergoeconomic factor [-] |

h | specific enthalpy [kJ (kg)^{−1}] |

d | throat diameter [-] |

i | interest rate [%] |

$\dot{m}$ | mass flow rate [kg (s) ^{−1}] |

n | economic life [year] |

p | pressure [bar] |

$\dot{Q}$ | heat rate [W] |

r | inflation rate [%] |

T | temperature [K, ^{o}C] |

$\dot{W}$ | power [W] |

y^{*}_{D} | exergy destruction ratio [%] |

$\dot{Z}$ | cost rate [USD (h)^{−1}] |

Greek symbols | |

α | exponent for size component |

ε | exergy efficiency [%] |

$\tau $ | annual operating hours [h (year)^{−1}] |

ω | entrainment ratio [-] |

η | efficiency [%] |

Abbreviations | |

AC | air conditioning |

BMC | bare module cost |

CAM | constant area mixing |

CC | carrying charges |

CELF | constant escalation levelization factor |

CPM | constant pressure mixing |

CRF | capital recovery factor |

DNI | direct normal irradiation |

ERC | ejector refrigeration cycle |

ERS | ejector refrigeration system |

FC | fuel cost |

FCI | fixed capital investment |

LCOE | levelized cost of electricity |

MF | module factor |

MPF | material and pressure correction factor |

OMCL | levelized operation and maintenance cost |

ORC | organic Rankine cycle |

PEC | purchased equipment cost |

PNL | primary nozzle location |

SERC | solar ejector refrigeration cycle |

TCI | total capital investment |

TRR | total revenue requirement |

VCRS | vapor compression refrigeration system |

Subs- and superscripts | |

0 | reference state (for exergy analysis) |

D | exergy destruction |

F | exergy of fuel |

k | kth component |

L | exergy losses, levelized |

P | product |

tot | overall system |

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**Figure 1.**(

**a**) The hybrid solar ejector refrigeration cycle (SERC) with organic Rankine cycle (ORC), (

**b**) the lg p-h diagram of the ERC, and (

**c**) the lg p-h diagram of the ORC.

**Figure 3.**Schematic and the thermodynamic parameters for the ejector refrigeration cycle (

**a**) and organic Rankine cycle (

**b**).

**Figure 4.**Effect of generator pressure on (

**a**) the coefficient of performance (COP) and condenser pressure; (

**b**) the COP and entrainment ratio; the effect of evaporator pressure on (

**c**) the COP and entrainment ratio; and (

**d**) the COP and condenser pressure, Pg = 33 bar, Tg = 363.9 K, respectively.

**Figure 5.**Exergy destruction [kW] and exergy destruction ratios [%] within the group of productive and dissipative components. ORC, organic Rankine cycle, Ejector Cooling Cycle ECC.

**Figure 7.**Bare module cost (BMC) (×10

^{3}USD) share of the system (

**a**) and individual components of ERC (

**b**) and ORC (

**c**).

Variable | Nomenclature | Unit | Model in [10] | Study Model |
---|---|---|---|---|

Working fluid | n-Butane | n-Butane | ||

Heat in | ${\dot{Q}}_{in}$ | kW | 138.17 | 138.13 |

Expander inlet | $\dot{m}$ | kg (s)^{−1} | 0.353 | 0.353 |

p | bar | 5.99 | 5.99 | |

T | °C | 62.0 | 62.0 | |

Expander outlet | $\dot{m}$ | kg (s)^{−1} | 0.353 | 0.353 |

p | bar | 3.28 | 3.28 | |

T | °C | 44.19 | 45.00 | |

Condenser inlet | $\dot{m}$ | kg (s)^{−1} | 0.353 | 0.353 |

p | bar | 3.28 | 3.28 | |

T | °C | 44.1 | 44.0 | |

Condenser outlet | $\dot{m}$ | kg (s)^{−1} | 0.353 | 0.353 |

p | bar | 3.28 | 3.28 | |

T | °C | 35.0 | 35.0 | |

Expander power | ${\dot{W}}_{ex}$ | kW | 8.37 | 8.49 |

Pump power | ${\dot{W}}_{p}$ | kW | 0.17 | 0.17 |

Net power | ${\dot{W}}_{\mathrm{net}}$ | kW | 8.20 | 8.31 |

Energetic efficiency | η | % | 5.93 | 6.14 |

State | Exergy Rate [kW] | State | Exergy Rate [kW] | State | Exergy Rate [kW] |
---|---|---|---|---|---|

1 | 4.36 | 10 | 4.35 | 19 | 7.46 |

2 | 2.74 | 11 | 2.15 | 20 | 7.42 |

3 | 2.97 | 12 | 2.33 | 21 | 9.64 |

4 | 7.25 | 13 | 2.65 | 22 | 9.56 |

5 | 1.62 | 14 | 12.04 | 23 | 3.41 |

6 | 1.56 | 15 | 18.07 | 24 | 5.79 |

7 | 2.03 | 16 | 75.94 | 25 | 1.78 |

8 | 7.39 | 17 | 22.37 | 26 | 3.66 |

9 | 5.20 | 18 | 14.91 |

**Table 3.**Parameters and assumptions for economic analysis. CRF, capital recovery factor; CELF, constant escalation levelization factor.

Parameters/Assumptions | Value |
---|---|

Plant economic life | 20 years |

Effective interest rate | 10% |

CRF | 0.117 |

Average general inflation rate | 4.5% |

Average nominal escalation rate of fuel costs | 1.7% |

CELF general | 1.2143 |

CELF fuel | 1.3171 |

Annual full load operational time | 2000 h |

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**MDPI and ACS Style**

Tashtoush, B.; Morosuk, T.; Chudasama, J.
Exergy and Exergoeconomic Analysis of a Cogeneration Hybrid Solar Organic Rankine Cycle with Ejector. *Entropy* **2020**, *22*, 702.
https://doi.org/10.3390/e22060702

**AMA Style**

Tashtoush B, Morosuk T, Chudasama J.
Exergy and Exergoeconomic Analysis of a Cogeneration Hybrid Solar Organic Rankine Cycle with Ejector. *Entropy*. 2020; 22(6):702.
https://doi.org/10.3390/e22060702

**Chicago/Turabian Style**

Tashtoush, Bourhan, Tatiana Morosuk, and Jigar Chudasama.
2020. "Exergy and Exergoeconomic Analysis of a Cogeneration Hybrid Solar Organic Rankine Cycle with Ejector" *Entropy* 22, no. 6: 702.
https://doi.org/10.3390/e22060702