# Thermodynamic and Exergoeconomic Analyses of a Novel Combined Cycle Comprised of Vapor-Compression Refrigeration and Organic Rankine Cycles

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## Abstract

**:**

## 1. Introduction

## 2. System Description

## 3. Modeling and Analyses

#### 3.1. Thermodynamic Analysis

- The system is at steady state.
- The ambient temperature and pressure are 25 °C and 1014 Pa, respectively.
- Pressure drops in the system (heat exchangers and pipes) are negligible.
- Expansion and compression processes, in all compression and expansion components, are adiabatic.
- Changes in kinetic and potential energies are negligible.
- The fluid flow exiting the condenser is a saturated liquid.
- Outlet fluid from the evaporator is a saturated vapor.

^{0}indicates the restricted dead state, which has the same temperature and pressure as the standard environment. Note that variations of other kinds of exergies like kinetic and chemical are neglected [21].

#### 3.2. Thermoeconomic Analysis

#### Economic Model and Analysis

## 4. Results

#### Performance Results

## 5. Parametric Study

#### 5.1. Effect of Turbine Inlet Pressure (TIP)

#### 5.2. Effect of Condenser Pressure (${P}_{cond}$)

#### 5.3. Effect of Condenser Temperature (${T}_{cond}$)

#### 5.4. Effect of Pinch-Point Temperature Difference ($\Delta {T}_{pp}$)

## 6. Conclusions

- The proposed configuration is proved to be an efficient cogeneration system.
- The largest exergy destruction occurs in the boiler and turbine, respectively.
- Among the three working fluids, the R143a has the best result from the viewpoint of both the second law of thermodynamics and economics.
- The highest product unit cost is achieved with R22 as the working fluid.
- Better thermodynamic and economic results are achieved with higher turbine inlet pressure and lower condenser pressure as well as lower pinch-point temperature difference.
- Increasing TIP results in an increase in all component exergy destruction ratios, except the boiler. The net change in exergy destruction; however, is negative because the boiler is dominant in this respect.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Nomenclature | $\dot{W}$ | Power (kW) | |

$A$ | Overall heat transfer area (${m}^{2}$) | ${\dot{W}}_{net}$ | Produced net power (kW) |

$\dot{C}$ | Cost rate ($/hour) | $Z$ | Investment cost ($) |

$c$ | Exergy unit cost ($/GJ) | $\dot{Z}$ | Investment cost rate ($/h) |

$\dot{E}$ | Exergy rate (kW) | Abbreviations | |

${\dot{E}}_{D}$ | Exergy destruction rate (kW) | CI | capital investment cost |

$e$ | Specific exergy (kJ/kg) | cond | condenser |

$h$ | Specific enthalpy (kJ/kg) | CRF | capital recovery factor |

${i}_{r}$ | Interest rate (%) | Eva | evaporator |

$M$ | Molar mass (kJ/mol) | ORC | Organic Rankine cycle |

Mass flow rate (kg/s) | OM | Operating and maintenance | |

${\dot{m}}_{ref}$ | Refrigeration cycle mass flow rate (kg/s) | VCC | Vapor-compression refrigeration cycle |

${\dot{m}}_{boiler}$ | Boiler air-stream mass flow rate (kg/s) | Greek symbols | |

$n$ | Number of operating years (year) | ${\gamma}_{k}$ | Fixed cost operation and maintenance cost ($/GJ-h) |

$P$ | Pressure (bar) | ${\eta}_{turbine}$ | Turbine isentropic efficiency |

${P}_{h}$ | Boiler inlet pressure (kPa) | ${\eta}_{pump}$ | pump isentropic efficiency |

${r}_{m}$ | Condenser mass flow split ratio | ${\eta}_{ex}$ | Exergy efficiency |

$s$ | Specific entropy (kJ/kg-K) | $\Delta {T}_{lm}$ | logarithmic average temperature difference |

$T$ | Temperature (K) | $\tau $ | Annual operation hours (h/yr.) |

${T}_{e}$ | Evaporator temperature (K) | Subscripts | |

${T}_{cd}$ | Condenser temperature (K) | 0 | Ambient condition |

${T}_{s}$ | Source temperature (K) | $e$ | output |

${T}_{cs}$ | Cooling space temperature (K) | $i$ | input |

${T}_{cw}$ | Cooling water temperature (K) | $k$ | component |

$U$ | Heat transfer coefficient ($\raisebox{1ex}{$kW$}\!\left/ \!\raisebox{-1ex}{${m}^{2}K$}\right.$) |

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**Figure 2.**Comparison between the results obtained in the present work with those reported by Kim and Perez-Blanco [10].

**Figure 4.**Effects of different working fluids on (

**a**) thermal and exergy efficiencies, (

**b**) total production unit cost, (

**c**) total exergy destruction rate, (

**d**) cooling capacity, and (

**e**) produced net power.

**Figure 5.**Effect of varying turbine inlet pressure (TIP) on thermal efficiency for several working fluids.

**Figure 14.**Effect of varying Pinch-Point Temperature Difference ($\Delta {T}_{pp}$) on thermal efficiency.

**Figure 15.**Effect of varying Pinch-Point Temperature Difference ($\Delta {T}_{pp}$) on exergy efficiency.

**Figure 16.**Effect of varying Pinch-Point Temperature Difference ($\Delta {T}_{pp}$) on net power $({\dot{W}}_{net})$.

Subsystem | Energy Relation | Exergy Analysis |
---|---|---|

Turbine | ${\dot{m}}_{8}{h}_{8}={\dot{m}}_{9}{h}_{9}+{\dot{W}}_{turbine}$ | ${\dot{E}}_{8}={\dot{E}}_{9}+{\dot{W}}_{turbine}$ |

Mixer | ${\dot{m}}_{4}{h}_{4}+{\dot{m}}_{10}{h}_{10}={\dot{m}}_{5}{h}_{5}$ | ${\dot{E}}_{4}+{\dot{E}}_{10}={\dot{E}}_{5}+{\dot{E}}_{destruction}$ |

Recuperator | ${\dot{m}}_{5}{h}_{5}+{\dot{m}}_{9}{h}_{9}={\dot{m}}_{10}{h}_{10}+{\dot{m}}_{7}{h}_{7}$ | ${\dot{E}}_{5}+{\dot{E}}_{9}={\dot{E}}_{7}+{\dot{E}}_{10}+{\dot{E}}_{destruction}$ |

Boiler | ${\dot{m}}_{7}{h}_{7}+{\dot{Q}}_{boiler}={\dot{m}}_{8}{h}_{8}$ | ${\dot{E}}_{7}+{\dot{E}}_{q,boiler}={\dot{E}}_{5}+{\dot{E}}_{destruction}$ |

Compressor | ${\dot{m}}_{3}{h}_{3}={\dot{m}}_{4}{h}_{4}+{\dot{W}}_{compressor}$ | ${\dot{E}}_{3}={\dot{E}}_{11}+{\dot{W}}_{compressor}$ |

Condenser | ${\dot{m}}_{1}{h}_{1}={\dot{Q}}_{condenser}+{\dot{m}}_{5}{h}_{5}$ | ${\dot{E}}_{1}+{\dot{E}}_{destruction}={\dot{E}}_{q,condenser}+{\dot{E}}_{5}$ |

Pump | ${\dot{W}}_{pump=}{\dot{m}}_{6}({h}_{1}-{h}_{6})$ | ${\dot{E}}_{1}={\dot{E}}_{6}+{\dot{W}}_{pump}$ |

Evaporator | ${\dot{m}}_{2}{h}_{2}+{\dot{Q}}_{evaporator}={\dot{m}}_{3}{h}_{3}$ | ${\dot{E}}_{2}+{\dot{E}}_{q,evaporator}={\dot{E}}_{5}+{\dot{E}}_{destruction}$ |

Component | Cost Rate Balance | Auxiliary Equations |
---|---|---|

Turbine | ${\dot{C}}_{2}+{\dot{Z}}_{turbine}={\dot{C}}_{3}+{\dot{C}}_{w,turbine}$ | ${c}_{w,pump}={c}_{w,turbine}$, ${c}_{2}={c}_{3}$ |

Mixer | ${\dot{C}}_{4}+{\dot{C}}_{12}={\dot{C}}_{5}$ | |

Separator | ${\dot{C}}_{9}+{\dot{C}}_{7}={\dot{C}}_{6}$ | ${c}_{7}={c}_{9}$ |

Boiler | ${\dot{C}}_{air\_in}+{\dot{Z}}_{boiler}+{\dot{C}}_{1}={\dot{C}}_{2}+{\dot{C}}_{air\_out}$ | ${c}_{air\_in}={c}_{air\_out}$ |

Compressor | ${\dot{C}}_{11}+{\dot{Z}}_{compressor}+{\dot{C}}_{w,compressor}={\dot{C}}_{12}$ | |

Condenser | ${\dot{C}}_{5}+{\dot{Z}}_{condenser}+{\dot{C}}_{15}={\dot{C}}_{6}+{\dot{C}}_{16}$ | ${c}_{5}={c}_{6}$, ${c}_{15}=0$ |

Pump | ${\dot{C}}_{7}+{\dot{Z}}_{pump}+{\dot{C}}_{w,pump}={\dot{C}}_{8}$ | ${c}_{w,pump}={c}_{w,compressor}$ |

Evaporator | ${\dot{C}}_{10}+{\dot{C}}_{13}+{\dot{Z}}_{evaporatpr}={\dot{C}}_{11}+{\dot{C}}_{14}$ | ${c}_{11}={c}_{10}$, ${c}_{13}=0$ |

Expansion valve | ${\dot{C}}_{9}={\dot{C}}_{10}$ |

Subsystem | Bare Module Cost [$] $({\mathit{C}}_{\mathit{p},\mathit{k}})$ |
---|---|

Turbine | $4405$ |

Heat exchanger | $16000$ |

Boiler | $17500$ |

Condenser | $16000$ |

Pump | $2100$ |

Evaporator | $16000$ |

**Table 4.**Relationships and values for logarithmic mean temperature difference (LMTD) and the total heat transfer coefficient (${U}_{k}$).

Subsystem | Logarithmic Mean Temperature Difference $(\mathit{L}\mathit{M}\mathit{T}\mathit{D}{}_{\mathit{k}})$ | Heat Transfer Coefficient ${\mathit{U}}_{\mathit{k}}(\frac{\mathit{W}}{{\mathit{m}}^{2}\mathit{K}})$ |
---|---|---|

Heat exchanger | $LMT{D}_{he}=\frac{{T}_{3}-{T}_{1}-({T}_{4}-{T}_{8})}{\mathrm{ln}[\frac{{T}_{3}-{T}_{1}}{{T}_{4}-{T}_{8}}]}$ | $1$ |

Boiler | $LMT{D}_{boiler}=\frac{{T}_{air}-{T}_{2}-({T}_{air,out}-{T}_{1})}{\mathrm{ln}[\frac{{T}_{air}-{T}_{2}}{{T}_{air,out}-{T}_{1}}]}$ | $0.9$ |

Evaporator | $LMT{D}_{eva}=\frac{{T}_{13}-{T}_{11}-({T}_{14}-{T}_{10})}{\mathrm{ln}[\frac{{T}_{13}-{T}_{11}}{{T}_{14}-{T}_{10}}]}$ | $1.5$ |

Condenser | $LMT{D}_{cond}=\frac{{T}_{5}-{T}_{16}-({T}_{6}-{T}_{15})}{\mathrm{ln}[\frac{{T}_{5}-{T}_{16}}{{T}_{6}-{T}_{15}}]}$ | $1.1$ |

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

Source temperature | ${T}_{S}=150\xb0C$ |

Cooling water temperature | ${T}_{cw}=25\xb0C$ |

Condenser temperature | ${T}_{cond}=25\xb0C$ |

Condenser pressure | ${P}_{cond}=1000kPa$ |

Dead state temperature | ${T}_{0}=25\xb0C$ |

Environment pressure | ${P}_{0}=101kPa$ |

Pinch-point temperature difference | $\Delta {T}_{pp}=10\xb0C$ |

Refrigeration space temperature | ${T}_{cs}=15\xb0C$ |

Evaporator temperature | ${T}_{e}=5\xb0C$ |

Plant useful life | $n=20years$ |

Annual interest rate | ${i}_{r}=15\%$ |

Plant annual operation hours | $\tau =8000\raisebox{1ex}{$h$}\!\left/ \!\raisebox{-1ex}{$year$}\right.$ |

Fluid mass flow rate | ${\dot{m}}_{ref}=60\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ |

Boiler mass flow rate (air) | ${\dot{m}}_{boiler}=100\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ |

Turbine inlet pressure | ${P}_{h}=3600kPa$ |

Condenser inlet water temperature | ${T}_{water,in}=15\xb0C$ |

Pump isentropic efficiency | ${\eta}_{pump}=0.8$ |

Turbine isentropic efficiency | ${\eta}_{turbine}=0.8$ |

Compressor isentropic efficiency | ${\eta}_{compressor}=0.8$ |

State | ${\dot{\mathit{m}}}_{\mathit{i}}$ (Mass Flow Rate) [kg/s] | ${\mathit{T}}_{\mathit{i}}$ (Temperature) [K] | ${\mathit{P}}_{\mathit{i}}$ (Pressure) [kPa] | ${\mathit{h}}_{\mathit{i}}$ (Enthalpy) [kJ/kg] | ${\mathit{s}}_{\mathit{i}}$ (Entropy) [kJ/kg-K] | ${\mathit{e}}_{\mathit{i}}$ (Exergy) [kW] | ${\dot{\mathit{c}}}_{\mathit{i}}$ (Product Unit Cost) [$/GJ] | ${\dot{\mathit{C}}}_{\mathit{i}}$ (Product Cost) [$/h] |
---|---|---|---|---|---|---|---|---|

1 | 50 | 338.4 | 3600 | 314.4 | 1.362 | 3788 | 70.08 | 955.6 |

2 | 50 | 430.1 | 3600 | 537.3 | 1.971 | 5854 | 46.09 | 971.4 |

3 | 50 | 382.1 | 1000 | 501.5 | 1.995 | 3712 | 46.09 | 615.9 |

4 | 50 | 318.8 | 1000 | 429.8 | 1.79 | 3184 | 46.09 | 528.4 |

5 | 60 | 314.4 | 1000 | 424.8 | 1.774 | 3803 | 67.59 | 925.5 |

6 | 60 | 298.2 | 1000 | 239.2 | 1.135 | 4094 | 67.59 | 996.1 |

7 | 50 | 298.2 | 1000 | 239.2 | 1.137 | 3387 | 68.09 | 830.1 |

8 | 50 | 300.9 | 3600 | 242.7 | 1.138 | 3537 | 68.14 | 867.5 |

9 | 10 | 298.2 | 1000 | 239.2 | 1.137 | 677.3 | 68.09 | 166 |

10 | 10 | 278.1 | 722.3 | 239.2 | 1.027 | 1004 | 45.94 | 166 |

11 | 10 | 278.2 | 722.3 | 390.3 | 1.684 | 556.2 | 45.94 | 91.98 |

12 | 10 | 292.8 | 1000 | 399.5 | 1.69 | 629.6 | 175.2 | 397.1 |

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

$EUF={\eta}_{thermal}$ | Thermal efficiency | $27.21\%$ |

${\eta}_{exergy}$ | Exergy efficiency | $51.95\%$ |

${\dot{W}}_{net}$ | Net power | $1523kW$ |

${\dot{Q}}_{evaporator}$ | Evaporator heat rate | $1511kW$ |

${\dot{E}}_{evaporator}$ | Evaporator exergy rate | $13.34kW$ |

${\dot{c}}_{p,overall}$ | Total product unit cost | $60.75\raisebox{1ex}{$\$$}\!\left/ \!\raisebox{-1ex}{$GJ$}\right.$ |

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## Share and Cite

**MDPI and ACS Style**

Javanshir, N.; Seyed Mahmoudi, S.M.; Rosen, M.A.
Thermodynamic and Exergoeconomic Analyses of a Novel Combined Cycle Comprised of Vapor-Compression Refrigeration and Organic Rankine Cycles. *Sustainability* **2019**, *11*, 3374.
https://doi.org/10.3390/su11123374

**AMA Style**

Javanshir N, Seyed Mahmoudi SM, Rosen MA.
Thermodynamic and Exergoeconomic Analyses of a Novel Combined Cycle Comprised of Vapor-Compression Refrigeration and Organic Rankine Cycles. *Sustainability*. 2019; 11(12):3374.
https://doi.org/10.3390/su11123374

**Chicago/Turabian Style**

Javanshir, Nima, S. M. Seyed Mahmoudi, and Marc A. Rosen.
2019. "Thermodynamic and Exergoeconomic Analyses of a Novel Combined Cycle Comprised of Vapor-Compression Refrigeration and Organic Rankine Cycles" *Sustainability* 11, no. 12: 3374.
https://doi.org/10.3390/su11123374