# Increasing Thermal Efficiency: Methods, Case Studies, and Integration of Heat Exchangers with Renewable Energy Sources and Heat Pumps for Desalination

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review on the Issue

#### 2.1. Design Solutions of Heat Exchangers

#### 2.2. Applied Methods of Increasing Efficiency

_{3}O

_{4}nanofluid and water in a compact finned heat exchanger to improve heat transfer. The thermophysical properties of the selected nanofluid are discussed with a focus on the specific heat capacity, density, viscosity, and thermal conductivity, as well as their dependence on temperature. The results show that the maximum increase in heat transfer was obtained by using magnetite nanoparticles in deionized water as a coolant.

#### 2.3. Advantages of the Organic Rankine Cycle

_{2}capture and storage, as well as emissions of pollutants into the atmosphere, can further affect the choice map of the CRO or PCR system. This study can be used as a guide for choosing optimal conditions for the use of waste heat in the power system in terms of maximum useful output power and minimum costs [19].

- Initialization.
- Fitness assessment.
- Selection.
- Crossing.
- Mutation.
- Substitution.
- Completion.

_{2}and ITC1 CRO, respectively. In order to increase the overall energy and exergetic efficiency of the system, it is important to reduce exergetic destruction in these key components. The main turbine (T1) and the secondary turbine (T2) of the Brayton S-CO

_{2}cycle have the highest energy and environmental efficiency. The heat exchanger (ITC1) in the ORC cycle has the greatest impact on the environment. Thermal oil also has a significant impact on the environment compared to other organic liquids. In turn, acetone had the greatest impact on the environment of the studied organic liquids. The conclusion reached by the authors: the integrated Brayton S-CO

_{2}-CR system provides high thermal and energy efficiency, as well as low environmental impact. The system is a promising option for sustainable energy production. It may be useful to further study alternative organic working fluids that have a comparative or lesser impact on the environment. The study provides valuable information about the efficiency and environmental characteristics of the Brayton S-CO

_{2}-CRO system, which makes it a suitable option for sustainable energy production [22].

#### 2.4. The Use of Exergetic Methods of Thermodynamic Analysis for the Organic Rankine Cycle

_{2}-based cycles powered by an LM2500+ gas turbine for electricity generation. It was found that the efficiency of CO

_{2}-TC + OTC is higher than that of CO

_{2}-TC/OTC. Carbon dioxide (CO

_{2}) is attractive for waste heat recovery in medium and high temperature sources due to its high thermal stability and ideal heat and mass transfer properties. By optimizing the parameters using a genetic algorithm, the net output power of the combined cycle can be maximized. The Organic Transarctic Cycle (OTC) uses lower critical temperatures and dry isentropic characteristics of organic working fluids. The solution is to introduce a recuperator to recover heat from the exhaust gases of the turbine and increase the thermal efficiency of the cycle. Echogen Power Systems LLC has linked this recuperative supercritical cycle (SC) with a waste heat recovery system. The influence of other cycle parameters on system performance is also considered. Parametric optimization was performed using Matlab and Genetic Algorithm; the results indicate better thermodynamic performance for two combined cycles. Pentane is found to be superior to R134a, as it can extract more heat from the emitted CO

_{2}with lower thermal cycle efficiency. Energy losses in each component are also analyzed. In CO

_{2}-TC/OTC, the greatest energy losses occur in a steam generator with heat recovery, followed by an intermediate heat exchanger, which is explained by poor temperature compliance. The main conclusion is that the net output power and thermal efficiency of the combined cycle increase with increasing CO

_{2}heat addition pressure [26].

_{2}/h 1.605 kg-CO

_{2}/h of reduction in CO

_{2}CO

_{2}emissions is possible when using rORC as the lower cycle in GT. When considering the total heat input from the fuel in the GT burner, it can be seen that the generation of electricity in the combined GT–rORC cycle can be increased up to 40.7%. In order to determine optimal performance in real operating conditions, the developed system can be used by ORC engine developers, manufacturers, and at facilities where simple gas turbines are available [31].

#### 2.5. Methods of Optimization of Designs of Heat Pumps and Equipment of the Organic Rankine Cycle

_{2}content in the mixture, which does not lead to an optimal ratio of nanoparticles in the mixture [36].

^{2}at a seawater temperature of 3.7 °C. In summer, the heat transfer rate is 150 W/m

^{2}at a seawater temperature of 24.6 °C [38].

#### 2.6. Complex Using of Renewable Sources: Prerequisites for Creating a Methodology Combining Elements of Thermodynamic Analysis and Exergetic Calculation Method

_{2}and NOx, are aerated with water and pass through the heat exchanger to the lower part of the chimney.

#### 2.7. Energy Analysis Applied to Organic Rankine Cycle Systems

- System Boundary: The first step is to define the boundary of the system, which includes all the components involved in the ORC system. As a rule, the ORC system consists of a heat source, an evaporator, an expander (turbine), a condenser, a pump, and a working fluid.
- Energy flows: Next, energy flows within the system are identified and quantified. This includes the heat supply from the heat source to the evaporator, the output power of the expander, and the heat removal from the condenser to the cooling medium. The pump operation required for the circulation of the working fluid is also taken into account.
- Energy balance: The energy balance equation is applied to the ORC system taking into account the energy flows in each component. This balance equation ensures that the energy entering the system is equal to the output energy, and any loss or gain of energy is taken into account.
- Efficiency analysis: After quantifying the energy flows and establishing the energy balance, various efficiency parameters can be calculated. These include thermal efficiency, which is the ratio of total output to heat consumed, as well as the efficiency of components such as evaporator efficiency, turbine efficiency, and pump efficiency.

- Total Energy Consumption: Energy Analysis provides a comprehensive breakdown of total energy flows in the ORC system. This helps to understand the distribution of energy between different components and processes, allowing for a detailed assessment of system performance.
- Inefficiency Detection: Energy analysis helps to identify areas where energy loss or inefficiency occurs in the ORC system. By quantifying the energy flows in each component, it becomes possible to pinpoint specific locations or processes where improvements can be made to improve overall efficiency.
- Optimization of operating parameters: Energy analysis allows you to evaluate various operating parameters, such as evaporation pressure or condensation temperature, and their impact on system performance. By analyzing the energy flows under various scenarios, it is possible to determine the optimal operating conditions, which will lead to an increase in thermal efficiency.
- Design and Retrofitting: Energy analysis is valuable at the design stage of an ORC system, as it helps in selecting suitable components, determining their technical characteristics, and evaluating expected performance. It is also useful for upgrading existing ORC systems, as it allows you to identify potential areas for improvement and optimization.

## 3. Discussion and Future Prospects

#### 3.1. Methodology: A Case Study of Energy Technological Complex

#### 3.2. Exergetic Method for Evaluating the Efficiency of a Heat Pump Installation

#### 3.3. Future Prospects: Exergetic Method for Evaluating the Efficiency of the Evaporation Plant

_{0}—Ambient temperature.

_{S.S}, r

_{S.S}—the saturation temperature of the pure solvent and its latent heat of vaporization. At a lower initial concentration of seawater (b ~ 20%), there is a decrease in the exergy spent on heating the solution, since the value of the physico–chemical depression decreases. If we take into account the dependence of the heat capacity on temperature and concentration, then Equation (8) will be reduced to the form

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

ε | Thermal coefficient of the cycle |

Q_{2} | The amount of heat required by the heater |

Q_{1} | The amount of heat transferred to water |

T | Absolute temperature, K |

s = dq/T | Specific entropy is a thermodynamic parameter of the state, kJ/(kg·K) |

P_{1} | Initial freon pressure |

t_{1} | Initial temperature of freon |

P_{4} | Freon pressure from Table 1 |

t_{4} | Freon temperature from Table 1 |

i_{1} | Enthalpy at Point 1 |

i_{2} | Enthalpy at Point 2 |

η_{ad} | Efficiency for freon compressors |

i_{a} | Enthalpy at Point A |

T_{к} | Condensate temperature |

X1 | Degree of dryness |

S_{1,2,3} | Entropy in points |

q_{1,2} | Specific amount of heat |

h_{1,2,3,4} | Enthalpy at the corresponding points |

l_{cycle} | Cycle operation |

e | Specific exergy |

G | Expenditure |

Q_{1,2} | The amount of heat |

i_{n.e.} | The enthalpy of the environment for a given refrigerant at a temperature of T_{n.e.} |

S_{n.e.} | The entropy of the environment for a given refrigerant at a temperature of T_{n.e.} |

T_{n.e.} | Ambient temperature |

P_{n.e.} | Pressure at temperature T_{n.e.} |

e_{1,2,3,4} | Values of specific exergies of the refrigerant at characteristic points |

Δe_{dse} | Difference of specific exergies |

V_{0} | Expenditure |

q_{v} | Specific amount of heat |

N_{V.e.} | Power |

E_{e}·η_{m}·η_{e}·η_{u} | Electrical energy input and efficiency (mechanical, electrical, useful) |

G_{ex}e_{1} | Exergetic consumption of the suction working agent |

G_{flow}e_{2} | Exergy of the working agent flow |

E | Exergy |

D | Media consumption |

E_{h1} | Exergetic heating capacity |

E_{total} | Total electrical power supplied to the installation, including its own needs |

a | Pure water activity |

T_{0} | Ambient temperature |

T_{S, S} | Saturation temperature of the pure solvent |

r_{S, S} | Its latent heat of vaporization |

${T}_{S}^{\prime}$, ${T}_{S}^{\u2033}$ и ${r}_{S}^{\prime}$, ${r}_{S}^{\u2033}$ | Boiling points and corresponding values of latent heat of vaporization at Initial b and Final bk concentrations of source water |

$\omega =\frac{{b}_{k}}{b}$ | The multiplicity of concentration |

${E}_{c}^{*}$ | Compressor energy |

${T}_{\mathrm{in}\text{}\mathrm{losses}}^{av}$ | Average value of internal loss temperature |

${T}_{\mathrm{in}\text{}\mathrm{losses}}^{\prime}$,${T}_{\mathrm{in}\text{}\mathrm{losses}}^{\u2033}$ | Temperature taking into account internal losses at the input and output, respectively |

${E}_{\mathrm{o}.\mathrm{n}}$ | Energy of own needs |

${E}_{\mathrm{in}.\mathrm{e}}$ | Supplied energy |

Acronyms and Abbreviations: | |

a | Average value |

av | Average |

c. | Compressor |

in losses | Internal losses |

in energy | Input energy |

o.n. | Own needs |

s.s. | Saturated solution |

s. | Solution |

n.e. | Natural environment |

d.s.e. | The difference of specific exergies |

a.d. | Adiabata |

GHE | Temperature field of the ground heat exchanger |

DE | Differential evolution |

TDE | Tsaillis differential evolution |

OCR | Organic Rankine cycle |

AT | Average temperature |

HT | High temperature |

SC | Serial circuit |

CC | Condensation circuit |

SC/CC | Hybrid scheme |

RIR | Return On Investment ratio |

WHR | Waste heat recovery |

RSC | Rankine steam cycle |

PGS | Power generation system |

ICE | Internal combustion engine |

NCE | Normalized cost of energy |

LCA | Life cycle analysis |

PCM | Predictive control model |

OTC | Organic Transarctic cycle |

SC | Supercritical cycle |

GT | Gas turbine |

RORC | Regenerative organic Rankine Cycle |

EF | Efficiency factor |

WHR | Waste heat recovery |

IHR | Internal heat exchanger |

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**Figure 1.**Scheme of air cooling and water heating of an electric generator: 1—Pump; 2—Water supply; 3—Solar concentrator; 4—Heat pump; 5—Water–air heat exchanger; 6—Heated water flow; 7—Electric generator; 8—Electric drive; 9—Atmospheric air inlet; 10—Atmospheric air outlet.

**Figure 2.**The old scheme of air cooling of the electric generator: 1—Atmospheric air input; 2—Centrifugal fan; 3—Electric drive; 4—Shut-off valve; 5—Electric generator; 6—Water–air heat exchanger; 7—Water; 8—Atmospheric air output.

**Figure 3.**This scheme offers the use of renewable energy sources for combined generation of cold and electricity (Notation further in the text).

**Figure 4.**Technological scheme using organic Rankine cycle: 1—Electric drive; 2—Pump; 3—Expander; 4—Electric generator; 5—Electric cable; 6—Heat exchanger; 7—Water heating line.

**Figure 8.**T–s diagram with heat pump cycle: 1–2—The process of adiabatic compression of the refrigerant in the compressor; 2–3—The process of heat removal from the condenser for water heating (pressure P

_{2}and temperature t

_{2}don’t change); 3–4—Throttling process; 4–1—The process of heat supply to the evaporator (pressure P

_{1}and temperature t

_{1}don’t change).

Point Number | Pressure P | Temperature | Enthalpy i, kJ/kg | Entropy s, kJ/(kg·K) | ||
---|---|---|---|---|---|---|

Bar | MPa | t, °C | T, K | |||

1 | 3.5 | 0.35 | 3 | 276 | 419 | 1.83 |

2 | 19 | 1.9 | 85 | 358 | 472.75 | 1.87 |

2 | 19 | 1.9 | 75 | 348 | 462 | 1.83 |

3 | 19 | 1.9 | 45 | 318 | 272 | 1.24 |

4 | 3.5 | 0.35 | −11 | 262 | 272 | 1.275 |

Formula/Method of Determination | Value | Units of Measurement |
---|---|---|

q_{1} = h_{2} − h_{3} | 200.75 | kJ/kg |

q_{2} = h_{1} − h_{4} | 147 | kJ/kg |

l_{cycle} = q_{1} − q_{2} = h_{2} − h_{1} | 56.75 | kJ/kg |

Formula/Method of Determination | Value | Units of Measurement |
---|---|---|

G = N/l_{cycle} | 0.003 | kg/s |

Q_{1} = q_{1}·G | 0.602 | kW |

Q_{2} = q_{2}·G | 0.441 | kW |

ε = q_{1}/l_{cycle} | 3.5 | - |

Point Number | Pressure P | Temperature | Enthalpy i, kJ/kg | Entropy s, kJ/(kg·K) | Exergy e, kJ/kg | ||
---|---|---|---|---|---|---|---|

Bar | MPa | t, °C | T, K | ||||

1 | 3.52 | 0.352 | 2.88 | 275.88 | 419 | 1.84 | 33.81 |

2 | 19 | 1.9 | 85 | 358 | 474 | 1.86 | 82.95 |

3 | 19 | 1.9 | 44 | 317 | 270 | 1.24 | 60.61 |

4 | 3.52 | 0.352 | −11 | 262 | 270 | 1.275 | 50.355 |

**Table 5.**Values of parameters for calculating specific exergies of refrigerant at characteristic points.

Parameters | Meaning | Units of Measurement |
---|---|---|

I_{n.e.} | 435 | kJ/kg |

S_{n.e.} | 2.01 | kJ/(kg·K) |

T_{n.e.} | 293 | K |

Point | Meaning | Units of Measurement |
---|---|---|

$e=i-{T}_{n.e}\cdot s-({i}_{n.e}\cdot {S}_{n.e})$ | ||

${e}_{1}$ | 33.81 | kJ/kg |

${e}_{2}$ | 82.95 | kJ/kg |

${e}_{3}$ | 60.61 | kJ/kg |

${e}_{4}$ | 50.355 | kJ/kg |

$\Delta e={e}_{i+1}-{e}_{i}$ | ||

$\Delta {e}_{2-1}$ | 49.14 | kJ/kg |

$\Delta {e}_{3-2}$ | 22.34 | kJ/kg |

$\Delta {e}_{4-3}$ | 10.255 | kJ/kg |

$\Delta {e}_{1-4}$ | 16.545 | kJ/kg |

$\Delta {e}_{dse}={\displaystyle \sum \Delta e}$ | ||

$\Delta {e}_{dse}$ | 0 | kJ/kg |

Formula/Method of Determination | Value | Units of Measurement |
---|---|---|

${V}_{o}={G}_{s}\cdot {v}_{1}$ | 0.00024 | m^{3}/s |

${q}_{v}=\frac{{Q}_{T}}{{V}_{o}}$ | 2587.5 | kJ/m^{3} |

${Q}_{o\u043a}={G}_{s}\cdot {q}_{o\u043a}$ | 0.009 | kW |

Q_{T} = Q_{1} + Q_{oк} | 0.621 | kW |

${\eta}_{m}=0.98-0.008\cdot \frac{{P}_{\u043a}}{{P}_{0}}$ | 0.936 | - |

${\eta}_{e}=0.97-0.02\cdot \frac{{P}_{\u043a}}{{P}_{0}}$ | 0.86 | - |

${N}_{v}=\frac{{N}_{i}}{{\eta}_{m}}$ | 0.17 | kW |

${N}_{e}=\frac{{N}_{v}}{{\eta}_{e}{\eta}_{u}}$ | 0.198 | kW |

${E}_{T}^{\prime}=\frac{{N}_{e}}{{Q}_{T}}$ | 0.31 | - |

$\Delta N=0.035+0.015\cdot {N}_{e}$ | 0.03797 | kW |

$\Delta {E}_{T}=\frac{\Delta N}{{Q}_{T}}$ | 0.061 | - |

${E}_{T}={E}_{T}^{\prime}+\Delta {E}_{T}$ | 0.371 | - |

${\mu}^{\prime}=\frac{{Q}_{T}}{{N}_{e}}=\frac{1}{{E}_{T}^{\prime}}$ | 3.136 | - |

$\mu =\frac{{Q}_{T}}{{N}_{e}+\Delta N}=\frac{1}{{E}_{T}}$ | 2.63 | - |

${E}_{c}^{*}=1-\frac{{T}_{n.e}}{{T}_{\mathrm{in}.\text{}\mathrm{losses}}^{\mathrm{av}}}$ | 0.21 | - |

${\eta}_{\u0442.e}^{\prime}=\frac{{E}_{c}^{*}}{{E}_{T}^{\prime}}$ | 0.677 | - |

${\eta}_{\u0442.e}=\frac{{E}_{c}^{*}}{{E}_{T}}$ | 0.566 | - |

Formula/Method of Determination | Value | Units of Measurement |
---|---|---|

${E}_{total}={N}_{e}+\Delta N$ | 0.23597 | kW |

${E}_{e}={N}_{e}$ | 0.198 | kW |

${E}_{\u0442}={G}_{s}({e}_{2}-{e}_{3})$ | 0.067 | kW |

${D}_{em}=(1-{\eta}_{m}\cdot {\eta}_{e}\cdot {\eta}_{u})\cdot {E}_{e}$ | 0.0386 | kW |

${D}_{km}={E}_{e}\cdot {\eta}_{m}\cdot {\eta}_{e}\cdot {\eta}_{u}-{G}_{s}({e}_{2}-{e}_{1})$ | 0.0119 | kW |

${T}_{\mathrm{in}\text{}\mathrm{losses}}^{av}=\frac{{T}_{\mathrm{in}\text{}\mathrm{losses}}^{\u2033}-{T}_{\mathrm{in}\text{}\mathrm{losses}}^{\prime}}{\mathrm{ln}\frac{{T}_{\mathrm{in}\text{}\mathrm{losses}}^{\u2033}}{{T}_{\mathrm{in}\text{}\mathrm{losses}}^{\prime}}}$ | 371 | K |

${E}_{T1}={Q}_{T}(1-\frac{{T}_{n.e}}{{T}_{BK}^{A\u0440}})$ | 0.13 | kW |

${E}_{\u0438}={G}_{xa}({e}_{4}-{e}_{1})$ | 0.0495 | kW |

${D}_{\u0438}={E}_{\u0438}$ | 0.0495 | kW |

${E}_{\mathrm{o}.\mathrm{n}}={E}_{\mathrm{in}.\mathrm{e}}\cdot (0.01\dots 0.03)$ | 0.00589 | kW |

Supplied Exergy | Diverted Exergy | |||
---|---|---|---|---|

Parish Articles | kW | Expense Items | kW | % к E_{total} |

Total electrical power supplied to the installation, including its own needs (E_{total}) | 0.23597 | Exergetic heating capacity, E_{т}_{1}:Losses: In the compressor: Electromechanical Internal In the evaporator: From the irreversibility of heat exchange own needs | 0.13 0.0386 0.0119 0.0495 0.00589 | 55% 16% 5% 20% 2.5% |

Total | 0.23597 | Total | 0.23589 |

Point Number | Pressure P | Temperature | Enthalpy i, kJ/kg | Entropy s, kJ/(kg·K) | Exergy e, kJ/kg | |
---|---|---|---|---|---|---|

MPa | t, °C | T, K | ||||

At the entrance | 0.1 | 80 | 353 | 334.9 | 1.07 | 21.9 |

In capacity | 0.047 | 80 | 353 | 340 | 1.08 | 24.07 |

Before the compressor | 0.047 | 82 | 355 | 2647 | 7.62 | 414.85 |

After the compressor In front of the coil | 0.052 | 90 | 363 | 2662 | 7.62 | 429.85 |

After the coil | 0.052 | 82 | 355 | 355 | 1.13 | 24.42 |

Point | Value | Units of Measurement |
---|---|---|

$e=i-{T}_{n.e}\cdot s-({i}_{n.e}-{T}_{n.e}\cdot {S}_{n.e})$ | ||

e_{1} | 21.9 | kJ/kg |

e_{2} | 24.07 | kJ/kg |

e_{3} | 414.85 | kJ/kg |

e_{4} | 429.85 | kJ/kg |

e_{5} | 24.42 | kJ/kg |

$\Delta e={e}_{i+1}-{e}_{i}$ | ||

Δe_{2-1} | 2.17 | kJ/kg |

Δe_{3-2} | 390.78 | kJ/kg |

Δe_{4-3} | 15 | kJ/kg |

Δe_{1-4} | −405.78 | kJ/kg |

$\Delta {e}_{dse}={\displaystyle \sum \Delta e}$ | ||

$\Delta {e}_{dse}$ | 2.17 | kJ/kg |

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## Share and Cite

**MDPI and ACS Style**

Osintsev, K.; Aliukov, S.; Kuskarbekova, S.; Tarasova, T.; Karelin, A.; Konchakov, V.; Kornyakova, O.
Increasing Thermal Efficiency: Methods, Case Studies, and Integration of Heat Exchangers with Renewable Energy Sources and Heat Pumps for Desalination. *Energies* **2023**, *16*, 4930.
https://doi.org/10.3390/en16134930

**AMA Style**

Osintsev K, Aliukov S, Kuskarbekova S, Tarasova T, Karelin A, Konchakov V, Kornyakova O.
Increasing Thermal Efficiency: Methods, Case Studies, and Integration of Heat Exchangers with Renewable Energy Sources and Heat Pumps for Desalination. *Energies*. 2023; 16(13):4930.
https://doi.org/10.3390/en16134930

**Chicago/Turabian Style**

Osintsev, Konstantin, Sergei Aliukov, Sulpan Kuskarbekova, Tatyana Tarasova, Aleksandr Karelin, Vladimir Konchakov, and Olga Kornyakova.
2023. "Increasing Thermal Efficiency: Methods, Case Studies, and Integration of Heat Exchangers with Renewable Energy Sources and Heat Pumps for Desalination" *Energies* 16, no. 13: 4930.
https://doi.org/10.3390/en16134930