Introduction

Due to rapid population growth and technological advancements, there is a pressing need to discover sustainable and long-term energy resources and use them efficiently. Furthermore, it is imperative to mitigate the escalating environmental pollution and greenhouse gas emissions. Waste heat is discharged into the environment from power plants that operate according to the thermodynamic cycle. This contributes to global warming, which is caused by many factors, including the effect of greenhouse gases and thermal environmental pollution.

The use of waste heat from power plants has gained attention in recent years due to its potential to increase energy efficiency and reduce greenhouse gas emissions [1]. Waste heat is generated during the electricity generation process in power plants. If not properly managed, it is released into the environment, contributing to global warming. The literature research has identified several areas of use for waste heat, including district heating systems [2, 3, 67], greenhouses [4], industrial processes and process heating [3], thermal energy storage [5, 6], seawater desalination [7,8,9,10], cooling systems and cold storage [10], agriculture and aquaculture [3], direct conversion of thermal energy into electrical current [11], and generating electricity (ORC) [12, 13]. This text will discuss recent studies on some important issues related to these areas.

Oyedepo and Fakeye [14] emphasize that the release of large quantities of low-temperature industrial waste heat into the environment is a serious problem, especially in developing countries. Waste heat can be difficult to identify and assess in terms of quantity and quality. Therefore, understanding the availability and recovery potential of waste heat offers the opportunity to reduce energy costs and minimize environmental impacts. The study states that the utilization of low-grade energy from waste heat sources can make a significant contribution to improving overall energy efficiency in energy-intensive industrial sectors. According to the results of the study, about 72% of global primary energy consumption is lost after conversion, 63% of the waste heat flows considered take place at temperatures below 100 °C, with electricity generation accounting for the largest share of these flows, followed by transport and manufacturing.

Theisinger et al. [15] performed modeling and simulation to evaluate the potential for the use of industrial waste heat in district heating systems. Considering the contributions of the industrial and building sectors to energy demand and CO2 emissions, the potential for waste heat utilization and local emission reduction is examined. The customized modeling approach is able to simulate heterogeneous industrial heating and cooling systems and dynamic waste heat and energy demands. Simulation results show that up to 66% energy recovery and 39% CO2 emission reductions are possible through the utilization of waste heat. Furthermore, integration with a district heating system can save up to 14% in operating costs.

Alkhaldi et al. [7] conducted an important study on desalination plants, which is one of the waste heat utilization areas mentioned above. This study examines the feasibility of integrating a low-temperature evaporation desalination plant and the APR1400 reactor. Waste steam outputs between 80 °C and 130 °C were evaluated, and energy requirements and water production costs were analyzed. Findings showed small decreases in operational efficiency and increases in water production capacity. While the use of multiple outputs keeps the power degradation rate low, cost analysis has revealed competitive prices. The research highlights the importance of integrating nuclear energy and desalination for sustainable water production.

Almomani et al. [8] in this study examines how electricity and purified water production can be increased through the integration of solar chimney power plants with nuclear power plants in Jordan. The study suggests that this integration can significantly improve the performance and water purification capacity of solar chimney power plants, thus contributing to the sustainable use of energy and water resources. It is also argued that this approach could be particularly useful for countries with high solar energy potential but limited freshwater resources, such as Jordan. It demonstrates the potential of this innovative solution to optimize the excess heat produced by a nuclear power plant and revolutionize the energy industry.

Common sources of waste heat that can be used in greenhouse farming and agriculture drying include power plants producing electricity [9], industrial processes such as petrochemical, metal processing, and furnaces [1, 9], steel production [1, 16], oil refineries [9, 17], and industrial furnaces and ovens [14]. In the literature, there are studies on the use of waste heat released from many different sources in the field of greenhouse farming, and one of the interesting studies was conducted by Chen et al. [4]. This study addresses the use of waste heat generated in data centers in ecological farms. However, there is a lack of research on the use of waste heat from nuclear power plants.

In their study, Jouhra et al. [16] comprehensively reviewed various waste heat recovery technologies and applications to prevent the disposal of unused energy generated in industrial processes into the environment. The study reviews current practices and procedures, evaluating heat recovery opportunities for energy optimization in the iron and steel, food and ceramic industries. Investigations were conducted on the operation and performance of commonly used technologies including recuperators, regenerators, passive air preheaters, regenerative and recuperative burners, plate heat exchangers and economizers, as well as waste heat boilers and recirculating coil (RAC) units. It had also determined that it is possible to recover waste heat with potential energy content such as direct contact condensate recovery, indirect contact condensate recovery, transport membrane condensation and heat pumps, heat recovery steam generators (HRSGs), heat pipe systems, Organic Rankine cycles, and Kalina cycle. Techniques such as the use of gain and change units are discussed [16]. It is seen that the techniques mentioned in this study can also be used for nuclear power plants.

Although historically fossil fuels have been the main heat source, it is not difficult to find Rankine cycles in which the heat source is the combustion of a nuclear fuel, of biomass or even the result of concentrating solar power [13]. The ideal Rankine cycle for nuclear power plants and the organic ideal Rankine cycle play an important role for efficient conversion of thermal energy and generation of electrical power. The ideal Rankine cycle works by utilizing steam and is widely preferred for converting high-temperature heat in nuclear reactors into electrical energy. The organic ideal Rankin cycle uses organic working fluids and operates at low temperatures and pressures, improving thermal efficiency. Both the ideal Rankin cycle and the organic ideal Rankin cycle help to make more efficient use of thermal energy resources in nuclear power plants, while contributing to minimizing environmental impacts [18]. Although historically fossil fuels have been the main heat source, it is not difficult to find Rankine cycles in which the heat source is the combustion of a nuclear fuel, of biomass or even the result of concentrating solar power [13]. Although there are many publications on the subject, a few studies that are relevant to our study will be presented here.

Meana-Fernández et al. [13] discussed the evolution toward sustainability and environmentally friendly technologies in power generation processes. The study highlights the importance of transitioning from traditional steam and gas turbine cycles to the Organic Rankine Cycle (ORC), Kalina Cycle and other innovative cycles that are more efficient and have less impact on the environment. While discussing the potential of these new cycles in energy production from low-temperature sources and their role in waste heat recovery, they also examine the challenges faced by these technologies and their future development paths. It reveals the critical role of these technologies in achieving the energy sector's goals of reducing carbon footprint and increasing energy efficiency. They also stated that for a typical Rankine cycle, efficiencies between 34 and 38% could be achieved.

Mahmoud et al. [18] conducted thermodynamic and exergoeconomic analyses, as well as performance evaluation of a novel configuration of a combined cooling and power generation system. The research suggests integrating gas turbine cycle, steam Rankine cycle, and combined organic Rankine cycle-vapor compression refrigeration (ORC-VCR) systems to achieve high efficiency from technical, economic, and environmental perspectives. The system was simulated and analyzed in terms of energy, exergy, and exergoeconomic models. Additionally, a sensitivity analysis was performed to better understand the impact of design parameters on the overall system performance. Based on a parametric study, it was noted that R602 exhibited advantageous features in the ORC-VCR subsystem, demonstrating higher thermal efficiency and improved exergetic efficiency. Overall, the analyses indicate that the proposed integrated system achieves total energy and exergy efficiencies of 46.1% and 40.57%, respectively. Furthermore, the overall configuration is shown to provide a net output power of 3810 kW and a cooling load of 303.8 kW. Exergoeconomic evaluation reveals an exergy cost of 49.84 ($ GJ−1) and an exergy cost rate of 826.4 (h−1).

Mohammadi et al. [19] carried out exergy and economic analyses of replacing feed water heaters in the [19] Rankine cycle with parabolic trough collectors. It was carried out on a Rankine cycle with integrated solar energy, and a thermal storage system was added to the cycle, enabling it to operate for 24 h. They determined that the total power production of the system increased by 8.14% compared to the base case. They revealed that the boiler had the highest rate of exergy destruction. The payback period of the proposed system is calculated as 1.5 years.

In their study, Arman and Fathollaf [20] examine advanced exergy and advanced exergoeconomic analyses of a partial heating supercritical CO2 power cycle for waste heat recovery. The research is conducted to better understand the true potential of improving both the thermodynamic and economic performance of each system component, as well as the simultaneous interactions between system components. According to the technological constraints within the system, they demonstrate that the maximum exergy efficiency achievable is 59.8%, with 38.4% (926.9 kW) of the total exergy destruction in the system and 46.18% (32.52 $ h−1) of the total exergy destruction cost being avoidable. They find that 97.8% of the system's total cost belongs to the endogenous part, indicating minimal cost resulting from interaction among components. While the turbine and compressor exhibit the most significant potential for cost savings, heaters are identified to have the lowest potential.

Today, approximately 80% of electrical energy is provided from nuclear energy and fossil-based fuels. In recent years, Nuclear Power Plants are an important potential for energy production [21,22,23]. Fission reactors, which are used in nuclear power plants, contribute approximately 10% of the world's total electricity [24].

Nuclear Power Plants are power plants where reactions that separate (fission) or combine (fusion—in development) atomic particles take place as an energy source. These plants operate according to the steam power cycle (Rankine cycle) [3]. It is expected to obtain the highest amount of energy from the fuel used [23]. However, it is impossible to convert all of the energy obtained from the fuel into mechanical energy. While the conversion of thermal energy into mechanical energy takes place, some of the energy is released to the environment as waste heat due to the steam cycle [25]. This situation causes thermal pollution of the environment [12, 26]. The more efficient use of waste heat to reduce thermal pollution is limited by exergy. At exergy limits, energy transformations take place. Energy production, conversion systems and the equipment that make up the systems are evaluated according to exergy. The analysis method performed in this way is called exergy analysis. With exergy analysis, losses occurring in systems due to irreversibilitys are determined and the improvements to be made in the system are determined. Only establishing the exergy balances and determining the losses is not sufficient in the energy planning of the facilities. In order to complete the analysis, the system must also be analyzed economically [27,28,29]. In this context, thermoeconomic analysis studies become a necessity. This analysis is a solution that takes into account the costs of the power plant based on the second law of thermodynamics [22].

Regarding the cost and investment period, the Turkish Atomic Energy Authority has stated that the construction period of nuclear power plants in the world is on average 6–7 years after the first concrete is poured, and when the entire project period is considered, this period can be around 10–12 years [30, 31].

Regarding the last reactors to be commissioned in the world and their construction times, it was reported that the Rostov-2 plant in Russia took 9 years to be built, the Rajastan-5 and 6 plants in India took 7 years each, Lingao-3 in China took 5 years, Qinshan-2 and 3 took 4.5 years, and the Tomari-3 plant in Japan took 4.5 years to be commissioned [32]. In explanations regarding the project cost, many parameters such as reactor type, power, location, credit conditions, legal and institutional conditions have an impact on the cost [33]. Moreover, nuclear reactors are energy facilities with high initial investment costs but low operating and fuel costs. Considering all factors rather than the direct cost of the reactor, it is important that the cost of electricity produced is comparable and competitive with other types of energy [34,35,36].

Terzi et al. [37] conducted a study to calculate the energy and exergy losses of each reactor component of the VVER-1000 type Nuclear Power Plant and determine the equipment with the highest losses. The condenser was found to have the highest energy loss, while the irreversibility and irreversibility reactors had the largest exergy loss according to the exergy analysis, followed by the steam generator and turbine. The VVER-1000 nuclear power plant has a thermodynamic efficiency of approximately 30%. The turbines experience an exergy loss of about 6%. The reactor pressure vessels and steam generator have irreversibility of 49% and 13%, respectively.

In studies related to cost evaluations with thermoeconomic analysis, Coşkun et al. [38] worked on Thermoeconomic Optimization of Cogeneration Plants. Energy and exergy analyses were performed in each unit of Aliağa Gas Turbines and Combined Cycle Power Plant using the first and second law of thermodynamics and EES package program. As a result of the analysis, the first and second law efficiencies of the power plant were determined as 32.8% and 43.4%, respectively. It is concluded that the highest exergy losses are in the combustion chamber, heat boiler and condenser units, and by reducing the exergy losses, the efficiency will increase and energy costs and harmful emissions to the environment will decrease.

Tozlu, Özahi and Abuşoğlu [39] realized a model of the organic Rankine cycle (ORC) adopting a gas turbine cycle using CO2 (S-CO2). They used Aspen Plus and EES package programs. As a result of the thermodynamic analysis, they evaluated the electricity generation capacity, energy, and exergy efficiency of the proposed system, respectively. For the thermoeconomic analysis of the system, they applied the specific exergy costing method (SPECO), which is widely used among second law-based methods. As a result, the electricity generation capacity of the system is 1530.88 kW, the energy and exergy efficiencies are evaluated as 23.30% and 59.60%, respectively, the unit cost of 1 kWh electricity generation is 7.28 ¢, the annual return is $ 741,146 and the payback period is calculated as 4.09 years. Similarly, Yılmaz and Kanoğlu [40], in the thermodynamic and thermoeconomic analysis of the geothermal assisted hydrogen liquefaction cycle, firstly thermodynamic analysis was performed and then SPECO analysis, which is a specific exergy cost analysis method, was used. As a result of the thermoeconomic analysis, they calculated the unit exergetic cost of electricity generated from the geothermal power plant and the unit exergetic cost of liquefied hydrogen. According to the results of the analysis, energy efficiency increased by 23.31% and exergy efficiency by 28.19%, net output power was 2726 kW and hydrogen production rate was 0.07453 kgs-1.

Mert [41] studied that as a result of process and operational improvements that can be made on the basis of energy and exergy analysis at Erdemir, a large amount of energy can be saved by using it efficiently, thus energy costs can be greatly reduced and emissions to the environment can be minimized.

Ünsal [42] created a simplified thermodynamic analysis model of CANDU 6 Nuclear Power Plant (NPP) in Cycle-Tempo 5.0 thermodynamic analysis program. With the model, exergy destruction and losses of the equipment in the plant were determined by using the thermodynamic analysis method. The calculated thermodynamic efficiency and irreversibility of the CANDU-6 system were approximately 31% and 54%, respectively. It is concluded that significant increases in power generation, total plant efficiency and reduction of electricity generation cost can be achieved by obtaining superheated steam with fossil fuel in NPPs.

Altunbaş [43] carried out an energy and exergy analysis of a lignite-fired thermal power plant located in Afşin-Elbistan region. In the study, the exergy losses of the system equipment and the system were calculated by determining the nodal points with the design values of the power plant and using the thermodynamic values of the fluids belonging to these nodal points. The study calculated the power plant's thermal efficiency as 35.7% and found the second law efficiency to be 58.29%. Based on these calculations, recommendations were made for system improvements and the recovery of inert steam.

Recovering unused waste heat energy below 100 °C can be a challenging task, despite investing in energy-retrieving technology. Various technologies can be used to recover low-temperature waste heat (LTWH) efficiently. However, it is crucial in several process industries and domestic applications [25].

Du et al. (2021) conducted a thermoeconomic analysis and optimized the intermediate pressure ratio for supercritical CO2 multi-stage re-pressurization in nuclear power plants. The research confirmed the existence of the optimal number of re-pressurization stages and the tendency of thermoeconomic parameters to balance. The distribution of the optimal pressure ratio increased the efficiency of the first cycle system from 46.89% to 48.07% and decreased the levelized cost of electricity from 57.40 MWh-1 to 55.87 MWh-1 [44].

Kindi et al. (2022) examine the thermoeconomic evaluation of flexible nuclear power plants and the role of thermal energy storage in low-carbon electricity systems. The analyzed configuration allows the plant to generate 2130 MW el during peak load, which corresponds to a 32% increase in its nominal rated power. Replacing the flexible nuclear plant configuration offers system cost savings, with benefits ranging from £24.3 myr-1 to £88.9 myr-1 [45].

Valencia-Ortega et al. (2023) examine the effects of thermoeconomic optimization on the price-demand balance for electricity generation. The thermoeconomic analysis determines the effects of heat transport parameters and intrinsic irreversibilities on the trade-off for asset turnover efficiency and returns to scale. The cost-output elasticity of different operating regimes is measured, and it is concluded that these regimes can be used as classification mechanisms to control the balance between price and demand, which is balanced by price-demand elasticity [46].

Ebadi et al. (2021) simulated a combined steam Rankine and organic Rankine cycle as the primary mover of the Allam generation cycle. The combined cycle is configured so that the high temperature waste heat is first used as the evaporator of the steam cycle and the waste heat from the vapor cycle evaporator is used as the low-temperature evaporator of the organic cycle. The study showed that the energy efficiency of the combined cycle is 57% and the exergy efficiency is 66%, the output work is 150,125 kW and the total irreversibility is 91,237 kW [47].

Carlson and Davidson (2020) examined the use of thermal energy storage (TES) to increase the operational flexibility of a baseload power plant and thereby promote renewable energy and decarbonize the grid. The four storage options are distinguished by where in the cycle the steam is routed for charging and whether the TES is discharged via the primary or secondary Rankine cycle. TES is compared with an alternative, steam bypass, to provide baseload flexibility. TES is significantly better than steam bypass and the storage option with the greatest thermodynamic benefit is charged by routing superheated steam from the moisture separator/heater outlet to charge the TES. The TES is discharged for peak power through an optimized secondary cycle. TES can increase the capacity factor by up to 15% compared to steam bypass at representative charge mass flow rates [48].

When the literature is examined, it is seen that various academic studies have been conducted on thermoeconomic analysis of nuclear power plants, cost evaluations, reliability analysis, political relations, and waste management. In this study, unlike the literature, a thermoeconomic analysis was conducted for Akkuyu NPP, which was signed between Turkey and Russia on July 15, 2010, within the scope of facility and operation cooperation, which is Turkey's first nuclear power plant, with four reactors of equivalent capacity, with a total power of 4800 MW and designed to generate an average of 35 billion kWh of electricity per year with full capacity operation. Depending on the results of the analysis, it has been analyzed to reduce the cost of energy production and prevent thermal pollution by indirectly recovering the heat discharged to the environment in accordance with the working principle of Nuclear Power Plants and using it for heating, hot water needs (district heating), greenhouse heating, agricultural heating and drying, taking into account the geographical conditions and livelihood of the region. In addition, the literature research shows that instead of using expensive waste heat recovery technologies [6] (such as Organic Rankine cycle, Kalina cycle), regional needs can be determined, and waste heat can be used cheaply and efficiently as we have shown in our study. This study enables the utilization of waste heat in accordance with regional conditions without requiring new technological investments. Furthermore, the waste heat from nuclear power plants established in regions with similar climatic conditions to Mersin Akkuyu will play an important role in drying greenhouse and agricultural products.

The utilization areas of the heat discharged from the condenser in the Akkuyu NPP cycle are presented in Fig. 1.

Fig. 1
figure 1

The cycle and waste heat utilization areas of the Akkuyu Nuclear Power Plant. The Akkuyu Nuclear Power Plant's cycle and waste heat utilization areas

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Materials and methods

In Nuclear Power Plants, Uranium ore, which is the raw material of nuclear energy, is extracted from uranium ore containing U-235 isotope with less than 1% purity. After this process, enrichment of the U-235 isotope in the composition of the ore is carried out to increase the concentration of U-235 from 3 to 5%, which ensures the chain reaction [49, 53]. The uranium fuel enriched is reacted in the Nuclear Reactor and the coolant released as a result of the reaction is used as a decelerator. The water used in this feature is called light water [50]. This type of reactors where light water is used as both moderator and coolant are considered to be among the safest reactors in the world. For this reason, the use of light water is accepted in all calculations [54]. Akkuyu NPP has four VVER-1200/509 (AE-2006) type reactors, each capable of producing 1200 MW. The steam generator PGV-1000MK, horizontal type, uses a single core recovery heat exchanger and steel 08X18H10T Y material. K-1000–60/3000 is designed as a condensing type of steam turbine, single shaft, five cylinders (2 LPC + HPC LPC), separation and steam superheating. GCNA -1391, a hydraulic casing, pump with internals, electric motor, upper and lower spacers, supports, and auxiliary systems are used [16, 51, 52].

The VVER-1200/509 (AE-2006) type reactors at Akkuyu NPP are upgraded versions of VVER-1000 type reactors. They have a higher power capacity, longer operational life, and enhanced safety features, and were designed and built in accordance with modern safety standards [21, 55]. The reactors have an electricity generation capacity of 1200 MWe, a design life of up to 60 years, and can operate with an efficiency of up to 36% [55]. Furthermore, these reactors are specifically designed to meet load-following conditions and can achieve a high load factor of 90% [7].

First of all, besides the similar characteristics of VVER-1200/509 type reactors, reactors located in different geographical regions need to comply with local regulations and standards. For example, there are VVER-1200 type reactors in Russia, China and Belarus. These reactors are similar in terms of design features and safety standards [56].

Similar VVER-1200 type reactors are also located at various facilities around the world, such as the Novovoronezh and Leningrad Nuclear Power Plants in Russia. These reactors were built as part of the AES-2006 design, based on the principle of ensuring safety for personnel, the public and the environment. The AES-2006 design was developed taking into account international standards, including IAEA and European Utility Requirements (EUR) [57].

VVER-1200 type reactors are equipped with features such as passive safety systems, advanced control and monitoring systems and a range of engineering and organizational measures designed to prevent accidents. These reactors include a comprehensive application of the depth of defense principle to enhance the safety of nuclear power plants [57].

In conclusion, the VVER-1200/509 (AE-2006) type reactors at Akkuyu NPP are known for their high safety standards, long lifespan, and efficiency compared to similar reactors worldwide. These reactors are designed to ensure the safe and efficient use of nuclear energy, making them a preferred technology in other nuclear power plants around the world [7, 57].

A simplified VVER reactor is shown in Fig. 1. As can be seen from this figure, the VVER design is very similar to the PWR design. The reactor system consists of two circulation loops: the primary loop, which carries coolant through the reactor core, and the steam generators, which typically operate in a once-through manner. VVERs consist of the reactor pressure vessel, primary coolant pumps, steam generators, pressurizer, and associated piping systems.

Heat energy is generated in the fuel zone in the reactor pressure vessel. After the coolant under pressure (16.2 MPa for VVER-1200 s) is heated in the reactor heart, it leaves the pressure vessel and goes to the steam generator. The steam generator transfers the heat energy from the first cycle to the second cycle (feedwater). The cooling water then leaves the steam generator and is returned to the reactor heart with the help of a pump. (As follows: 1- reactor heart, 2- cooling water pipes, 3- main cooling water pumps, 4- steam generators, 5- emergency safety system water accumulators, 6- pressurizers).

Akkuyu Power Unit is equipped with a safety system to minimize accidents and/or possible consequences of the project. The Power Unit consists of two cycles: the reactor island and the turbine island (see Fig. 1). The first (main) cycle is radioactive and includes the reactor, four main recirculation systems, four main recirculation pumps, four steam generators and a pressurizer. The thermal energy transferred to the water washing the reactor island is released. The water is heated up to approximately 328 °C. It remains liquid because it is under high pressure. The water in the reactors is delivered to the steam generator (see Fig. 1). The thermal energy from the primary cycle is transferred to the secondary cycle [16, 50].

The second cycle of the Power Unit, shown in Fig. 2, is non-radioactive. This section includes feed pumps, water recleaning system, high pressure heaters, steam generator, steam outlet, fresh steam line, condenser pumps, low pressure cleaning heater system, condenser system, degassing system, feed water system, turbine and turbine steam cleaning system. There is also a compressor unit in the turbine, feed water cleaning heating system, water-steam separators-steam heaters and steam unloading plant, additional heated water intake system which is not continuous for its own needs and chemically treated to the cycle [53].

Fig. 2
figure 2

Akkuyu NPP Second Cycle FlowChart

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Since the water is under lower pressure here, boiling occurs and enters the turbine in the vapor phase. The wet steam coming out of the turbine is transferred to the condenser under equal pressure. The waste heat discharged from the condenser is given to the environment. Waste heat constitutes 66% of the plant cycle and 33% is converted into electrical energy [58]. In order to convert waste heat into process heat, specific exergy cost analysis (SPECO) and Engineering Equation Solver (EES) program are used with Akkuyu NPP equivalent plant data according to the Ideal Rankine Cycle.

According to the Specific Exergy Costing (SPECO) approach, fuels and products are systematically defined by accounting for exergy additions and losses for each material and energy flow. This method consists of three main steps: (1) defining exergy flows, (2) identifying fuels and products for each system component, and (3) cost balance equations. This method has been extensively and successfully utilized by researchers in the field of thermo-economics and applied to thermal systems. Additionally, SPECO is considered the most realistic and applicable approach to thermal systems, allowing for easy and rapid results. This approach is more flexible compared to others, enabling engineers to actively participate in the cost determination process and yielding results closer to expected values. It is the simplest and most general approach among exergoeconomic methods. [59]

Thermodynamic data of the plant were prepared in accordance with the State Program for environmental safety, including IEA-TECDOC-1391, published in 2004. Equivalent equipment values of the reactor plant V-392, V392 and Belene NPP in Bulgaria based on the AES-92 evolutionary NPP design were used [60]. The reference environmental conditions for Akkuyu NPP are selected as 25 °C temperature and 1 bar pressure. Engineering Equation Solver (EES) program was used for thermodynamic calculations. In the non-radioactive secondary cycle of the Akkuyu NPP, flow numbering has been done for each equipment. The evaporator between flow points 1–4, shown in Fig. 2, is designated as the starting equipment. For the temperature characteristics at the inlet and outlet flow points of the evaporator, the isentropic turbine between flow points 1–2 and the co-pressurized condenser between flow points 2–3, the temperature value was determined in line with the literature research, aiming to maximize the heat discharged from the plant [54].

The thermodynamic analyses for Akkuyu NPP were performed using the assumptions given below and the relevant equations in Table 1 (see Eq. 1–20). Thermodynamic analysis solution steps can be found in the related literatures [55, 61].

Table 1 Thermodynamic Equations
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Assumptions

1

The evaporator located between flow points 1–4 is considered as the starting equipment

2

For the temperature characteristics at the inlet and outlet flow points of the evaporator, the isentropic turbine between flow points 1–2 and the co-pressure condenser between flow points 23, the temperature value was determined in line with the literature research, aiming to have the highest rate of heat discharged from the plant

3

The assumed values for the dead state (reference state) are as follows:

\({T}_{0}=25^\circ C\)

\({h}_{0}=104.9 kj {kg}^{-1}\)

\({s}_{0}=0.3669 kj {kg}^{1-}. {K}^{-1}\)

4

It is calculated as 8040 h if Akkuyu NPP operates at full capacity over 8760 h, which is the total operating hours of Akkuyu NPP for 20 years

In the thermoeconomic analysis solution steps of the plant, initial investment cost, fuel cost, operation and maintenance costs, discount rate, thermoeconomic factor, relative cost difference, exergy destruction costs, exergy destruction, product and fuel exergy were calculated for each equipment. All these calculations were performed using the relevant equations given in Table 2 (Eq. 21–22).

Table 2 Thermoeconomic Equations
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The data in Tables 3, 4 and 5 were used for the thermoeconomic solution steps. The energy and exergy equations used in the equipment inputs and outputs of the plant are presented in Table 3.

Table 3 Energy and exergy equations
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Table 4 Product and Fuel Exergy
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Table 5 Exergy-dependent cost equations and unit exergy cost equations
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The equations used to calculate the product and fuel exergies of the equipment are given in Table 4.

Table 5 presents the exergy-related cost balance equations and unit exergy cost equivalents of the plant equipment.

Equation 9 was used to determine the amount of heat entering the system from the evaporator located between points 1 and 4.

Equation 25 was used to calculate the amount of heat rejected to the environment, i.e., the amount of waste heat from the condenser located between points 2 and 3.

When comparing the incoming and outgoing heat quantities in the power plant, 32% of the heat is utilized, while 68% is released as waste heat to the environment.

Equation 5 was used to find the net amount of work produced by the turbine located between points 1 and 2.

The work of the pump between points 3 and 4 was calculated using Eq. 6. There is no heat exchange in the pump. Kinetic and potential energies in the system were neglected.

The amount of heat entering the evaporator was calculated using Eq. 3.

The amount of heat released from the evaporator was calculated using Eq. 15.

Equation 5 was used to calculate the amount of work output from the turbine.

Equation 20 was used to calculate the amount of work input to the pump.

Equation 7 was used to calculate the net amount of work produced in the power plant.

Equation 11 was used to calculate the net amount of power generated in the power plant.

Equation 16 was used to calculate the efficiency of the evaporator, which is located between points 1 and 4.

Equation 16 was used to calculate the efficiency of the turbine, which is located between points 1 and 2.

Equation 16 was used to find the efficiency of the condenser located between points 2 and 3.

Equation 16 was used to find the efficiency of the pump located between points 3 and 4.

Equation 16 was used to calculate the energy efficiency of the power plant.

To calculate the exergy efficiency of the power plant, Eq. 14 was first used to find the exergy heat, and then Eq. 18 was used to calculate the exergy efficiency of the power plant.

Monthly consumption amounts per dwelling for heating and hot water use were requested from the natural gas distribution company serving, through an official letter, in the province where the Akkuyu Nuclear Power Plant is located (Mersin). Consumption data is provided in standard cubic meters and converted to kWh and presented in Fig. 3 and 4 [62].

Fig. 3
figure 3

The monthly average amount of natural gas per residence for heating purposes for Mersin [62]

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Fig. 4
figure 4

Monthly average amount of natural gas per house for hot water use in Mersin [62]

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The average household in Mersin province uses natural gas for both heating and hot water, with the consumption presented in sm3 and kWh on a monthly basis in Figs. 3 and 4, respectively. Total consumption amounts for heating data shown in Fig. 3 are 739 sm3 and 7783 kWh. Similarly for the hot water data shown in Fig. 4, the total consumption amounts are 193 sm3 and 2057 kWh.

Greenhouse indoor temperature values were selected as 16 °C day and night and 25 °C ventilation starting temperature. Calculations were made for tomato plants and for the growing period from October 01 to March 31. A steel pipe heating system placed close to the floor was selected as the heating system and the water inlet temperature was set to 90 °C and the outlet temperature was set to 70 °C. Three different greenhouse characteristics used in the study of a province in the Mediterranean climate zone were taken as an example for Mersin. The calculation for the greenhouse types suitable for the regional conditions was determined using Table 6 [63]. The greenhouse types given in Table 6 are classified as Type-1, 2 and 3 according to the covering materials used in the greenhouses [63].

Table 6 Greenhouse types and features [63]
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Çaylı and Temizkan [63], in their literature study, calculated that the type of greenhouse with the highest heat requirement is Type-1 without heat curtain and if heat curtain is used, 34%, 32% and 31% heat can be saved in Type-1, Type-2 and Type-3 greenhouses, respectively. For this reason, the calculated values are given in Table 7 in order to compare the heat requirements of some provinces in the Mediterranean climate zone for the Type-1 greenhouse with a day/night temperature of 16 °C and a ventilation temperature of 25 °C.

Table 7 Monthly heat requirement for Type-1 greenhouse of some provinces in the Mediterranean climate zone [63]
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The average per capita electricity consumption (kWh) for Mersin province is shown in Fig. 5, according to statistical information from the official website of the Turkish Statistical Institute (TÜİK) [64]. The data were compared with the sector report of Turkish Electricity Distribution Company (TEDAŞ). The values were found to be the same on average.

Fig. 5
figure 5

Electricity consumption per capita in Mersin [64]

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According to the pre-feasibility study report of the fruit and vegetable drying facility, the amount of power drawn from the grid by the machinery and equipment used in the production process is around 20 kW. According to the results of the "Cold Storage with Renewable Energy Sources" feasibility study prepared by Aydın Commodity Exchange for the Development Bank, it is assumed that 100 square meters of cold storage will draw 100,000 kWh of energy annually [65]. Fruit and Vegetable Drying Plant Electricity Expenses are given in Table 8. Using these data, the agricultural drying values presented in Tables 16 and 17 were calculated.

Table 8 Electricity Costs of Fruit and Vegetable Drying Plant [65]
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Investment costs are shown in Table 9 The economic lifespan of the facility is determined as minimum 20 years, as indicated in Table 9 [66], with operating hours calculated at 8040 h based on total working hours of 8760 h when operating at full capacity. The difference of 720 h is the time allocated for periodic maintenance of the system [39].

Table 9 Cost Analysis of Akkuyu Nuclear Power Plant [66]
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Using this table, Eq. 23 was used for the annual capital investment, Eq. 24 for the maintenance/repair cost and Eq. 25 for the total annual capital investment of each equipment in the plant. The discount rate of Akkuyu NPP was determined as 10% [66]. The calculation steps for annual capital investment, maintenance/repair cost and total annual capital investment for the evaporator are shown as an example.

$${\dot{Z}}_{{\text{k}}}^{\text{Cl}}=\frac{PEC}{h}$$
(23)
$$\begin{array}{ll} {\dot{Z}}_{{\text{evaporator}}}^{\text{Cl}}=\frac{696785\$}{8040h}& \quad {\dot{Z}}_{{\text{evaporator}}}^{\text{Cl}}=86.66 \$ {h}^{-1}\\ {\dot{Z}}_{{\text{evaporator}}}^{\text{OM}}=\left(86.66 \$ {h}^{-1}\right)0.10 &\quad {\dot{Z}}_{{\text{evaporator}}}^{\text{OM}}=8.66 \$ {h}^{-1}\\ {\dot{Z}}_{{\text{evaporator}}}^{\text{T}}=86.66 \$ {h}^{-1}+8.66 \$ {h}^{-1}&\quad {\dot{Z}}_{{\text{evaporator}}}^{\text{T}}=95.226 \$ {h}^{-1}\end {array}$$

Result and discussion

Exergy analysis was carried out with the help of thermodynamic equations using equipment values equivalent to the Akkuyu Nuclear Power Plant operating according to the real steam power cycle. Specific exergy costing (SPECO) method, which is the most widely used cost analysis method based on the second law of thermodynamics, was used to calculate exergy-related product, fuel costs, relative cost difference, performance evaluation variable, exergy destruction costs and total investment costs. With the tabular data generated as a result of the analysis, heat discharged from the plant, heat entering the plant, electricity generation cost, annual profit amount and depreciation period were determined.

The values calculated for the six points using the equations (see Eq. 1–20) given in Table 1 are presented in Table 10.

Table 10 Thermodynamic properties of Akkuyu Nuclear Power Plant
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Based on the first and second law of thermodynamics, energy equations were calculated using Eq. 12 and exergy equations were calculated using Eq. 13 with the data in Table 10. The values obtained are presented in Table 11 and Fig. 6.

Table 11 Energy and Exergy values
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Fig. 6
figure 6

Energy and Exergy values and fractions

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The detailed energy and exergy balances for six points (see Fig. 2) are shown in Table 11 and Fig. 6. There is a notable difference in the energy and exergy balances represented. These ratios show the difference between energy and exergy analysis. Exergy analysis reveals the causes of process inefficiency more thoroughly than energy analysis. According to [68], there was a similar finding reported. In the first cycle, it is observed that points 5 and 6 have the highest energy and exergy values. This can be attributed to the relatively small temperature difference between these two points (see Table 11). In the second cycle, it is observed that the highest energy and exergy ratio is associated with flow region number 1. These figures also demonstrate the difference between energy and exergy analysis [43, 68].

Product and fuel exergy were calculated using the equations given in Table 4 and exergy destruction was calculated using Eq. 29. The heat transfer rates, work, specific flow exergy, exergy destruction, products, exergetic efficiency values obtained as a result of all these calculations are presented in Table 12.

Table 12 Thermodynamic results of Akkuyu Nuclear Power Plant
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According to Table 12 and Fig. 7, the energy and exergy efficiencies of the plant are calculated as 35% and 68%, respectively. It is seen that the equipment with the highest exergy destruction in the system is the evaporator. It is lower exergy efficiency when compared to other sub-components in the power plant due to their high exergy destructions. This can be explained by the temperature and phase difference of the flows entering and leaving the evaporator. The energy efficiencies of the equipment were calculated as 35.34% for the evaporator, 98% for the turbine, 54.66% for the condenser and 70.44% for the pump. This energy efficiency value is within the range of the values provided in [13], and the exergy efficiency value is in concordance with the values provided in [39]. When we look at the evaporator and condenser in the plant, it is seen that they have lower energy efficiency than the other equipment.

Fig. 7
figure 7

Exergy destruction and Exergy efficiency of the Akkuyu Nuclear power plant components

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The most exergy destruction is related to the evaporator 3,399,033 kW (%90), the condenser 341,283 kW (%9), the turbine 47,155 kW (%1) and the pump 13,571 kW (%0.1), respectively, which implies a large amount of irreversibility in these components due to the high temperature difference. The results in the cited reference [20] are in agreement with these results.

The purchase cost (PEC) and initial capital cost ratio, operation and maintenance cost ratio, total capital cost ratio of the equipment in the plant are presented in Table 13.

Table 13 Total cost ratios related to initial investment (IC), operation and maintenance costs (OM) for Akkuyu Nuclear Power Plant components
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For the purchased equipment cost (PEC), the amounts of the equipment in the plant were determined with ratios over the total PEC amount in line with the literature research. Accordingly, initial investment costs [69] constitute the purchased equipment costs. The PEC amount is composed of the construction costs shown in Fig. 8. The PEC amount is calculated as 5% for the evaporator, 6% for the turbine, 5% for the condenser and 4% for the pump. The remaining amount over the total PEC amount constitutes the other components of the plant. SPECO method is applied then the results are evaluated for all components. The capital investment cost rate, the operating and maintenance costs rate, and the total cost rate of the turbine are found to be 109.937 $ h-1, 10.993 $ h−1, and 120.930 $ h−1, respectively. The total cost rate of turbine is found to be 241.86 $h−1. It has the highest value among the components.

Fig. 8
figure 8

PEC, IC and OM for Power Plant components

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Using the exergy values calculated in Table 11 and the total cost ratios calculated in Table 13 for each equipment, exergy costs were calculated with the exergy-dependent cost equations created in Table 5. Using the exergy costs and exergy values and Eq. 21, the cost ratios at the flow points of each equipment were calculated.

For each equipment, the cost ratio was calculated using the above example steps and Eq. 21. The calculated exergy values, cost ratios and exergy-related costs are presented in Table 14.

Table 14 Total cost ratios of Akkuyu Nuclear Power Plant components
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As can be seen from the table, the highest cost ratio is observed at flow points 5 and 6 of the first cycle. On the other hand, the cost ratios based on exergy are the lowest. This is due to the small temperature difference.

Equation 31 was created to calculate the electricity generation cost of the plant. In Eq. 31, the amount of heat entering and leaving the plant, exergy-related unit cost ratios and total cost ratio of the plant, operation, maintenance activities, annual capital investment and the operating hours of the plant at full capacity are used. For 1 kWh, the unit price of electricity was found as 0.01969 $ kWh−1.

According to the October 6, 2010, official gazette announcement, the amount of electricity purchased by the.

Turkish Electricity Trade and Contracting Corporation of the Republic of Türkiye (TETAŞ):

The purchased amount of electricity is \(17.5x{10}^{10}kWh\)

The unit cost of electricity production for Akkuyu NGS is 0.0196 $/kWh.

Electricity production cost=\(17.5 x{10}^{9}\) kWh (0.0196 $ kWh−1).

Electricity production cost = \(343x{10}^{6}\mathrm{ \$}\)

The purchased amount of electricity is \(17.5x{10}^{10}kWh\)

The purchase price of electricity is 0.1235 $ kWh−1.

Amount of electricity sold and purchased = \(17.5x{10}^{10}kWh (0.1235\mathrm{ \$ }{kWh}^{-1})\)

Amount of electricity sold = \(216125x{10}^{4}\mathrm{ \$}\)

Annual profit amount of the power plant = (Amount of electricity sold)—(Cost of electricity production).

Annual profit of the power plant = \(216125x{10}^{4}-343x{10}^{6}\)= \(181825x{10}^{4}\) $

Amortization period = Investment Cost / Annual profit.

Amortization period = \((13963636x{10}^{3}\mathrm{\$})/(181825x{10}^{4}\mathrm{ \$})=7.68\mathrm{ years}\)

The annual amount of electricity purchased by the Government of the Republic of Turkey from Türkiye Electricity Trading and Contracting Inc. (TETAŞ) 216,125 × 104 $ is calculated as the cost of electricity generated by Akkuyu NPP. Cost of electricity generated by Akkuyu NPP 343 × 106 $ as the annual profit of the power plant. The profit amount of the power plant is calculated as 181,825 × 104 calculated as $.

The amortization period for the power plant's initial investment is estimated to be within a commendable range of 7 to 8 years, underpinning its financial viability.

Considering the inlet and outlet of the flow points for each equipment, the exergy costs of the products and fuels of the equipment were calculated with the unit exergy cost equations in Table 5. Exergy-dependent product for evaporator \({(c}_{{\text{p}},{\text{k}}})\), and fuel costs \({(c}_{{\text{f}},{\text{k}}})\), relative cost difference, which is a thermoeconomic evaluation variable \(({r}_{{\text{k}}})\), performance evaluation variable \({(f}_{{\text{k}}})\), exergy destruction costs \({(\dot{D}}_{{\text{D}},{\text{k}}})\) calculations were calculated with the help of the equations given in Table 2.

For all other equipment, calculations were made using the example process steps above. As a result of the calculations, the exergy-dependent product \({(c}_{{\text{p}},{\text{k}}})\) and fuel costs (\({c}_{{\text{f}},{\text{k}}})\), relative cost difference, which is a thermoeconomic evaluation variable \(({r}_{{\text{k}}})\), the thermoeconomic factor \({(f}_{{\text{k}}})\), exergy destruction costs \({(\dot{D}}_{{\text{D}},{\text{k}}})\), and total investment costs \(({\dot{Z}}^{T})\) is presented in Table 15.

Table 15 Exergy-related product and fuel costs, exergy destruction costs, exergoeconomic factors and total investment costs of Akkuyu Nuclear Power Plant components
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It is seen that the equipment with the highest exergy and fuel related product cost is the pump, while the equipment with the highest exergy destruction cost is the evaporator. Since the condenser is the equipment with the highest cost in terms of thermoeconomic factor, the improvements in the condenser will not increase the investment cost of the system. Improvements in the turbine will change the performance of the system. Efficiency of the process units is tried to be increased by increasing the initial investment cost. The explanations in [39, 61] are consistent with this result.

According to the technological constraints in the system, the maximum achievable exergy efficiency is 68%, total exergy destruction is 3,801,568 kW and the total exergy destruction cost is 240,168 $ h−1 [20].

In accordance with the literature research, the amount of usable heat was calculated based on the plant efficiencies determined according to the areas of use and the heat entering the plant. The amount of usable heat according to the areas of use is presented in Table 16.

Table 16 Available heat quantities according to areas of use
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The highest amount of usable heat is observed in electricity generation, as shown in Table 16, with an efficiency of 88%. In contrast, the efficiency of use for residential heating and hot water needs, although equal, is around 85%. Subsequently, greenhouse agriculture and agricultural drying applications follow, presenting an efficiency rate of 60%.

The annual consumption for heating and hot water use at the Akkuyu Nuclear Power Plant is calculated for the construction of approximately 2500 residential units (living space for 4500 people). The annual consumption is calculated for an area of 10,000 square meters for greenhouse and 1000 square meters for agricultural drying. The amount of electricity consumption is considered for a living area of 4500 people. In line with this information, waste heat utilization rates are presented in Table 17.

Table 17 Waste heat utilization rates
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Tables 16 and 17 show that the data pertaining to greenhouse farming and agricultural drying have similar values. The same applies to residential heating and hot water.

As illustrated in Table 17, it is evident that the maximum benefit can be derived from waste heat, approximately 60%. The emission of the remaining 8% of waste heat into the environment minimizes thermal pollution. However, it is important to note, as mentioned in the introduction based on references, that exploiting this potential requires expensive technological infrastructures for electricity. Conversely, traditional methods for residential heating, hot water, greenhouse agriculture, and agricultural drying do not necessitate such costly technological frameworks. It should also be noted that the sustainability of greenhouse agriculture in winter and agricultural drying in summer can be maintained depending on the geographical and climatic conditions of the region. While approximately 10% of waste heat is released into the environment for residential heating or hot water needs, this figure is approximately 27% for greenhouse agriculture and agricultural drying.

In this context, to achieve sustainability and minimize waste heat, a combined use of residential heating, hot water, greenhouse agriculture, and agricultural drying would be appropriate. This integrated approach not only maximizes the utilization of waste heat but also contributes to the reduction of environmental impact, showcasing a synergistic model that leverages seasonal variations and local climatic conditions for optimized energy efficiency.

In accordance with the data presented in Fig. 3, the annual natural gas consumption for heating purposes has been calculated for approximately 2500 dwellings (living space for 4500 people) for Akkuyu NPP employees and their families, using the annual natural gas consumption of a dwelling for heating purposes. With the indirect recovery of waste heat, the heating needs of 568 dwellings in the living area can be met from waste heat. Of the 67.99% waste heat discharged from the NPP, 57.80% was converted into useful heat (see Table 17).

Figure 5 compares the annual electricity consumption data per capita from the official website of TÜİK with the TEDAŞ sector report. At the same time, if the VAT (18%) rate is added to the June 2022 1 kWh electricity price of 1.593 TL kWh−1 for residential consumers, this amount becomes 1.880 TL kWh−1. In our study, since calculations are made in dollars, the dollar equivalent of this amount is calculated as 0.125 kWh−1. Plant efficiency for electricity distribution and generation is calculated at 88%.

If the annual electricity demand is purchased from the distribution company in the province:

$${\text{Annual electricity consumption }} = {\text{ Usable heat }} \times {\text{ Electricity purchase price per}}\;kWh$$
$$\left(4320831 kWh\right)x\left(0.125\mathrm{ \$ }{kWh}^{-1}\right)=540104\mathrm{ \$}$$

If the waste heat is used to meet the electricity demand, the cost of the used amount is calculated as:

$${\text{Electricity production cost }} = {\text{Usable heat }} \times {\text{ Electricity production price per}}\;kWh$$
$$\mathrm{Electricity production cost }= \left(4320831 kWh\right)x(0.0196\mathrm{ \$ }{kWh}^{-1})= 84688\mathrm{ \$}$$

As a result of the above calculation, if the electricity need in the living area of the power plant is purchased from the distribution company serving in the province, 540,104 $ will be paid. However, if the electricity need is met from waste heat, waste heat worth 84,688 $ will be utilized.

Conclusions

Thermodynamics and thermoeconomic analysis for Türkiye’s first nuclear power plant, Akkuyu Nuclear Power Plant in Mersin were performed in the current study was analyzed. The key parameters such as electricity production cost, annual profit, and depreciation period were calculated using Engineering Equation Solver (EES) software. The important outcomes are grouped as follows:

Economic Efficiency:

  • The electricity cost was calculated as low as $0.0196 per kWh.

  • Annual revenue of $1.82 billion can be generated from the sale of electricity.

  • The amortization period is calculated to be 7–8 years.

Sustainable Energy Utilization:

In addition to reducing environmental impact and costs by using plant waste heat to meet residential heating and hot water needs,

  • An innovative approach in using of waste heat from the plant would satisfy heating demands of 568 households and hot water requirements for 2029 households. The suggested is approach not only recycles 58% of the waste heat (originally around 68%), but also significantly reduces environmental impact, resulting in substantial decrease in thermal pollution by the same margin, and heat discharge is limited to 10%.

  • Compared to the conventional use of natural gas, this method of meeting heating and hot water needs through waste heat recovery represents about a 16% improvement in energy cost efficiency.

Agricultural and Residential Benefits:

  • The region's geographical conditions and livelihood allow by the utilization of about 41% of waste heat (originally around 68%) for greenhouse heating or agricultural drying, thereby enhancing thermal efficiency which is a significant environmental benefit.

  • The waste heat from nuclear power plants constructed in regions with a climate similar to Mersin Akkuyu will serve a significant role in greenhouse farming and agricultural product drying, eliminating the need for additional technological investments.

  • Providing electricity through waste heat recovery instead of purchasing electricity from the distribution company can save about $540,000 per year, which is about %84 improvement in unit energy consumption efficiency.

  • Indirect recycling of the heat from the cycle can meet the electricity needs of 1,521 people and reduce thermal pollution by approximately 60%, with around 8% waste heat released to the environment.

The current study not only leveraging waste heat presents a promising opportunity to enhance economic viability, reduce environmental footprint, and fulfill our responsibility toward sustainable energy practices but may also serve as a benchmark for the nuclear plant to be established in developing countries.

Widespread adoption of waste heat recovery systems in similar facilities is regarded as essential to reduce energy costs and environmental impact. Further optimization studies can be conducted to enhance efficiency and profitability. Long-term studies can also be conducted to assess the sustainability and scalability of waste heat utilization in various contexts.