TY - JOUR
AU1 - El Haj Assad, Mamdouh
AU2 - Aryanfar, Yashar
AU3 - Javaherian, Amirreza
AU4 - Khosravi, Ali
AU5 - Aghaei, Karim
AU6 - Hosseinzadeh, Siamak
AU7 - Pabon, Juan
AU8 - Mahmoudi, SMS
AB - Abstract The need for energy is increasing worldwide as the population has a continuous trend of increase. The restrictions on energy sources are becoming tougher as the authorities set these developed and developing countries. This leads to looking for other alternative energy sources to replace the conventional energy sources, leading to greenhouse emissions. Environmentally friendly energy sources (renewable energies), for example, geothermal, solar and wind, are viewed as clean and sustainable energy sources. Among these kinds of energy sources, geothermal energy is one of the best options because, like solar and wind energy sources, it does not depend on weather conditions. In this work, a single flash geothermal power plant is used to power a transcritical CO2 power plant is proposed. The energy and exergy analysis of the proposed combined power plant has been performed and the best possible operating mode of the power plant has been discussed. The effects of parameters such as separator pressure, CO2 condenser temperature and CO2 turbine inlet pressure and the pinch point on the energy efficiency, exergy efficiency and output power are determined and discussed. Our results indicate that the highest exergy destruction is in the CO2 vapor generator of 182.4 kW followed by the CO2 turbine of 106 kW, then the CO2 condenser of 82.81 kW and then the CO2 pump 58.76 kW. The lowest exergy destruction rates occur in the single flash geothermal power plant components where the separator has exactly zero exergy destruction rate. The results also show that the combined power plant produces more power and has better efficiencies (first law and second law) than the stand-alone geothermal power plant. Finally, Nelder–Mead simplex method is applied to determine the optimal parameters such as separator pressure, power output and pumps input power and second law efficiency. The results show that the power plant should be operated at a lower pinch temperature to reduce damage to the environment. As the condenser pressure increases, the environmental damage effectiveness coefficient decreases sharply until it reaches the minimum value of 1.2 to 1.7 MPa and then starts to increase. The trend of the impact of sports on environmental improvement is exactly the opposite of the trend of the effectiveness of environmental damage. Therefore, from an environmental point of view, it is recommended to operate the gas turbine at a high inlet pressure. 1. INTRODUCTION Nowadays, pollution caused by population growth, increased consumption of energy and fossil fuels usage, the need for energy production from renewable sources or the production of electricity from less valuable heat sources is more prominent [1]. Because of the crisis in the energy and environmental sectors, the use of low-quality heat and renewable energy has recently been the focus of many researchers [2]. Most of the technologies previously used to convert low-grade heat into usable electricity were focused to the solar and geothermal organic Rankine cycle (ORC) [3]. Geothermal energy has been applied for electricity generation [4], district cooling using geothermal absorption chillers [5] and freshwater production by geothermal desalination plants [6]. It is difficult to maximize the output of heat-limited power sources because it relies on evaporation at constant temperature. However, the transcritical cycle has a higher energy production potential than the traditional ORC. Compared with subcritical evaporation at constant temperature, temperature slips above the critical point through a better temperature distribution. Most of the research on the transcritical power cycle has focused on systems that use carbon dioxide. The most important feature of carbon dioxide is its low critical temperature, which in the compression cycle leads to a reduction in system dimensions. Because the supercritical compression cycle of carbon dioxide operates at high pressures, the strength of the materials used in the components increases, which is compensated by reducing the components’ size and also leads to significant heat dissipation in the gas cooler, high latent heat, high thermal conductivity, thermal resistance and low viscosity compared with other refrigerants [7]. Vélez et al. [8] compared the dual power cycle of CO2 with and without an internal heat exchanger. Wang et al. [9] emphasized the matter of energy production from the transcritical carbon dioxide cycle rather than thermal efficiency. They use genetic algorithms (GAs) and artificial neural networks to maximize useful work obtained from a limited heat source with the lowest temperature in a fixed cycle. Baik et al. [10] optimized and compared the power output between the CO2 dual cycle and dual cycle operating with R125. El Haj Assad et al. [11] performed energy and exergy analysis to determine the optimal performance of a single-flash geothermal power plant. A new derivation of the optimum temperature of the separator was obtained that led to the maximum power. Supercritical CO2 Rankine cycle using low-temperature heat source was used instead of a mechanical pump by Lakew et al. [12] to achieve better performance. Chen et al. [13] conducted a low-temperature-driven carbon dioxide transcritical cycle analysis. At the same average thermodynamic heat dissipation temperature, their power output is slightly higher than ORC. Other experimental studies [14, 15] were carried out to verify the viability of the transcritical CO2 cycle. Few studies have been conducted on fluids other than CO2 used in supercritical cycles driven by low heat sources. Cayer et al. [16] points out that R125 and ethane can be used as working fluids for transcritical cycles driven by low-grade heat sources. In a study, Zare [17] studied and compared the thermodynamics and thermodynamic economics of the simple Rankine cycle, the Rankine cycle using a heat exchanger installed internally and the recycled Rankine cycle of three working fluids. The best cycle efficiency was achieved in Rankine cycle using that heat exchanger. Compared with other cycles, the simple Rankine cycle is evaluated as the most economical option. Shokati et al. [18] in a study investigated thermodynamics and compared the performance of two cycles of geothermal power evaporation, single-stage-Rankine and two-stage evaporation for four operating fluids R141b, R113, N-heptane and water vapor. As a result, Rankine’s single evaporation cycle has the highest value in the first and second laws of thermodynamics. However, the two-stage evaporation cycle is economically preferable. In another study, Shokati et al. [19] analyzed exergo-economic analysis and compared the performance of the ORC, the double ORC, Kalina and the double pressure Rankine cycle with internal heat exchangers. According to this study, the dual-pressure ORC has the highest production capacity, and the Kalina cycle has the most economical cycle under study. In a study, Yari et al. [20] compared and analyzed the organic Rankin cycle, the Kalina cycle and the 3D Rankine cycle for low-temperature heat sources. In this study, the 3D Rankine cycle had better productivity than other cycles. Ameri et al. [21] analyzed energy and exergy and optimized the two-stage instant evaporation cycle for the Sabalan geothermal powerhouse during a study. During this study, the two-stage evaporation cycle has shown better ends up in terms of the primary law and power generation than the instantaneous one-stage evaporation. Hoseinzadeh and Stephan Heyns [22] investigated the energy cycle that combined greenhouse gas emissions and heat sources to produce the reverse osmosis desalination energy needed to produce fresh water. The optimum inlet discharge rate of the antibacterial generator is 62% of the desalination system brine outlet discharge rate. In addition, compared with the typical situation where 100% of the brine discharged from the desalination system enters the disinfectant generator, the total cost ratio is reduced by 10%. Gholizadeh et al. [23] has launched a new three-generation system for the production of fresh water, electricity and cooling, using a 170°C flash steam binary geothermal source. In this designed three-phase system, the humidification and dehumidification device were used as a binary cycle. Then, they applied the GA method to optimize the system performance by establishing different optimization modes. Mohammadi and Mehrpooya [24] added a Kalina cycles unit and reverse osmosis unit to a double flash geothermal heat source to produce heating, cooling, desalination and power. They point out that the separator pressure is an important parameter of the proposed system plan and needs to be considered when optimizing the configuration. Today, project developers assume certain operating conditions of the plant based on the life requirements of the project. These operating conditions laid the foundation for the thermal and mechanical design of the waste heat recovery boiler. In addition, economic demands such as fuel costs and energy prices are constantly changing operating conditions. These changes in operating conditions may cause the operating profile of the system to be different from the profile assumed during the design phase [25, 26]. In recent years, a large amount of waste heat such as flue gas generated by combined cycles and power plants has been distributed to the environment, causing pollution to surrounding areas. Therefore, efforts must be made to recover waste heat and use renewable energy to reduce the consumption of fossil fuels in order to solve environmental problems. We also need to find a suitable method to optimize and improve the efficiency and performance of thermal power systems. However, craftsmen, governments and scholars have observed an increase in the use and understanding of energy, exergy, economic, and exergoenvironmental analyses methods. The main reason for this type of analysis in thermal energy systems and power plants is to minimize entropy production and cycle irreversibility, which ultimately leads to improved combined cycle efficiency. Efficiency is the standard for economic evaluation of initial investment, fuel and operating costs [27, 28]. In this research, the energy, exergy, economic and environmental analysis of a power generation system using a combined geothermal heat source with transcritical carbon dioxide cycle has been investigated. The effect of important parameters such as separator pressure and inlet pressure of carbon dioxide turbine on system performance in order to determine the optimal operating point has been investigated and in addition to the basic state, the optimal state of the system has been investigated using the Nelder–Mead simplex algorithm. The results are presented. From the above discussion, we can conclude that a CO2 cycle using low-grade heat more effectively can meet the diverse needs of power plants for exhaust energy recovery. According to a review of the literature, it is observed that most geothermal systems based on recycling cycles are focused on the production of electricity. However, the preliminary conceptual design of a transcritical carbon dioxide cycle powered by a single-flash geothermal power plant has not been specifically studied. With this in mind, this paper conceptually designs a new transcritical carbon dioxide cycle powered by a single-flash geothermal power plant. The mathematical model of the 4E analysis system is established in detail. The main novelties and objectives of the current work are multifaceted, which can be summarized as follows: analyze and compare the performance of a single flash transcritical CO2 geothermal system with a single flash basic geothermal cycle; perform a complete comparison of the two cycles from thermodynamic, economic and environmental points of view; investigate the impact of key parameters on overall system performance, such as power produced, energy and exergy efficiency; optimize the system based on the GA and the Nelder–Mead simplex method and find the best system performance and reduce the exergy destruction rate of components. 2. SYSTEM ANALYZING Figure 1 shows the single flash geothermal power plant’s schematic diagram, where the active geofluid is water. The principal ingredients of a single flash plant are the production well, expansion valve, separator, turbine, condenser, pump and injection well. This power plant will be used to power the transcritical cycle of CO2, which will be discussed in detail below. Single flash geothermal power plant. Figure 1 Open in new tabDownload slide Figure 1 Single flash geothermal power plant. Open in new tabDownload slide Geothermal/transcritical CO2 hybrid power plant. Figure 2 Open in new tabDownload slide Figure 2 Geothermal/transcritical CO2 hybrid power plant. Open in new tabDownload slide In the power plant presented in Figure 2, the hot geofluid (water) in the saturated liquid state enters the cycle from the production well (State 1). After expanding it via expansion valve, State 2, it enters the adiabatic separator in the form of a saturated mixture. The saturated liquid and saturated vapor phases of the working liquid are separated from each other, and the saturated vapor leaves the separator in State 3 and the saturated liquid leaves the separator in State 4. Saturated fluid enters the turbine and generates work, then leaves it at State 5. Also, the saturated liquid (State 4) moves toward the vapor generator (VG) heat exchanger, and after supplying the required heat of the trans-critical carbon dioxide cycle, it leaves the VG at State 8. In condenser 1, the working fluid loses a certain amount of heat and leaves it as a saturated liquid at State 6. Finally, by pumping the fluid and combining it with State 8, the geothermal fluid returns to the ground through the discharge pipes and the cycle completes. In the trans-critical carbon dioxide cycle, the working fluid enters the VG heat exchanger from State 9 and receives heat up to State 10 from the other side flow. Then it generates power in Turbine 2 and cools in Condenser 2 to the saturated liquid phase (State 12). Finally, by pumping the fluid to State 9, the trans-critical carbon dioxide cycle completes. For simulation purposes, we assume some initial input data that was used due to the cycle description presented above. The working fluid of the geothermal cycle’s entering temperature from the production well is 170°C with 10 kg/s of mass flow rate. At State 2, the pressure is reduced to 500 kPa through an expansion valve. Furthermore, the isentropic turbine efficiency and outlet pressure are 80% and 20 KPa, respectively [29]. The inlet pressure of the working fluid to the CO2 transcritical turbine is assumed to be 15 MPa. Furthermore, the isentropic efficiency of the turbine is the same as that of the geothermal cycle. The temperature difference between State 4 and State 10 in the steam generator heat exchanger is 10°C. The pressure loss in the connecting pipe and the heat exchanger is ignored, and it is assumed that all component processes are a steady state flow in steady state. Temperature and entropy diagrams of stand-alone single-flare geothermal power plants and transcritical CO2 power plants are shown in Figure 3 and Figure 4, respectively. T-s diagram of single flash geothermal power plant. Figure 3 Open in new tabDownload slide Figure 3 T-s diagram of single flash geothermal power plant. Open in new tabDownload slide T-s diagram of CO2 power plant. Figure 4 Open in new tabDownload slide Figure 4 T-s diagram of CO2 power plant. Open in new tabDownload slide 2.1. Thermodynamic analysis In the current simulation, these assumptions will be used: ▪ all processes are steady state; ▪ pressure losses are neglected; ▪ separator is adiabatic; ▪ pumps and turbines are not isentropic; ▪ dead state is P = 101.3 kPa and T = 20°C. The mass balance of each component of the cycle can be described as follows from the viewpoint of conservation of mass: $$\begin{equation} \sum{\dot{m}}_i=\sum{\dot{m}}_e. \end{equation}$$(1) The energy balance for any components of the system can be expressed as $$\begin{equation} \sum \dot{Q}+\sum{\dot{m}}_i{h}_i=\sum \dot{W}+\sum{\dot{m}}_e{h}_e. \end{equation}$$(2) The output power of the turbine is written with specific input and output enthalpies as $$\begin{equation} {\dot{\mathrm{W}}}_{\mathrm{tur}}={\dot{\mathrm{m}}}_{\mathrm{i}}\left({\mathrm{h}}_{\mathrm{i}}-{\mathrm{h}}_{\mathrm{e}}\right), \end{equation}$$(3) where h is the specific enthalpy and the subscripts i and e refer to the input and output states. The isentropic efficiency of the turbine is defined as $$\begin{equation} {\upeta}_{\mathrm{tur}}=\frac{{\mathrm{h}}_{\mathrm{i}}-{\mathrm{h}}_{\mathrm{e},\mathrm{s}}}{{\mathrm{h}}_{\mathrm{i}}-{\mathrm{h}}_{\mathrm{e}}}, \end{equation}$$(4) where |${h}_{e,s}$| is the isentropic specific enthalpy at the turbine exit. The pump power and its isentropic efficiency are expressed as $$\begin{equation} {\dot{\mathrm{W}}}_{\mathrm{pump}}={\dot{\mathrm{m}}}_{\mathrm{i}}\left({\mathrm{h}}_{\mathrm{e}}-{\mathrm{h}}_{\mathrm{i}}\right) \end{equation}$$(5) $$\begin{equation} {\upeta}_{\mathrm{pump}}=\frac{{\mathrm{h}}_{\mathrm{i}}-{\mathrm{h}}_{\mathrm{e}}}{{\mathrm{h}}_{\mathrm{i}}-{\mathrm{h}}_{\mathrm{e},\mathrm{s}}}. \end{equation}$$(6) The exergy rate is defined as $$\begin{equation} \dot{\mathrm{Ex}}=\dot{\mathrm{m}}\left(\mathrm{h}-{\mathrm{h}}_0-{\mathrm{T}}_0\left(\mathrm{s}-{\mathrm{s}}_0\right)\right), \end{equation}$$(7) where |${h}_o$| is the specific enthalpy and |${s}_o$| is the specific entropy at the reference temperature |${T}_O$| and pressure |${P}_O$|⁠.The exergy rate balance for any component of the power plant is written as $$\begin{equation} {\dot{Ex}}_{heat}+\sum \dot{Ex_i}=\sum \dot{Ex_e}+\dot{W}+{\dot{Ex}}_D. \end{equation}$$(8) The rate of exergy destruction is obtained as $$\begin{equation} {\dot{Ex}}_D={\dot{Ex}}_f-{\dot{Ex}}_p. \end{equation}$$(9) The component exergy efficiency can be defined as the ratio of exit exergy rate to inlet exergy rate, which is expressed as $$\begin{equation} {\upeta}_{ex\ i}=\frac{{\dot{Ex}}_{p\ i}}{{\dot{Ex}}_{f\ i}}. \end{equation}$$(10) The ratio of exergy destruction rate of the whole power plant is defined as $$\begin{equation} {\mathrm{Y}}_{D\ i}=\frac{{\dot{Ex}}_{D\ i}}{{\dot{Ex}}_{D\ total}}. \end{equation}$$(11) Table 1 shows the balances of energy and exergy for each component of the power plant. Energy and exergy balances of the hybrid system components. Table 1 Energy and exergy balances of the hybrid system components. Component . Exergy balance . Energy balance . Expansion valve |${\dot{Ex}}_{D, ev}={\dot{Ex}}_1-{\dot{Ex}}_2$| |${h}_1={h}_2$| Separator |${\dot{Ex}}_{D, sep}={\dot{Ex}}_2-{\dot{Ex}}_3-{\dot{Ex}}_4$| |${h}_3={h}_{2g}$| |${h}_4={h}_{2l}$| Steam turbine |${\dot{Ex}}_{D, steam, tur}={\dot{Ex}}_3-{\dot{Ex}}_5-{\dot{W}}_{steam, tur}$| |${\dot{W}}_{steam, tur}={\dot{m}}_3\big({h}_3-{h}_5\big)$|,|${\eta}_{tur}=\frac{h_3-{h}_5}{h_3-{h}_{5S}}$| Condenser 1 |${\dot{Ex}}_{D, cond1}=\big(\ {\dot{Ex}}_5-{\dot{Ex}}_6\big)-{\dot{Q}}_{cond1}\big(1-\frac{{\mathrm{T}}_0}{{\mathrm{T}}_6}\big)$| |${\dot{Q}}_{cond1}={\dot{m}}_5\big({h}_5-{h}_6\big)$| Pump1 |${\dot{Ex}}_{D, pump1}={\dot{W}}_{pump1}-\big(\ {\dot{Ex}}_7-{\dot{Ex}}_6\big)$| |${\dot{W}}_{pump1}={\dot{m}}_6\big({h}_7-{h}_6\big)$|,|${\eta}_{pump}=\frac{h_6-{h}_{7S}}{h_6-{h}_7}$| VG |${\dot{Ex}}_{D, eva}=\big(\ {\dot{Ex}}_4-{\dot{Ex}}_8\big)-\big(\ {\dot{Ex}}_{10}-{\dot{Ex}}_9\big)$| |${\dot{Q}}_{eva}={\dot{m}}_4\big({h}_4-{h}_8\big)$|,|${\dot{Q}}_{eva}={\dot{m}}_{10}\big({h}_{10}-{h}_9\big)$| |${\Delta \mathrm{T}}_{\mathrm{Pinch},\mathrm{VG}}={T}_4-{T}_{10}$| |${\Delta \mathrm{T}}_{\mathrm{Pinch},\mathrm{VG}}={T}_8-{T}_9$| CO2 Turbine |${\dot{Ex}}_{D, CO2, tur}={\dot{Ex}}_{10}-{\dot{Ex}}_{11}-{\dot{W}}_{CO2, tur}$| |${\dot{W}}_{CO2, tur}={\dot{m}}_{10}\big({h}_{10}-{h}_{11}\big)$|,|${\eta}_{tur}=\frac{h_{10}-{h}_{11}}{h_{10}-{h}_{11S}}$| Condenser 2 |${\dot{Ex}}_{D, cond2}=\big(\ {\dot{Ex}}_{11}-{\dot{Ex}}_{12}\big)-{\dot{Q}}_{cond1}\Big(1-\frac{{\mathrm{T}}_0}{{\mathrm{T}}_{12}}\Big)$| |${\dot{Q}}_{cond2}={\dot{m}}_{11}\big({h}_{11}-{h}_{12}\big)$| Pump2 |${\dot{Ex}}_{D, pump2}={\dot{W}}_{pump2}-\big(\ {\dot{Ex}}_9-{\dot{Ex}}_{12}\big)$| |${\dot{W}}_{pump2}={\dot{m}}_{12}\big({h}_9-{h}_{12}\big)$|, |${\eta}_{pump}=\frac{h_{12}-{h}_{9S}}{h_{12}-{h}_9}$| Component . Exergy balance . Energy balance . Expansion valve |${\dot{Ex}}_{D, ev}={\dot{Ex}}_1-{\dot{Ex}}_2$| |${h}_1={h}_2$| Separator |${\dot{Ex}}_{D, sep}={\dot{Ex}}_2-{\dot{Ex}}_3-{\dot{Ex}}_4$| |${h}_3={h}_{2g}$| |${h}_4={h}_{2l}$| Steam turbine |${\dot{Ex}}_{D, steam, tur}={\dot{Ex}}_3-{\dot{Ex}}_5-{\dot{W}}_{steam, tur}$| |${\dot{W}}_{steam, tur}={\dot{m}}_3\big({h}_3-{h}_5\big)$|,|${\eta}_{tur}=\frac{h_3-{h}_5}{h_3-{h}_{5S}}$| Condenser 1 |${\dot{Ex}}_{D, cond1}=\big(\ {\dot{Ex}}_5-{\dot{Ex}}_6\big)-{\dot{Q}}_{cond1}\big(1-\frac{{\mathrm{T}}_0}{{\mathrm{T}}_6}\big)$| |${\dot{Q}}_{cond1}={\dot{m}}_5\big({h}_5-{h}_6\big)$| Pump1 |${\dot{Ex}}_{D, pump1}={\dot{W}}_{pump1}-\big(\ {\dot{Ex}}_7-{\dot{Ex}}_6\big)$| |${\dot{W}}_{pump1}={\dot{m}}_6\big({h}_7-{h}_6\big)$|,|${\eta}_{pump}=\frac{h_6-{h}_{7S}}{h_6-{h}_7}$| VG |${\dot{Ex}}_{D, eva}=\big(\ {\dot{Ex}}_4-{\dot{Ex}}_8\big)-\big(\ {\dot{Ex}}_{10}-{\dot{Ex}}_9\big)$| |${\dot{Q}}_{eva}={\dot{m}}_4\big({h}_4-{h}_8\big)$|,|${\dot{Q}}_{eva}={\dot{m}}_{10}\big({h}_{10}-{h}_9\big)$| |${\Delta \mathrm{T}}_{\mathrm{Pinch},\mathrm{VG}}={T}_4-{T}_{10}$| |${\Delta \mathrm{T}}_{\mathrm{Pinch},\mathrm{VG}}={T}_8-{T}_9$| CO2 Turbine |${\dot{Ex}}_{D, CO2, tur}={\dot{Ex}}_{10}-{\dot{Ex}}_{11}-{\dot{W}}_{CO2, tur}$| |${\dot{W}}_{CO2, tur}={\dot{m}}_{10}\big({h}_{10}-{h}_{11}\big)$|,|${\eta}_{tur}=\frac{h_{10}-{h}_{11}}{h_{10}-{h}_{11S}}$| Condenser 2 |${\dot{Ex}}_{D, cond2}=\big(\ {\dot{Ex}}_{11}-{\dot{Ex}}_{12}\big)-{\dot{Q}}_{cond1}\Big(1-\frac{{\mathrm{T}}_0}{{\mathrm{T}}_{12}}\Big)$| |${\dot{Q}}_{cond2}={\dot{m}}_{11}\big({h}_{11}-{h}_{12}\big)$| Pump2 |${\dot{Ex}}_{D, pump2}={\dot{W}}_{pump2}-\big(\ {\dot{Ex}}_9-{\dot{Ex}}_{12}\big)$| |${\dot{W}}_{pump2}={\dot{m}}_{12}\big({h}_9-{h}_{12}\big)$|, |${\eta}_{pump}=\frac{h_{12}-{h}_{9S}}{h_{12}-{h}_9}$| Open in new tab Table 1 Energy and exergy balances of the hybrid system components. Component . Exergy balance . Energy balance . Expansion valve |${\dot{Ex}}_{D, ev}={\dot{Ex}}_1-{\dot{Ex}}_2$| |${h}_1={h}_2$| Separator |${\dot{Ex}}_{D, sep}={\dot{Ex}}_2-{\dot{Ex}}_3-{\dot{Ex}}_4$| |${h}_3={h}_{2g}$| |${h}_4={h}_{2l}$| Steam turbine |${\dot{Ex}}_{D, steam, tur}={\dot{Ex}}_3-{\dot{Ex}}_5-{\dot{W}}_{steam, tur}$| |${\dot{W}}_{steam, tur}={\dot{m}}_3\big({h}_3-{h}_5\big)$|,|${\eta}_{tur}=\frac{h_3-{h}_5}{h_3-{h}_{5S}}$| Condenser 1 |${\dot{Ex}}_{D, cond1}=\big(\ {\dot{Ex}}_5-{\dot{Ex}}_6\big)-{\dot{Q}}_{cond1}\big(1-\frac{{\mathrm{T}}_0}{{\mathrm{T}}_6}\big)$| |${\dot{Q}}_{cond1}={\dot{m}}_5\big({h}_5-{h}_6\big)$| Pump1 |${\dot{Ex}}_{D, pump1}={\dot{W}}_{pump1}-\big(\ {\dot{Ex}}_7-{\dot{Ex}}_6\big)$| |${\dot{W}}_{pump1}={\dot{m}}_6\big({h}_7-{h}_6\big)$|,|${\eta}_{pump}=\frac{h_6-{h}_{7S}}{h_6-{h}_7}$| VG |${\dot{Ex}}_{D, eva}=\big(\ {\dot{Ex}}_4-{\dot{Ex}}_8\big)-\big(\ {\dot{Ex}}_{10}-{\dot{Ex}}_9\big)$| |${\dot{Q}}_{eva}={\dot{m}}_4\big({h}_4-{h}_8\big)$|,|${\dot{Q}}_{eva}={\dot{m}}_{10}\big({h}_{10}-{h}_9\big)$| |${\Delta \mathrm{T}}_{\mathrm{Pinch},\mathrm{VG}}={T}_4-{T}_{10}$| |${\Delta \mathrm{T}}_{\mathrm{Pinch},\mathrm{VG}}={T}_8-{T}_9$| CO2 Turbine |${\dot{Ex}}_{D, CO2, tur}={\dot{Ex}}_{10}-{\dot{Ex}}_{11}-{\dot{W}}_{CO2, tur}$| |${\dot{W}}_{CO2, tur}={\dot{m}}_{10}\big({h}_{10}-{h}_{11}\big)$|,|${\eta}_{tur}=\frac{h_{10}-{h}_{11}}{h_{10}-{h}_{11S}}$| Condenser 2 |${\dot{Ex}}_{D, cond2}=\big(\ {\dot{Ex}}_{11}-{\dot{Ex}}_{12}\big)-{\dot{Q}}_{cond1}\Big(1-\frac{{\mathrm{T}}_0}{{\mathrm{T}}_{12}}\Big)$| |${\dot{Q}}_{cond2}={\dot{m}}_{11}\big({h}_{11}-{h}_{12}\big)$| Pump2 |${\dot{Ex}}_{D, pump2}={\dot{W}}_{pump2}-\big(\ {\dot{Ex}}_9-{\dot{Ex}}_{12}\big)$| |${\dot{W}}_{pump2}={\dot{m}}_{12}\big({h}_9-{h}_{12}\big)$|, |${\eta}_{pump}=\frac{h_{12}-{h}_{9S}}{h_{12}-{h}_9}$| Component . Exergy balance . Energy balance . Expansion valve |${\dot{Ex}}_{D, ev}={\dot{Ex}}_1-{\dot{Ex}}_2$| |${h}_1={h}_2$| Separator |${\dot{Ex}}_{D, sep}={\dot{Ex}}_2-{\dot{Ex}}_3-{\dot{Ex}}_4$| |${h}_3={h}_{2g}$| |${h}_4={h}_{2l}$| Steam turbine |${\dot{Ex}}_{D, steam, tur}={\dot{Ex}}_3-{\dot{Ex}}_5-{\dot{W}}_{steam, tur}$| |${\dot{W}}_{steam, tur}={\dot{m}}_3\big({h}_3-{h}_5\big)$|,|${\eta}_{tur}=\frac{h_3-{h}_5}{h_3-{h}_{5S}}$| Condenser 1 |${\dot{Ex}}_{D, cond1}=\big(\ {\dot{Ex}}_5-{\dot{Ex}}_6\big)-{\dot{Q}}_{cond1}\big(1-\frac{{\mathrm{T}}_0}{{\mathrm{T}}_6}\big)$| |${\dot{Q}}_{cond1}={\dot{m}}_5\big({h}_5-{h}_6\big)$| Pump1 |${\dot{Ex}}_{D, pump1}={\dot{W}}_{pump1}-\big(\ {\dot{Ex}}_7-{\dot{Ex}}_6\big)$| |${\dot{W}}_{pump1}={\dot{m}}_6\big({h}_7-{h}_6\big)$|,|${\eta}_{pump}=\frac{h_6-{h}_{7S}}{h_6-{h}_7}$| VG |${\dot{Ex}}_{D, eva}=\big(\ {\dot{Ex}}_4-{\dot{Ex}}_8\big)-\big(\ {\dot{Ex}}_{10}-{\dot{Ex}}_9\big)$| |${\dot{Q}}_{eva}={\dot{m}}_4\big({h}_4-{h}_8\big)$|,|${\dot{Q}}_{eva}={\dot{m}}_{10}\big({h}_{10}-{h}_9\big)$| |${\Delta \mathrm{T}}_{\mathrm{Pinch},\mathrm{VG}}={T}_4-{T}_{10}$| |${\Delta \mathrm{T}}_{\mathrm{Pinch},\mathrm{VG}}={T}_8-{T}_9$| CO2 Turbine |${\dot{Ex}}_{D, CO2, tur}={\dot{Ex}}_{10}-{\dot{Ex}}_{11}-{\dot{W}}_{CO2, tur}$| |${\dot{W}}_{CO2, tur}={\dot{m}}_{10}\big({h}_{10}-{h}_{11}\big)$|,|${\eta}_{tur}=\frac{h_{10}-{h}_{11}}{h_{10}-{h}_{11S}}$| Condenser 2 |${\dot{Ex}}_{D, cond2}=\big(\ {\dot{Ex}}_{11}-{\dot{Ex}}_{12}\big)-{\dot{Q}}_{cond1}\Big(1-\frac{{\mathrm{T}}_0}{{\mathrm{T}}_{12}}\Big)$| |${\dot{Q}}_{cond2}={\dot{m}}_{11}\big({h}_{11}-{h}_{12}\big)$| Pump2 |${\dot{Ex}}_{D, pump2}={\dot{W}}_{pump2}-\big(\ {\dot{Ex}}_9-{\dot{Ex}}_{12}\big)$| |${\dot{W}}_{pump2}={\dot{m}}_{12}\big({h}_9-{h}_{12}\big)$|, |${\eta}_{pump}=\frac{h_{12}-{h}_{9S}}{h_{12}-{h}_9}$| Open in new tab Input parameters. Table 2 Input parameters. Parameters . Values . Reference . Geothermal water tempretaure T1 170°C [29] Geothermal water flowrate |$\dot{m}$|1 10 kg/s [29] Geothermal water pressure P1 Saturated Separator pressure P2 500 kPa [29] Steam turbine outlet pressure P5 20 kPa [29] CO2 turbine inlet pressure P10 15000 kPa CO2 condenser temprature Tcond 30°C Turbine isentropic efficiency|${\eta}_{tur}$| 80% Pump isentropic efficiency|${\eta}_{pump}$| 75% Evaporator inlet outlet difference temperature, ΔTTTD,eva 20°C Parameters . Values . Reference . Geothermal water tempretaure T1 170°C [29] Geothermal water flowrate |$\dot{m}$|1 10 kg/s [29] Geothermal water pressure P1 Saturated Separator pressure P2 500 kPa [29] Steam turbine outlet pressure P5 20 kPa [29] CO2 turbine inlet pressure P10 15000 kPa CO2 condenser temprature Tcond 30°C Turbine isentropic efficiency|${\eta}_{tur}$| 80% Pump isentropic efficiency|${\eta}_{pump}$| 75% Evaporator inlet outlet difference temperature, ΔTTTD,eva 20°C Open in new tab Table 2 Input parameters. Parameters . Values . Reference . Geothermal water tempretaure T1 170°C [29] Geothermal water flowrate |$\dot{m}$|1 10 kg/s [29] Geothermal water pressure P1 Saturated Separator pressure P2 500 kPa [29] Steam turbine outlet pressure P5 20 kPa [29] CO2 turbine inlet pressure P10 15000 kPa CO2 condenser temprature Tcond 30°C Turbine isentropic efficiency|${\eta}_{tur}$| 80% Pump isentropic efficiency|${\eta}_{pump}$| 75% Evaporator inlet outlet difference temperature, ΔTTTD,eva 20°C Parameters . Values . Reference . Geothermal water tempretaure T1 170°C [29] Geothermal water flowrate |$\dot{m}$|1 10 kg/s [29] Geothermal water pressure P1 Saturated Separator pressure P2 500 kPa [29] Steam turbine outlet pressure P5 20 kPa [29] CO2 turbine inlet pressure P10 15000 kPa CO2 condenser temprature Tcond 30°C Turbine isentropic efficiency|${\eta}_{tur}$| 80% Pump isentropic efficiency|${\eta}_{pump}$| 75% Evaporator inlet outlet difference temperature, ΔTTTD,eva 20°C Open in new tab The whole system exergy efficiency is written as $$\begin{equation} {\upeta}_{ex, sys}={\dot{W}}_{net}/{Ex}_{in}, \end{equation}$$(12) where the net power of the hybrid system is function of pressure and evaporator temperature difference; hence, we can write |${\dot{W}}_{net}\big(\ {P}_2,{P}_{10},{\varDelta T}_{Pinch, VG}\big)$| and the operating pressures and evaporator pinch point are considered in the following ranges, respectively as $$ 200<{P}_2(kPa)<600 $$ $$ 12000<{P}_{10}(kPa)<1800 $$ $$ 5{}^{\circ}C<{\varDelta T}_{Pinch, VG}<20{}^{\circ}C $$ The input parameters necessary to perform the energy and exergy analyses of the plant are presented in Table 2. 2.2. Economic analysis This section presents the mathematical formulas needed to advance the economic analysis of power plants. Tables 3 and 4 show the capital investment and invested economic parameters for each component of each power plant. As can be seen from Table 3, the cost function of power components such as turbines and pumps is a function of the power of the components, while the cost function of heat exchangers is a function of the surface area of the heat exchanger. Costs of capital investment cost for different power plant components [ 30]. Table 3 Costs of capital investment cost for different power plant components [ 30]. Component . Cost functions . Turbine |$4405\ast{{\dot{W}}_T}^{0.89}$| Pump |$1120\ast{{\dot{W}}_p}^{0.8}$| Condenser |$1397\ast{A_{CD}}^{0.89}$| VG |$1397\ast{A_{VG}}^{0.514}$| Component . Cost functions . Turbine |$4405\ast{{\dot{W}}_T}^{0.89}$| Pump |$1120\ast{{\dot{W}}_p}^{0.8}$| Condenser |$1397\ast{A_{CD}}^{0.89}$| VG |$1397\ast{A_{VG}}^{0.514}$| Open in new tab Table 3 Costs of capital investment cost for different power plant components [ 30]. Component . Cost functions . Turbine |$4405\ast{{\dot{W}}_T}^{0.89}$| Pump |$1120\ast{{\dot{W}}_p}^{0.8}$| Condenser |$1397\ast{A_{CD}}^{0.89}$| VG |$1397\ast{A_{VG}}^{0.514}$| Component . Cost functions . Turbine |$4405\ast{{\dot{W}}_T}^{0.89}$| Pump |$1120\ast{{\dot{W}}_p}^{0.8}$| Condenser |$1397\ast{A_{CD}}^{0.89}$| VG |$1397\ast{A_{VG}}^{0.514}$| Open in new tab Values used in economic analysis [ 30]. Table 4 Values used in economic analysis [ 30]. Parameter . Value . N 7300 hours I 14% N 15 years |$\varphi$| 1.06 Parameter . Value . N 7300 hours I 14% N 15 years |$\varphi$| 1.06 Open in new tab Table 4 Values used in economic analysis [ 30]. Parameter . Value . N 7300 hours I 14% N 15 years |$\varphi$| 1.06 Parameter . Value . N 7300 hours I 14% N 15 years |$\varphi$| 1.06 Open in new tab The balance of the cost rate for the total system is expressed as [30]. $$\begin{equation} {\dot{C}}_{tot}={\dot{C}}_{fuel}+\sum_k{\dot{\Big(Z}}_{CI}+{\dot{Z}}_{O\&M}\Big){}_k, \end{equation}$$(13) where |${\dot{C}}_{tot}$| is the total cost rate, |${\dot{C}}_{fuel}$| is the fuel cost rate, |${\dot{Z}}_{CI}$| is the cost rate of capital investment and |${\dot{Z}}_{O\&M}$| is the cost rate of operation and maintenance, which is given as [21]. $$\begin{equation} {\dot{Z}}_{CI,k}+{\dot{Z}}_{O\&M,k}=\frac{{\dot{Z}}_k\ast \varphi }{N\ast 3600} CRF, \end{equation}$$(14) where |${\dot{Z}}_k$| is the cost rate of the capital investment for component k, N is the number of hours in a year, |$\varphi$| is the maintenance factor and CRF is the capital recovery factor that is expressed as [21]. $$\begin{equation} CRF=\frac{i{\left(1+i\right)}^n}{{\left(1+i\right)}^n-1}, \end{equation}$$(15) where i is the annual interest rate and n is the power plant lifetime. Among the important parameters in the economic analysis is the levelized energy cost (LEC), which is estimated as $$\begin{equation} LEC=\frac{CRF\ast{\dot{C}}_{tot}+{C}_{om}}{{\dot{W}}_{net}\ast{t}_{op}}, \end{equation}$$(16) where |${\dot{W}}_{net}$| is the net power output of the power plant; Com is the operation and maintenance cost, which is assumed to be 1.5% of |${\dot{C}}_{tot}$|⁠; and |${t}_{op}$| is the annual operation time, which is assumed to be 7300 hours. 2.3. Exergo-environmental analysis The exergo-environmental evaluation can be used to predict the performance of the proposed hybrid plant from environmental factor of view. The exergue-environmental evaluation is based totally on using exergy analysis; in other phrases, it takes into consideration the total exergy destruction rate, input and outlet exergy rate. The factor that describes the power plant performance based on environmental effects is called exergo-environmental factor, which is defines as $$\begin{equation} {f}_{ei}=\frac{Ex_{tot, des}}{\sum{Ex}_{in}}. \end{equation}$$(17) The exergy stability factor is expressed as $$\begin{equation} {f}_{es}=\frac{Ex_{tot, des}}{{E\mathrm{x}}_{tot, out}+{Ex}_{tot, des}+1}. \end{equation}$$(18) It can be seen from the two equations above that these factors depend on the total rate of exergy loss. The exergo-environmental impact of the exergy is expressed by the efficiency of the exergy as $$\begin{equation} {C}_{ei}=\frac{1}{\eta_{ex}}. \end{equation}$$(19) The environmental damage effectiveness factor is given as $$\begin{equation} {\uptheta}_{ei}={f}_{ei}.{C}_{ei}. \end{equation}$$(20) The positive impact of the environment on the power plant performance is expressed by the inverse of the environmental damage effectiveness factor is called exergoenvironmental impact enhancement, which is defined as $$\begin{equation} {\uptheta}_{ei i}=\frac{1}{\uptheta_{ei}}. \end{equation}$$(21) 3. RESULTS AND DISCUSSIONS The accuracy of EES software used in this study is checked by calculating the inlet specific enthalpy, pressure and temperature at the inlet of the evaporator, turbine, condenser and pump for the CO2 gas cycle. These parameters are then compared with the results obtained from [31] as shown in Table 5, which shows an acceptable match with those obtained in the present study. Validation of the current work result with [ 31]. Table 5 Validation of the current work result with [ 31]. . gas . T (°C) . P (MPa) . h (kJ/kg) . State |$\mathrm{C}{\mathrm{O}}_2$| Ref [31] Present work Ref [31] Present work Ref [31] Present work VG |$\mathrm{C}{\mathrm{O}}_2$| −41.18 −41.18 12.6316 12.6316 113.00 113.01 |$\mathrm{Turbine}\ \mathrm{inlet}$| |$\mathrm{C}{\mathrm{O}}_2$| 120.00 120.00 12.0000 12.0000 519.68 519.68 Condenser inlet |$\mathrm{C}{\mathrm{O}}_2$| −46.00 −46.00 0.8000 0.8000 425.40 425.40 Pump inlet |$\mathrm{C}{\mathrm{O}}_2$| −47.31 −47.31 0.7600 0.7600 98.27 98.28 . gas . T (°C) . P (MPa) . h (kJ/kg) . State |$\mathrm{C}{\mathrm{O}}_2$| Ref [31] Present work Ref [31] Present work Ref [31] Present work VG |$\mathrm{C}{\mathrm{O}}_2$| −41.18 −41.18 12.6316 12.6316 113.00 113.01 |$\mathrm{Turbine}\ \mathrm{inlet}$| |$\mathrm{C}{\mathrm{O}}_2$| 120.00 120.00 12.0000 12.0000 519.68 519.68 Condenser inlet |$\mathrm{C}{\mathrm{O}}_2$| −46.00 −46.00 0.8000 0.8000 425.40 425.40 Pump inlet |$\mathrm{C}{\mathrm{O}}_2$| −47.31 −47.31 0.7600 0.7600 98.27 98.28 Open in new tab Table 5 Validation of the current work result with [ 31]. . gas . T (°C) . P (MPa) . h (kJ/kg) . State |$\mathrm{C}{\mathrm{O}}_2$| Ref [31] Present work Ref [31] Present work Ref [31] Present work VG |$\mathrm{C}{\mathrm{O}}_2$| −41.18 −41.18 12.6316 12.6316 113.00 113.01 |$\mathrm{Turbine}\ \mathrm{inlet}$| |$\mathrm{C}{\mathrm{O}}_2$| 120.00 120.00 12.0000 12.0000 519.68 519.68 Condenser inlet |$\mathrm{C}{\mathrm{O}}_2$| −46.00 −46.00 0.8000 0.8000 425.40 425.40 Pump inlet |$\mathrm{C}{\mathrm{O}}_2$| −47.31 −47.31 0.7600 0.7600 98.27 98.28 . gas . T (°C) . P (MPa) . h (kJ/kg) . State |$\mathrm{C}{\mathrm{O}}_2$| Ref [31] Present work Ref [31] Present work Ref [31] Present work VG |$\mathrm{C}{\mathrm{O}}_2$| −41.18 −41.18 12.6316 12.6316 113.00 113.01 |$\mathrm{Turbine}\ \mathrm{inlet}$| |$\mathrm{C}{\mathrm{O}}_2$| 120.00 120.00 12.0000 12.0000 519.68 519.68 Condenser inlet |$\mathrm{C}{\mathrm{O}}_2$| −46.00 −46.00 0.8000 0.8000 425.40 425.40 Pump inlet |$\mathrm{C}{\mathrm{O}}_2$| −47.31 −47.31 0.7600 0.7600 98.27 98.28 Open in new tab 3.1. Energy and exergy results Table 6 shows the pressure, temperature, specific enthalpy and specific entropy, mass flow rate and exergy rate for each state of the single flash geothermal power plant, while Table 7 shows the same parameters for the geothermal-transcritical CO2 power plant. Basic cycle thermodynamic information. Table 6 Basic cycle thermodynamic information. Stage . Pressure (kPa) . Temperature (°C) . Specific enthalpy (kJ/kg) . Specific entropy (kJ/kg K) . Mass flow rate (kg/s) . Exergy rate (kW) . 1 791.5 170 719.3 2.042 10 1236 2 500 151.9 719.3 2.047 10 1223 3 500 151.9 2749 6.821 0.3742 281.7 4 20 60.07 2348 7.122 0.3742 98.55 5 20 60.07 251.5 0.8321 0.3742 3.863 6 500 60.13 252.1 0.8326 0.3742 4.053 7 500 151.9 640.4 1.861 9.626 941.1 8 500 148.5 625.9 1.827 10 932.9 Stage . Pressure (kPa) . Temperature (°C) . Specific enthalpy (kJ/kg) . Specific entropy (kJ/kg K) . Mass flow rate (kg/s) . Exergy rate (kW) . 1 791.5 170 719.3 2.042 10 1236 2 500 151.9 719.3 2.047 10 1223 3 500 151.9 2749 6.821 0.3742 281.7 4 20 60.07 2348 7.122 0.3742 98.55 5 20 60.07 251.5 0.8321 0.3742 3.863 6 500 60.13 252.1 0.8326 0.3742 4.053 7 500 151.9 640.4 1.861 9.626 941.1 8 500 148.5 625.9 1.827 10 932.9 Open in new tab Table 6 Basic cycle thermodynamic information. Stage . Pressure (kPa) . Temperature (°C) . Specific enthalpy (kJ/kg) . Specific entropy (kJ/kg K) . Mass flow rate (kg/s) . Exergy rate (kW) . 1 791.5 170 719.3 2.042 10 1236 2 500 151.9 719.3 2.047 10 1223 3 500 151.9 2749 6.821 0.3742 281.7 4 20 60.07 2348 7.122 0.3742 98.55 5 20 60.07 251.5 0.8321 0.3742 3.863 6 500 60.13 252.1 0.8326 0.3742 4.053 7 500 151.9 640.4 1.861 9.626 941.1 8 500 148.5 625.9 1.827 10 932.9 Stage . Pressure (kPa) . Temperature (°C) . Specific enthalpy (kJ/kg) . Specific entropy (kJ/kg K) . Mass flow rate (kg/s) . Exergy rate (kW) . 1 791.5 170 719.3 2.042 10 1236 2 500 151.9 719.3 2.047 10 1223 3 500 151.9 2749 6.821 0.3742 281.7 4 20 60.07 2348 7.122 0.3742 98.55 5 20 60.07 251.5 0.8321 0.3742 3.863 6 500 60.13 252.1 0.8326 0.3742 4.053 7 500 151.9 640.4 1.861 9.626 941.1 8 500 148.5 625.9 1.827 10 932.9 Open in new tab Geothermal-CO2 cycle thermodynamic information. Table 7 Geothermal-CO2 cycle thermodynamic information. Stage . Pressure (kPa) . Temperature (°C) . Specific enthalpy (kJ/kg) . Specific entropy (kJ/kg K) . Mass flow rate (kg/s) . Exergy rate (kW) . 1 791.5 170 719.3 2.042 10 1236 2 500 151.9 719.3 2.047 10 1223 3 500 151.9 2749 6.821 0.3742 281.7 4 500 151.9 640.4 1.861 9.626 941.1 5 20 60.07 2348 7.122 0.3742 98.55 6 20 60.07 251.5 0.8321 0.3742 3.863 7 500 60.13 252.1 0.8326 0.3742 4.053 8 500 71.5 299.7 0.9729 9.626 166.3 9 15000 51.5 −188.2 -1.389 16.34 3592 10 15000 131.9 12.53 -0.8275 16.34 4183 11 7214 72.72 −18.03 -0.8052 16.34 3577 12 7214 30 −204 -1.401 16.34 3392 Stage . Pressure (kPa) . Temperature (°C) . Specific enthalpy (kJ/kg) . Specific entropy (kJ/kg K) . Mass flow rate (kg/s) . Exergy rate (kW) . 1 791.5 170 719.3 2.042 10 1236 2 500 151.9 719.3 2.047 10 1223 3 500 151.9 2749 6.821 0.3742 281.7 4 500 151.9 640.4 1.861 9.626 941.1 5 20 60.07 2348 7.122 0.3742 98.55 6 20 60.07 251.5 0.8321 0.3742 3.863 7 500 60.13 252.1 0.8326 0.3742 4.053 8 500 71.5 299.7 0.9729 9.626 166.3 9 15000 51.5 −188.2 -1.389 16.34 3592 10 15000 131.9 12.53 -0.8275 16.34 4183 11 7214 72.72 −18.03 -0.8052 16.34 3577 12 7214 30 −204 -1.401 16.34 3392 Open in new tab Table 7 Geothermal-CO2 cycle thermodynamic information. Stage . Pressure (kPa) . Temperature (°C) . Specific enthalpy (kJ/kg) . Specific entropy (kJ/kg K) . Mass flow rate (kg/s) . Exergy rate (kW) . 1 791.5 170 719.3 2.042 10 1236 2 500 151.9 719.3 2.047 10 1223 3 500 151.9 2749 6.821 0.3742 281.7 4 500 151.9 640.4 1.861 9.626 941.1 5 20 60.07 2348 7.122 0.3742 98.55 6 20 60.07 251.5 0.8321 0.3742 3.863 7 500 60.13 252.1 0.8326 0.3742 4.053 8 500 71.5 299.7 0.9729 9.626 166.3 9 15000 51.5 −188.2 -1.389 16.34 3592 10 15000 131.9 12.53 -0.8275 16.34 4183 11 7214 72.72 −18.03 -0.8052 16.34 3577 12 7214 30 −204 -1.401 16.34 3392 Stage . Pressure (kPa) . Temperature (°C) . Specific enthalpy (kJ/kg) . Specific entropy (kJ/kg K) . Mass flow rate (kg/s) . Exergy rate (kW) . 1 791.5 170 719.3 2.042 10 1236 2 500 151.9 719.3 2.047 10 1223 3 500 151.9 2749 6.821 0.3742 281.7 4 500 151.9 640.4 1.861 9.626 941.1 5 20 60.07 2348 7.122 0.3742 98.55 6 20 60.07 251.5 0.8321 0.3742 3.863 7 500 60.13 252.1 0.8326 0.3742 4.053 8 500 71.5 299.7 0.9729 9.626 166.3 9 15000 51.5 −188.2 -1.389 16.34 3592 10 15000 131.9 12.53 -0.8275 16.34 4183 11 7214 72.72 −18.03 -0.8052 16.34 3577 12 7214 30 −204 -1.401 16.34 3392 Open in new tab Figure 5 represents the variation of total power output (summation of steam and gas turbine power), the energy and exergy efficiencies for stand-alone geothermal power plant of Figure 1 and the hybrid power plant of Figure 2 separator pressure. The figure shows that the new power output and efficiencies are higher for the hybrid power plant, which means adding the CO2 recovery cycle would significantly improve performance. The results also show that as the separator pressure increases, the net power output and exergy efficiency of both power plants increase to reach maximum values. They start to decrease. Therefore, an optimum separator pressure with different values exists for each of these parameters. It can be proved that these results are correct by checking the maximum power output of the stand-alone geothermal power plant for which the maximum value is obtained at the average temperature of the production well and condenser pressure [29]. It is seen from Figure 5 that the energy efficiency for the hybrid power plant is monotonically increasing as the separator pressure increases; however, for the energy efficiency of the stand-alone geothermal power plant, the trend is decreasing since increasing separator pressure increases the geofluid specific enthalpy of the production well. Power output, energy and exergy efficiencies variation with pressure. Figure 5 Open in new tabDownload slide Figure 5 Power output, energy and exergy efficiencies variation with pressure. Open in new tabDownload slide Figure 6 shows the influence of CO2 condenser outlet temperature on generated power, energy and exergy efficiencies. It indicates that increasing the condenser outlet temperature results in a significant drop in net power output; however, neither of these two efficiency reductions has a significant reduction. This is a logical result because less power from the gas turbine will be obtained. Power output, energy and exergy efficiencies variation with CO2 condenser exit temperature. Figure 6 Open in new tabDownload slide Figure 6 Power output, energy and exergy efficiencies variation with CO2 condenser exit temperature. Open in new tabDownload slide Figure 7 shows the change in net output energy and accelerator efficiency due to CO2 turbine inlet pressure in a hybrid power plant. The results show that the net power output and exergy and energy efficiencies have similar trend, and their maximum values occur at around 15 MPa. This can be explained by the fact that increasing the inlet pressure of the gas turbine increases the inlet temperature of the gas turbine, which leads to an increase in the temperature of the condenser (turbine outlet gas). As a result, an optimal gas turbine inlet temperature is achieved, thereby operating the hybrid power plant with optimal performance. Power output, energy and exergy efficiencies variation with CO2 turbine inlet pressure. Figure 7 Open in new tabDownload slide Figure 7 Power output, energy and exergy efficiencies variation with CO2 turbine inlet pressure. Open in new tabDownload slide The exergy destruction rate for various parts of the hybrid power plant is shown in Figure 8, where it can be seen that the highest destruction rate is in the VG that connecting the geofluid with CO2, which corresponds to 38% of the total exergy rate of all components. This is expected because the temperature difference between hot fluid and cold fluid is very high. The second highest exergy destruction rate occurs in the gas turbine because of the high-temperature difference between the gas inlet and exit. Then followed by the exergy destruction rate in the CO2 condenser and then by the CO2 pump, steam turbine and CO2 evaporator. The separator, condenser and pump of the geothermal power plant has the lowest exergy destruction rate, exactly zero for the separator and condenser. Exergy destruction rate for each component. Figure 8 Open in new tabDownload slide Figure 8 Exergy destruction rate for each component. Open in new tabDownload slide Figure 9 shows the effect of the pinch point (TDD) on the net power production, the energy and exergy efficiency of a hybrid power plant. The graph shows that as TDD increases, net power production decreases at a high rate. This is because as TDD increases, the efficiency of both will decrease. This is to be expected because a larger temperature difference will lead to a higher rate of exergy destruction, leading to lower exergy efficiency. Power output, energy and exergy efficiencies variation pinch point. Figure 9 Open in new tabDownload slide Figure 9 Power output, energy and exergy efficiencies variation pinch point. Open in new tabDownload slide 3.2. Optimization The Nelder–Mead simplex method is an applied mathematical strategy used to locate the extremum of a target function in a multidimensional space. It is a direct search and is regularly applied to nonlinear optimization problems for which derivatives may not be known. For instance, Wang and Shoup [32] introduced an investigation of the affectability of the boundaries of the Nelder-drug simplex strategy for arbitrary revision. Streamlining of the creation boundaries for bread rolls with the Nelder–Mead simplex strategy was performed by Zettel and Hitzmann [33]. Bai et al. [34] presented an adaptable Nelder–Mead simplex estimation to alternately reproduce the non-uniform strain field from the reflected power scope of the fiber granulating sensor. In this section, Nelder–Mead is implemented for the proposed combined power plant in this work for which the optimal parameters are shown in Table 8. Optimum parameters using Nelder–Mead simplex method. Table 8 Optimum parameters using Nelder–Mead simplex method. Parameter . Initial mode . Optimal mode . Unit . Separator pressure 500 293.2 kPa Carbon dioxide turbine inlet pressure 15000 14261 kPa Evaporator terminal temperature difference 20 5 °C Power production of steam turbine 150.1 248.3 kW Power production of carbon dioxide turbine 499.2 461.4 kW Electricity consumption of pump 1 0.2436 0.4839 kW Electricity consumption of pump 2 260.4 235.6 kW Net power production 388.7 473.6 kW Exergy efficiency 31.44 38.31 % Parameter . Initial mode . Optimal mode . Unit . Separator pressure 500 293.2 kPa Carbon dioxide turbine inlet pressure 15000 14261 kPa Evaporator terminal temperature difference 20 5 °C Power production of steam turbine 150.1 248.3 kW Power production of carbon dioxide turbine 499.2 461.4 kW Electricity consumption of pump 1 0.2436 0.4839 kW Electricity consumption of pump 2 260.4 235.6 kW Net power production 388.7 473.6 kW Exergy efficiency 31.44 38.31 % Open in new tab Table 8 Optimum parameters using Nelder–Mead simplex method. Parameter . Initial mode . Optimal mode . Unit . Separator pressure 500 293.2 kPa Carbon dioxide turbine inlet pressure 15000 14261 kPa Evaporator terminal temperature difference 20 5 °C Power production of steam turbine 150.1 248.3 kW Power production of carbon dioxide turbine 499.2 461.4 kW Electricity consumption of pump 1 0.2436 0.4839 kW Electricity consumption of pump 2 260.4 235.6 kW Net power production 388.7 473.6 kW Exergy efficiency 31.44 38.31 % Parameter . Initial mode . Optimal mode . Unit . Separator pressure 500 293.2 kPa Carbon dioxide turbine inlet pressure 15000 14261 kPa Evaporator terminal temperature difference 20 5 °C Power production of steam turbine 150.1 248.3 kW Power production of carbon dioxide turbine 499.2 461.4 kW Electricity consumption of pump 1 0.2436 0.4839 kW Electricity consumption of pump 2 260.4 235.6 kW Net power production 388.7 473.6 kW Exergy efficiency 31.44 38.31 % Open in new tab 3.3. Economic results In this subsection, the influence of several parameters of single flash cycle and hybrid T-CO2 cycle on the economic indicator are presented. In Figures 10 and 11, the total cost of power plant |$({\dot{C}}_{tot})$| and the cost of produced energy |$({c}_{product})$| are presented. Figure 10a and b shows the increase of |${\dot{C}}_{tot}$| with augmentation of steam mass flow rate and water inlet temperature in both cycles. Due to increase in the size of equipment, the initial cost growth. Also, Figure 10a and b presents the |${c}_{product}$|⁠, the steam mass flow rate does not affect the cost of energy and the water inlet temperature is more sensitive for basic cycle than the T-CO2 cycle. Figure 10c shows the slight effect of separator inlet pressure in the |${\dot{C}}_{tot}$| for both cycles. In the case of |${c}_{product}$|⁠, the separator inlet pressure produces huge changes for basic cycle and the energy efficiency improves with high flash pressure. The last conclusion is the cost of energy for T-CO2 is always lower than basic cycle. Effect of water parameters on |${\dot{C}}_{tot}$| and |${c}_{product}$|⁠. Figure 10 Open in new tabDownload slide Figure 10 Effect of water parameters on |${\dot{C}}_{tot}$| and |${c}_{product}$|⁠. Open in new tabDownload slide Effetcs of T-CO2 cycle parameter on |${\dot{C}}_{tot}$| and |${c}_{product}$|⁠. Figure 11 Open in new tabDownload slide Figure 11 Effetcs of T-CO2 cycle parameter on |${\dot{C}}_{tot}$| and |${c}_{product}$|⁠. Open in new tabDownload slide Figure 11 presents the effect of condenser temperature and difference of temperature in the VG of T-CO2 cycle on the |${\dot{C}}_{tot}$| and |${c}_{product}$|⁠. For the parameter of T-CO2 cycle, there is not any chance in the cost of plant because they do not change the size of equipment. However, the increase of these parameters became an increase of cost of energy produced; it is due to the power net decrease (Figure 13). Figure 12 describes the behavior of power |$({\dot{W}}_{net})$| and levelized energy cost |$(LEC)$| with variations in parameters of flash geothermal cycle. When the steam mass flow rate and water inlet temperature increase the power produced rise and consequently the |$LEC$| decrease. In Figure 12c, it can be seen that there is an optimal flash pressure to maximize the power energy production. In all cases, T-CO2 cycle has the higher |$LEC$| than the basic cycle. Effect of water parameters on |${\dot{W}}_{net}$| and |$LEC$|⁠. Figure 12 Open in new tabDownload slide Figure 12 Effect of water parameters on |${\dot{W}}_{net}$| and |$LEC$|⁠. Open in new tabDownload slide Figure 13a and b presents the decrease of power energy production with the increase in the condenser temperature and pinch difference temperature of VG. In these cases, the LEC always increase because the LEC is inversely proportional to power energy production. There is an optimal pressure in the inlet of CO2-turbine to maximize the energy production (Figure 13c), but the LEC always increases due to the increase of turbine cost. Effects of T-CO2 cycle parameter on |${\dot{W}}_{net}$| and |$LEC$|⁠. Figure 13 Open in new tabDownload slide Figure 13 Effects of T-CO2 cycle parameter on |${\dot{W}}_{net}$| and |$LEC$|⁠. Open in new tabDownload slide 3.4. Exergo-environmental results Figure 14a shows the effects of the geofluid mass flow rate of the production well on the exergoenvironmental and exergy constancy parameters. It is apparent from the figure that the mass flow rate has almost no effect on the exergoenvironmental and exergy constancy parameters. Figure 13 shows that the exergoenvironmental and exergy stability are higher for the CO2 transcritical recovery cycle than the basic cycle. The higher values of these parameters are not favorable as can be seen from the mathematical expressions of these two factors that are directly proportional to the exergy destruction rate. Adding CO2 to the basic cycle results in higher exergy destruction rate, which usually is highest in the CO2 gas turbine. Effect of water parameters on |${f}_{ei}$| and |${f}_{es}$|⁠. Figure 14 Open in new tabDownload slide Figure 14 Effect of water parameters on |${f}_{ei}$| and |${f}_{es}$|⁠. Open in new tabDownload slide Effects of T-CO2 cycle parameter on |${f}_{ei}$| and |${f}_{es}$|⁠. Figure 15 Open in new tabDownload slide Figure 15 Effects of T-CO2 cycle parameter on |${f}_{ei}$| and |${f}_{es}$|⁠. Open in new tabDownload slide Effect of water parameters on |${\theta}_{ei}$| and |${\theta}_{eii}$|⁠. Figure 16 Open in new tabDownload slide Figure 16 Effect of water parameters on |${\theta}_{ei}$| and |${\theta}_{eii}$|⁠. Open in new tabDownload slide Effects of T-CO2 cycle parameter on |${\theta}_{ei}$| and |${\theta}_{eii}$|⁠. Figure 17 Open in new tabDownload slide Figure 17 Effects of T-CO2 cycle parameter on |${\theta}_{ei}$| and |${\theta}_{eii}$|⁠. Open in new tabDownload slide The variation of the exergoenvironmental and exergy stability factors with the geofluid temperature of the production well is represented in Figure 14b. The figure shows that these parameters are decreasing for the combined power plant as the geofluid increases; however, the trend of these parameters is increasing for the basic cycle as the geofluid temperature increases. Indeed, as the temperature of the geofluid increases, the exergy destruction rate of the hybrid plant decreases while the exergy destruction rate of the basic cycle increases. The effect of the separator pressure on the exergoenvironmental and exergy stability factors is shown in Figure 13c, which shows that as the pressure increases, the exergoenvironmental and stability factors for the combined power plant decrease at low pressure to reach a minimum value after which they increase with increasing the separator pressure. However, as the increasing separator pressure, the exergoenvironmental and exergy stability is increasing sharply for the basic cycle. Figure 15a shows the effect of the CO2 gas condenser temperature on the exergoenvironmental and exergy stability factors for the geothermal/CO2 transcritical cycle. As it can be seen from the figure, the exergoenvironmental factor is almost linearly decreasing as the condenser temperature increases due to the lower exergy destruction rate of the whole combined cycle. The figure also shows that the stability factor increases to reach a maximum value at around 27°C condenser temperature after which it starts to decrease as the condenser temperature increases. The variation of the exergoenvironmental and exergy stability factors for the geothermal/transcritical CO2 with pinch temperature of the VG is illustrated in Figure 15b where it is shown that the exergoenvironmental factor is sharply increasing with the pinch point temperature to reach a maximum value at ~20°C after which it starts to decrease with the increase in pinch point temperature. However, the variation is completely different for the exergy stability factor, which is monotonically decreasing with increasing the pinch point temperature. Figure 15c shows the effect of CO2 turbine inlet pressure on the exergoenvironmental and exergy stability factors. It is shown in the figure that there is a sharp decrease in factors as the pressure increases; however, at pressure ~18 MPa, these factors almost remain constant. The increase in the turbine pressure results in higher power output of the turbine and hence in better turbine performance, which leads to lower exergy destruction rate of the combined power plant. The effect of geofluid mass flow rate on the environmental damage effectiveness factor and exergoenvironmental enhancement impact is shown in Figure 16a. The figure shows that the environmental damage effectiveness factor for both power plants is not much affected by the geofluid mass flow rate, but this parameter is higher for the combined power plant, which means adding CO2 transcritical recovery cycle to the basic cycle increases environmental damage effectiveness factor. Since the variation of environmental damage effectiveness factor is almost not affected by the geofluid mass flow rate, the exergoenvironmental enhancement impact that is the inverse of it will not be affected, too, by the geofluid mass flow rate. Figure 16b shows the effect of the production well geofluid temperature on the environmental damage effectiveness factor and exergoenvironmental enhancement impact, which shows that the environmental damage effectiveness factor for combined power plant is linearly decreasing with the geofluid temperature while this factor increases with the geofluid temperature for the basic cycle. The trend of the exergoenvironmental enhancement impact will be simply opposite to that of environmental damage effectiveness factor. The effect of separator pressure on the environmental damage effectiveness factor and exergoenvironmental enhancement impact is shown in Figure 16c where the environmental damage effectiveness factor has a minimum value at a certain pressure (~250 kPa) as the case for the exergoenvironmental effect for the combined power plant, while the basic cycle has a continuous decreasing trend with increasing the separator pressure for the basic cycle. The trend of the exergoenvironmental enhancement impact will be simply opposite to that of environmental damage effectiveness factor. The effect of the CO2 condenser temperature on the environmental damage effectiveness factor and exergoenvironmental enhancement impact for the combined power plant is shown in Figure 17a where the environmental damage effectiveness factor has a minimum value at a certain pressure (~250 kPa) as the case for the exergoenvironmental effect for the combined power plant, while the basic cycle has a continuous decreasing trend with increasing the separator pressure for the basic cycle. The trend of the exergoenvironmental enhancement impact will be simply opposite to that of environmental damage effectiveness factor. The results of this figure suggest in order to have low environmental impact that the gas condenser should operate at lower temperature. The effects of the VG pinch temperature on the environmental damage effectiveness factor and exergoenvironmental enhancement impact for the combined power plant are shown in Figure 17b where the environmental damage effectiveness factor is monotonically increasing with the increase in the pinch temperature of the VG. The figure shows that the trend of the exergoenvironmental enhancement impact is opposite to that of environmental damage effectiveness factor due to the inverse mathematical definition of that factor. The results of this figure suggest that the power plant should be operated at low pinch temperature to have lower environmental damage. Figure 17c shows the effect of the CO2 turbine inlet pressure on the environmental damage effectiveness factor and exergoenvironmental enhancement impact for the combined power plant. The figure shows that the environmental damage effectiveness factor is sharply decreasing as the condenser pressure increases until it reaches a minimum value of 1.2 at ~1.7 MPa after which it starts to increase. The trend of the exergoenvironmental enhancement impact is simply opposite to that of environmental damage effectiveness factor. It is thus recommended to operate the gas turbine at high inlet pressure from environmental point of view. 4. CONCLUSIONS This study presented a transcritical CO2 cycle energy and exergy analysis powered by a single flash geothermal power plant. Comparison of performance of stand-alone geothermal power plant and combined cycle power plant has been demonstrated in terms of output energy efficiency and exergy efficiency. We can conclude that a combined power plant is more efficient and has more electricity than a stand-alone geothermal power plant. Based on current research, there is an optimal separation pressure to have maximum power output and maximum exergy efficiency. The maximum power output and maximum exergy efficiency for the combined power plant were ~400 kW and 35% at ~300 kPa separator pressure, respectively. The maximum power output, maximum exergy efficiency and maximum energy efficiency of the proposed combined power plant are obtained under a CO2 turbine inlet pressure of 1.5 MPa. The results showed that the performance is substantially improved by decreasing the CO2 condenser exit temperature. The pinch point effect was obtained on the combined power plant performance, it shows that power output and exergy efficiency decrease as the pinch point increases. Each component’s exergy destruction rate was calculated as 182.4 kW for the CO2 VG of 182.4 kW, followed by 106 kW for the CO2 turbine, followed by 82.81 kW the CO2 condenser and 58.75 kW for the CO2 pump. The Nelder–Mead simplex method was used to find the best system performance and reduce the exergy destruction rate of power plant various components; this optimization is based on GAs. In summary, the power production, energy efficiency and exergy efficiency of combined power plants are always higher than that of single geothermal power plants. Geothermal energy source is a continuous source of energy that is not affected by weather conditions as solar and wind energy sources. Hence, this makes it the best option for electricity production; in addition, cooling and heating can be also generated using geothermal energy by combining it to other devices for cooling and heating. Combining CO2 cycle with geothermal energy source as a combined power plant is very efficient and economically effective. 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TI - Energy, exergy, economic and exergoenvironmental analyses of transcritical CO2 cycle powered by single flash geothermal power plant
JF - International Journal of Low-Carbon Technologies
DO - 10.1093/ijlct/ctab076
DA - 2021-11-01
UR - https://www.deepdyve.com/lp/oxford-university-press/energy-exergy-economic-and-exergoenvironmental-analyses-of-tkBIiK9chQ
SP - 1
EP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -