Geothermal power plants are considered important renewable energy resources for clean energy production. Flash steam type plants constitute a significant portion of worldwide geothermal power. In this study, single, double, triple, and quadruple flash steam geothermal power plants are investigated with reinjection options. The optimal operating points are determined specifically through optimal flashing pressures. The turbine power outputs, energy efficiencies, and exergy efficiencies are further studied. A rise in the flashing stages from single to double is found to increase the power outputs considerably. However, when the flashing stages are increased from double to triple and triple to quadruple, the increase in turbine power outputs is found to drop significantly. Also, both exergy efficiency and energy efficiency are found to reduce with increasing number of flash stages. The energy efficiencies are obtained as 28%, 25.5%, 24.2%, and 23.5% for single, double, triple, and quadruple plants, respectively. Furthermore, the exergy efficiencies are found to be 72.6%, 70.9%, 70.2%, and 69.8% for these plants, respectively.

Introduction

In the past few decades, energy consumption and generation have increased considerably. Such an increasing trend is further forecasted to rise at a higher rate [1]. Increased energy production results in a rise in the consumption of fossil fuels. Fossil fuels are not environmentally benign and colossal amounts of harmful environmental emissions have been estimated to be emitted to the atmosphere due to the usage of fossils for energy production. Currently, the majority of the world's power generation is conducted relying on fossil fuels.2 Hence, numerous efforts are being carried out across the globe to reduce the dependence on fossils and increase the usage of clean and environmentally benign resources of energy. Geothermal resource for power production is a promising option, especially in areas where there is sufficient supply of geothermal fluid. Geothermal energy refers to the utilization of heat present in the earth's crust. Geothermal power plants utilize the hot geothermal water or fluid present in the ground to generate power. Thus, providing an environmentally benign method of power generation [215]. Different configurations and methodologies of geothermal entailing power generation exist depending on the method of energy transfer from the hot geothermal fluid to the power cycle working fluid. For instance, a binary geothermal plant comprises an indirect energy transfer method. The geothermal fluid is circulated through heat exchangers to transmit the heat to a secondary cycle utilized for power production, which are generally organic fluid-based cycles that have low boiling points. Another configuration of geothermal power production is direct steam type facility that includes a production well which generates steam that is fed directly to the steam turbine. However, in cases where direct steam generation is not possible from a production well, a flash steam plant is utilized. In this type of geothermal facility, the production well fluid is in a saturated mixture state that is flashed to a lower pressure to increase the vapor content. The fluid is then divided into saturated vapor and saturated liquid, where the vapor is passed to turbines and the liquid is either pumped back to the reinjection well or is flashed further to generate more vapor.

In flash steam geothermal power plants, it is essential to analyze the number of flash stages to be used. A single-flash plant comprises only one flash chamber and separator that provide the steam required for power generation. However, multistage flash geothermal plants consist of more flashing stages that produce steam in stages and send the separated steam to different turbines. Thus, generating more power and providing higher efficiencies. The flashing pressure that should be utilized in a geothermal power plant is a crucial decision that affects the power outputs and efficiencies. Further, when multiple flashing stages are used, it is vital to determine the flashing pressure ratios to be used at each stage. However, only a few studies have been conducted on analyzing the effects of the number of flashing stages on the geothermal power plant performance. Ozgener et al. [16] performed an exergy analysis of an operational geothermal plant. The study was performed by utilizing actual system parameters. The geothermal plant considered had heat as a useful system output. The system was analyzed both energetically and exergetically and the overall energy and exergy efficiencies were determined. They found that the primary sources of exergy destructions exist in the reinjection phase as well as natural system discharge. These were found to contribute by 22.7% and 24.1%, respectively. Furthermore, the energy efficiency of the geothermal system analyzed was determined to be 37.6% and the exergetic efficiency was found to be 42.9%. Zhao et al. [17] investigated and evaluated the optimum evaporation and flash temperatures for different types of geothermal plants. They studied the single- and double-flash plants as well as the binary-flash type configurations. They found that the optimum flash temperatures for the single-flash and double-flash plants are 150 °C and 100 °C, respectively. The geothermal plants were only investigated up to double-flash type plants. Nevertheless, it is also essential to investigate more than two flash stages for the given well pressures and temperatures to determine the options providing higher thermodynamic performance. Lee and Reistad [18] conducted a thermodynamic analysis of aquifer recovery-based geothermal systems entailing power and heating as useful outputs. They analyzed a couple of single discharging–charging wells employed in an aquifer extensively horizontal. They reported that for such aquifer systems, the high temperature entailing aquifers with temperatures of more than 162 °C are appropriate for power generation as they result in better system performance results. Also, they investigated systems comprising heat pumps and district heating systems and concluded that combining such systems would need a study about the load conditions as well as geological parameters and conditions as they determine the overall system performance. Selek-Murathan et al. [19] investigated a double-flash geothermal electricity generation plant and found the optimum flash temperatures that result in the maximum turbine power output. They considered the geothermal wells present in the Canakkale Tuzla region in Turkey, the optimum temperature was found to be 120 °C for the high-pressure flashing chamber and 73 °C for the low-pressure flash. Although the study investigated temperatures and pressures for optimum plant operation, it did not entail the investigation of more than two flash stages for geothermal plants. Ezzat and Dincer [20] studied a new integrated multigeneration system utilizing the geothermal resource. The system useful commodities were drying, cooling, hot water, and power. A single-flash type geothermal plant was considered and the efficiency of 69.6% was found energetically. Also, a 42.8% efficiency was found exergetically. Kanoglu and Cengel [21] studied the performance improvement of a binary type geothermal power plant. An air-cooled type plant was considered. Specific emphasis was given to the seasonal changes that occur in the climate and thus affect the performance of geothermal plants. They chose Nevada as the location of study and reported that owing to the dry climatic conditions, the power plant performance could be considerably improved if the air temperature was reduced to its wet bulb temperature. The power output was reported to be increased by 29% in this case. Further, they also found that the maximum cycle pressure also plays an important role and the power output could be increased by 2.8% at the optimum maximum cycle pressure. In addition, isobutane was found to be the favorable organic fluid to be utilized in such power plants. Kanoglu and Cengel [22] analyzed a geothermal power plant with a 12.8 MW capacity. A single-flash type plant was considered. Actual operating parameters of the plant were utilized for the study. They reported that the amount of geothermal fluid reinjected contained nearly 50% of the energy entailed in the geothermal fluid coming from the well. Also, it entailed 40% of the exergy content. Further, the energy efficiency of the power plant was evaluated to be 6% and the exergetic efficiency was reported to be 22%. Siddiqui and Dincer [23] investigated a geothermal trigeneration system for power, space cooling, and heating. A 32.4% efficiency was determined energetically and 36.1% efficiency was reported exergetically. Significant increases in the efficiencies were reported as compared with a single-generation geothermal plant with only power as the output. However, a constant flashing pressure and one flash stage were considered for the thermodynamic analysis. The effect of double or triple flashing was not embarked upon in their study.

Hence, although previous studies were conducted on the thermodynamic investigation of geothermal entailing power generation, only single- and double-flash type configurations were considered. However, it is essential to investigate geothermal power plants with multiple flashing stages as the number of flashing stages affect the power outputs as well as the overall exergy efficiency and energy efficiency. Thus, we present a comprehensive investigation of the performance of the geothermal power plants with single, double, triple, and quadruple flashing stages. Also, previous studies have not directed efforts toward investigating the geothermal power plant performances at several combinations of inlet and flashing pressures. However, these are important investigations that need to be performed to provide associated stakeholders with essential information. Therefore, in this study, we also investigate the optimal flashing pressures for a wide range of inlet pressures. In addition, the energy efficiencies and exergy efficiencies of single to quadruple flash steam geothermal power plants are determined. The specific objectives of this study are: (i) investigating the performance of single, double, triple, and quadruple flash steam geothermal power plants, (ii) determining the optimal flashing pressures for an inlet pressure range of 100 kPa to 10 MPa for single through quadruple flash steam plants, and (iii) evaluating the exergy efficiency as well as the exergy efficiency of these four types of geothermal plants at different flashing pressures.

System Description

A geothermal power plant with single, double, triple, and quadruple flashing stages is investigated. A single-flash steam type configuration for geothermal power generation is depicted in Fig. 1. The geothermal fluid enters the system at state 1 in a saturated liquid state. It is then flashed to a lower pressure and thus temperature at state 2 through a throttle valve (TV−1). Although the pressure and temperature decrease, the quality increases. Hence, state 2 comprises a saturated liquid–vapor mixture with a given quality. This saturated mixture is passed to a separator (S−1), which separates the vapor and liquid parts. The saturated vapor exits the separator at state 3 and saturated liquid exits at state 6. The separated vapor at state 3 is allowed to enter the steam turbine (T−1) to generate power, whereas the separated liquid is reinjected in the reinjection well at state 6. The vapor at state 3 enters the steam turbine, generates power, and exits at a lower pressure and temperature at state 4. At state 4, a saturated vapor mixture is formed again that passes through the condenser (C−1) where it releases heat and reaches the saturated liquid state (state 5). This saturated liquid is also reinjected into the reinjection well. However, the double-flash steam type configuration is depicted in Fig. 2. In this type of configuration, the saturated liquid leaving the first separator (S−1) at state 6 is flashed to a lower pressure and temperature again through another throttle valve (TV−2). This converts the saturated liquid at state 6 to a saturated liquid–vapor mixture at state 7 that is allowed to pass through the second separator (S−2). The second separator separates the saturated vapor (state 8) from the saturated mixture that is passed through the second turbine (T−2) to generate more power. Thus, producing more power than a single-flash plant. The saturated liquid separated in S−2 is sent back to the reinjection well. However, the saturated vapor entering T−2 (state 8) leaves the turbine as a mixture of liquid and vapor (state 9) at the same pressure as the exit stream of T−1. Further, it is passed through the second condenser (C−2), where heat is given out and converts to a saturated liquid before being pumped to the reinjection well at state 11. Furthermore, the triple flash steam geothermal plant is shown in Fig. 3. As can be observed from the figure, the triple flash type configuration further flashes the saturated liquid exiting the separator 2 (S−2) by throttling it to a lower pressure by TV−3 and separating the saturated vapor through separator S−3. The saturated vapor exiting S−3 is passed through the third turbine (T−3) to generate power. The exit stream (state 15) of the turbine is in a saturated mixture state at the same pressure as the exit streams of turbine 1 and 2 (T−1 and T−2). Similar to the single- and double-flash plants, this stream loses heat in condenser 3 (C−3) to reach the saturated liquid state before being sent to the reinjection well. Moreover, a quadruple flash steam type configuration is depicted in Fig. 4. In a similar way, as described above for the triple flash, the quadruple flash passes the saturated liquid leaving S−3 through a throttle to drop the pressure and increase the quality. This increased quality stream (state 19) is passed through a separator and the separated vapor is passed through turbine 4 (T−4) to generate more power. Further, steam leaves T−4 at the same pressure as the exit streams of T−1, T−2, and T−3 and is reinjected with these streams after rejecting heat in condenser 4 (C−4).

Analysis

The four types of flash steam geothermal power plants described above are analyzed through thermodynamic approaches of energy and exergy analyses. The thermophysical properties required for the analysis are obtained from engineering equation solver. The assumptions made to thermodynamically analyze and compare the four types of geothermal power plants are listed below:

• The systems operate at steady-state conditions.

• The variations in the potential as well as kinetic energies are negligibly small.

• Piping and condenser pressure losses are negligible.

• The flashing process is isenthalpic.

• The turbines and pumps are isentropic.

• The condensers operate at a saturation pressure of 7.381 kPa.

• The geothermal well fluid has a mass flow rate of 1 kg/s.

The flashing pressure is a significant system condition that impacts the power outputs as well as the exergy efficiency along with the energy efficiency. There are two opposing relationships when deciding what pressure to flash the supply water. The lower the pressure, the higher the quality of the mixture and thus the greater the amount of steam produced. However, the lower the pressure, the lower the specific enthalpy and exergy of steam. This is better depicted in Fig. 5, where the variation of the specific enthalpy and exergy are presented along with the quality of steam at different flashing pressures considering a constant inlet pressure of 10,000 kPa. As can be depicted from the figure, the choice of flashing pressure is a key system parameter. For instance, flashing the steam to 5000 kPa would provide a quality of 0.15 and an enthalpy of 2795 kJ/kg. However, flashing to a lower pressure of 1000 kPa would provide a higher quality of 0.33 and a lower enthalpy of 2780 kJ/kg. Higher quality would correspond to a higher amount of saturated vapor that can be sent to the steam turbine for power generation, however, lower steam enthalpy would decrease the amount of turbine work output it can produce. In order to determine the optimal pressures, it is essential to investigate the turbine work outputs. A set of combinations of inlet and flashing pressures and the corresponding work outputs are analyzed in the present study to determine the optimal points for each combination.

Considering a thermodynamic control volume, the mass balance equation on a rate basis is denoted for steady-state operation as
$∑m˙i=∑m˙o$
(1)
Here, i represents the inlet and o represents the outlet. Further, the energy balance equation on a rate basis for a control volume operating at steady-state conditions is written as
$Q˙+∑m˙ihi=W˙+∑m˙oho$
(2)
where $Q˙$ represents the net heat input that can be evaluated as
$Q˙=Q˙i−Q˙o$
(3)
The parameter $W˙$ denotes the net work output that can be evaluated as
$W˙=W˙o−W˙i$
(4)
For a given control volume operating at steady-state conditions with a net heat input of $Q˙,$ the entropy balance is applied according to the following equation:
$Q˙T+∑m˙isi+S˙gen=∑m˙oso$
(5)
Further, the balance equation for exergetic analysis is denoted as
$E˙xQ+∑im˙iexi=∑em˙eexe+E˙xw+E˙xdest$
(6)
where $m˙$ represents the mass flow rate, ex is the specific exergy, $E˙xQ$ denotes the exergy rate associated with the net heat input $(Q˙)$, $E˙xw$ represents the exergy rate associated with the net work output $(W˙)$, and $E˙xdest$ denotes the exergy destruction rate.
The physical exergy of any given system state point is determined from
$exx=hx−ho−T0(sx−s0)$
(7)
where hx denotes the specific enthalpy at state x, h0 represents the enthalpy at reference conditions, and sx is the entropy at state x, whereas s0 is the specific entropy at the reference conditions.

The saturated liquid enters the system at state 1 and is throttled by TV−1, the thermodynamic balance equations for this component are written as

Energy balance:
$m˙1h1=m˙2h2$
(8)
Entropy balance:
$m˙1s1+S˙gen,TV−1=m˙2s2$
(9)
Exergy balance:
$m˙1ex1=m˙2ex2+E˙xdest,TV−1$
(10)

After leaving TV−1, the separator (S−1) is used to separate saturated liquid and vapor states. The thermodynamic analysis on S−1 is conducted as

Energy balance:
$m˙2h2=m˙3h3+m˙6h6$
(11)
Entropy balance:
$m˙2s2+S˙gen,S−1=m˙3s3+m˙6s6$
(12)
Exergy balance:
$m˙2ex2=m˙3ex3+m˙6ex6+E˙xdest,S−1$
(13)

The saturated vapor separated in S−1 is allowed to enter the turbine T−1. The turbine is analyzed thermodynamically as

Energy balance:
$m˙3h3=m˙4h4+W˙T−1$
(14)
Entropy balance:
$m˙3s3+S˙gen,T1=m˙4s4$
(15)
Exergy balance:
$m˙3ex3=m˙4ex4+W˙T−1+E˙xdest,T−1$
(16)
After leaving T−1, the saturated steam enters condenser 1 (C−1) where it rejects heat and reaches a saturated liquid state at the saturation pressure of 7.38 kPa. The thermodynamic analysis for C−1 is described by the equations below
$m˙4h4=Q˙C−1+m˙5h5$
(17)

$m˙4s4+S˙gen,C−1=Q˙C−1Tc−1+m˙5s5$
(18)

$m˙4ex4=Q˙C−1(1−T0TC−1)+m˙5ex5+E˙xdest,c−1$
(19)

For the double-flash steam plant, the saturated liquid at state 6 is throttled again by TV−2. The thermodynamic analysis of TV−2 is conducted as

Energy balance:
$m˙6h6=m˙7h7$
(20)
Entropy balance:
$m˙6s6+S˙gen,TV−2=m˙7s7$
(21)
Exergy balance:
$m˙6ex6=m˙7ex7+E˙xdest,TV−2$
(22)

The separator (S−2) is used to separate saturated liquid and vapor states for the second flash. The thermodynamic analysis on S−2 is conducted by the following equations:

Energy balance:
$m˙7h7=m˙8h8+m˙12h12$
(23)
Entropy balance:
$m˙7s7+S˙gen,S−2=m˙8s8+m˙12s12$
(24)
Exergy balance:
$m˙7ex7=m˙8ex8+m˙12ex12+E˙xdest,S−2$
(25)
The saturated vapor at state 8 enters T−2 that is analyzed as
$m˙8h8=m˙9h9+W˙T−2$
(26)

$m˙8s8+S˙gen,T−2=m˙9s9$
(27)

$m˙8ex8=m˙9ex9+W˙T−2+E˙xdest,T−2$
(28)
Furthermore, for a triple flash steam plant, the saturated liquid leaving S−2 is further throttled by TV−3. TV−3 is analyzed thermodynamically as
$m˙12h12=m˙13h13$
(29)

$m˙12s12+S˙gen,TV−3=m˙13s13$
(30)

$m˙12ex12=m˙13ex13+E˙xdest,TV−3$
(31)
The third turbine (T−3) that utilizes steam produced by S−3 is analyzed thermodynamically as
$m˙14h14=m˙15h15+W˙T−3$
(32)

$m˙14s14+S˙gen,T−3=m˙15s15$
(33)

$m˙14ex14=m˙15ex15+W˙T−3+E˙xdest,T−3$
(34)
The saturated steam leaving T−3 enters condense C−3 that is analyzed as
$m˙15h15=Q˙C−3+m˙16h16$
(35)

$m˙15s15+S˙gen,C−3=Q˙C−3Tc−3+m˙16s16$
(36)

$m˙15ex15=Q˙C−3(1−T0TC−3)+m˙16ex16+E˙xdest,c−3$
(37)
In case of the quadruple flash steam plant, the saturated liquid leaving S−3 at state 18 is flashed by TV−4, which is thermodynamically analyzed as
$m˙18h18=m˙19h19$
(38)

$m˙18s18+S˙gen,TV−4=m˙19s19$
(39)

$m˙18ex18=m˙19ex19+E˙xdest,TV−4$
(40)

The separator (S−4) is used in the quadruple flash steam plant that separates the saturated vapor, which is allowed to enter the fourth turbine (T−4). The separator (S−4) is analyzed as

Energy balance:
$m˙19h19=m˙20h20+m˙24h24$
(41)
Entropy balance:
$m˙19s19+S˙gen,S−4=m˙20s20+m˙24s24$
(42)
Exergy balance:
$m˙19ex19=m˙20ex20+m˙24ex24+E˙xdest,S−4$
(43)
The turbine T−4 is analyzed thermodynamically by the following equations:
$m˙20h20=m˙21h21+W˙T−4$
(44)

$m˙20s20+S˙gen,T−4=m˙21s21$
(45)

$m˙20ex20=m˙21ex21+W˙T−4+E˙xdest,T−4$
(46)
The saturated steam leaving T−4 rejects heat in the condenser C−4 which can be analyzed as
$m˙21h21=Q˙C−4+m˙22h22$
(47)

$m˙21s21+S˙gen,C−4=Q˙C−4Tc−4+m˙22s22$
(48)

$m˙21ex21=Q˙C−4(1−T0TC−4)+m˙22ex22+E˙xdest,c−4$
(49)
The energy efficiencies of the single, double, triple, and quadruple geothermal power plants are evaluated, respectively, by the following equations:
$ηen,SF=W˙T−1m˙1h1−(m˙6h6+m˙5h5)$
(50)

$ηen,DF=W˙T−1+W˙T−2m˙1h1−(m˙12h12+m˙11h11)$
(51)

$ηen,TF=W˙T−1+W˙T−2+W˙T−3m˙1h1−(m˙18h18+m˙17h17)$
(52)

$ηen,QF=W˙T−1+W˙T−2+W˙T−3+W˙T−4m˙1h1−(m˙24h24+m˙23h23)$
(53)
Further, the exergy efficiencies of the four types of power plants are evaluated as
$ηex,SF=W˙T−1m˙1ex1−(m˙6ex6+m˙5ex5)$
(54)

$ηex,DF=W˙T−1+W˙T−2m˙1ex1−(m˙12ex12+m˙11ex11)$
(55)

$ηex,TF=W˙T−1+W˙T−2+W˙T−3m˙1ex1−(m˙18ex18+m˙17ex17)$
(56)

$ηex,QF=W˙T−1+W˙T−2+W˙T−3+W˙T−4m˙1ex1−(m˙24ex24+m˙23ex23)$
(57)

The optimal inlet and flashing pressures that provide the maximum turbine work output for a single-flash plant are first analyzed. Further, the optimal point found for the first flash is utilized as the geothermal well inlet source pressure for the double-flash type plant.

Results and Discussion

The turbine work outputs for single-flash steam power plant for different combinations of inlet source and flashing pressures are depicted in Fig. 6. The inlet source pressures are varied from 100 kPa to 10 MPa and the optimal turbine work output for each case can be observed in the figures. Once the optimum points are determined for single-flash plant as shown in Fig. 6, these are used to analyze and optimize the double-flash steam plant. The exergy efficiency and the energy efficiency are also assessed to determine the appropriate operational points. Figure 7 depicts this investigation, where a comparison of inlet source pressures of 5000 kPa and 10,000 kPa is shown. An inlet source pressure of 10,000 kPa is thus chosen as it results in higher efficiencies than lower source pressures. Furthermore, the optimal flash pressure for an inlet source pressure of 10,000 kPa is found to be 1029 kPa as can be depicted from Fig. 6(b). For the analysis of the double-flash plant, these are considered as the inlet and flash pressures of the first flash stage, respectively. The optimization is then performed for the second flash stage depicted in Fig. 8. The optimal flash pressure for the second flash is found to be 134.7 kPa, which provides a total power output of 273 kW and a T−2 power output of 41 kW. Thus, in this way, the optimal pressures for the first and second flash stages are determined. Next, for the triple flash steam power plant, these optimal pressure values for inlet source pressure, first flash, and second flash are used to analyze and optimize the third flash stage. With an optimal second flash pressure of 134.7 kPa, the effect of flash pressures in the third flash (TV−3) on the total turbine power output and T−3 power output is analyzed. This is depicted in Fig. 9(a). The optimal flash pressure for the third flashing chamber is determined to be 35.43 kPa. This flash pressure provides a total power output of 282.1 kW and a T−3 power output of 8.5 kW. For the quadruple flash steam-based configuration, the optimal pressure values obtained above are used to analyze and optimize the fourth flashing stage. Figure 10(a) depicts the effect of various flashing pressures for the fourth flash for the inlet pressure of 35.43 kPa. The optimal point is obtained at a flash pressure of 15.7 kPa, which provides a total power output of 284 kW and a turbine 4 output of 1.9 kW. Also, the exergy efficiencies and energy efficiencies of the double, triple, and quadruple flash plants are depicted in Figs. 8(b), 9(b), and 10(b), respectively, for different flash pressures. The thermophysical properties determined for all state points at the optimal operating conditions for single through quadruple flash plants are listed in Table 1.

Effect of Number of Flash Stages on the Turbine Power Outputs.

When the number of flashing stages is increased from 1 to 2, the total turbine power output at the optimal point increases from 232.7 kW to 273.6 kW. However, for an increase in the number of flashing stages from 2 to 3 and 3 to 4, the rise in the total turbine power output at the optimal point drops. The power output increase from double to triple flash plant is to 8.5 kW. This is lower as compared with the rise observed in case of an increase in flash stages from 1 to 2, where the increase in power output is 40.9 kW. Moreover, the power output increase reduces to 1.9 kW when the flashing stages are increased from 3 to 4. Thus, it is recommended to utilize double-flash steam power plants. However, when increasing the number of stages higher than 2, an appropriate analysis needs to be made to assess the cost and power outputs associated to ensure the small power output rise would be a viable option.

Effect of Flashing Pressures on the Turbine Power Outputs.

The effect of flashing pressures on the turbine power outputs can be comprehended from Fig. 6. As discussed earlier, in case of geothermal power plants, a trade-off between the quality of steam and the enthalpy and exergy exists, which are affected by the flashing pressures. Hence, it is essential to analyze the optimum flashing pressures for a given geothermal power plant to attain high energy efficiency and exergy efficiency. As can be observed from the figures, for every inlet source pressure there exists an optimum flashing pressure that would provide the highest turbine power output. For instance, for an inlet source pressure of 5 MPa, the optimum flash pressure can be specified as 417.3 kPa, which provides the highest turbine power output of 152.3 kW. Similarly, for any given geothermal well, if the well pressures are known, this analysis should be conducted to determine the optimum flashing point.

Effect of Flashing Pressures on Exergy Efficiency and Energy Efficiency.

The results of the flashing pressure analysis on the exergy efficiency as well as the energy efficiency are shown in Figs. 7, 8(b), 9(b), and 10(b) for single, double, triple, and quadruple flash steam power plants. Figure 7 depicts the results of the flashing pressure effect on the energy and exergy efficiency of a single-flash steam plant for inlet source pressures of 5 MPa and 10 MPa. The efficiencies are observed to rise sharply until they approach the optimal point, after which the rise in efficiencies reduces. For instance, for a 10 MPa inlet source pressure, energy efficiency and exergy efficiency are found to rise rapidly from nearly 1.8% and 5.5% at a flash pressure of 10 kPa to 23.2% and 62.2% at a flash pressure of 417.7 kPa. However, for any higher flashing pressures, the rise is lower. For example, when the flashing pressure rises from 417.7 kPa to 825.4 kPa, energy efficiency increases by merely 3.7%, whereas exergy efficiency rises by 7.9%. Similar trends are found for the exergy efficiency and energy efficiencies of double, triple, and quadruple flash power plants. However, for these plants, another interesting trend is found in the efficiencies. The energy efficiency continues to increase with increasing flashing pressures, nevertheless, exergetic efficiency stabilizes once it attains a maximum value. This is more evident in Figs. 8(b) and 9(b). Hence, this signifies the importance of exergy analyses for any given energy system. It is recommended to perform a similar study for any given geothermal power plant to determine which operational conditions, parameters, or changes would be suitable to achieve higher efficiencies.

Effect of Number of Flashing Stages on the Exergy Efficiency and Energy Efficiency.

Energy efficiency of the single-flash steam configuration is determined as 28% and exergy efficiency is determined as 72.6%. However, as the number of flash stages is increased to 2, the energetic efficiency and the exergetic efficiency reduced to 25.5% and 70.9%, respectively. Furthermore, the efficiencies of triple and quadruple flash plants are observed to be lower. The triple flash plant is calculated to entail an energetic efficiency of 24.2% and an exergetic efficiency of 70.2%. Also, the quadruple flash plant is determined to entail an energetic efficiency of 23.5% and an exergetic efficiency of 69.8%. Thus, although increasing the number of flashing stages increases the total power outputs, the geothermal power plants with reinjection would have their efficiencies decrease with the increasing number of flash stages. This is attributed to the drop in a significant increase of power outputs with a higher number of flash stages. Thus, it is recommended to conduct a comprehensive thermodynamic analysis during the design phase of any geothermal power plant to ensure the required power outputs are achieved with optimal exergy efficiency as well as energy efficiency.

Effect of Turbine Isentropic Efficiency on the Power Plant Efficiencies.

In the above analysis, the turbines were assumed to be isentropic. However, to consider the effect of turbine isentropic efficiency on the system performance, a parametric study is conducted as depicted in Fig. 11. The effect on the energy efficiencies of single through quadruple power plants are depicted in Fig. 11(a) and the effect on the exergy efficiency is shown in Fig. 11(b). The energy efficiency of the single-flash type plant is observed to drop to 21% as the turbine isentropic efficiency reduces to 75%. Further, the exergetic efficiency of the same plant type reduces from 72.6% to 54.5% for the same decrease in isentropic efficiency. In addition, for this change in the isentropic efficiency, the energetic efficiencies of the double, triple, and quadruple plants are observed to drop to 19.1%, 18.2%, and 17.6%, respectively. Also, the exergetic efficiencies of these plants are observed to reduce to 53.2%, 52.7%, and 52.4%, respectively, as the turbine isentropic efficiency reduces to 75%. The parametric study considers the change in isentropic efficiencies of all turbines. For instance, at an isentropic efficiency value of 75%, all turbines (T−1 to T−4) are considered to entail this isentropic efficiency and the system is modeled and analyzed at this condition. As the results depict, the exergy efficiencies are more significantly reduced than the energetic efficiencies with a decrease in isentropic efficiency. This is attributed to an increase in the irreversibilities and exergy destruction rates with a reduction in isentropic efficiency. It is thus recommended to develop and utilize turbines with higher isentropic efficiencies to attain better system performances.

Effect of Condenser Pressure on the Power Plant Efficiencies.

The condenser pressure is assumed to be 7.381 kPa at steady-state operating conditions. However, it is essential to study the effect of this pressure on the overall system performances. Hence, Fig. 12 depicts the effect of condenser pressure on the power plant energetic and exergetic efficiencies. At lower condenser pressures, higher system efficiencies are observed. For instance, the energetic efficiencies of the single, double, triple, and quadruple power plants increase from 26.3%, 23.6%, 22.3%, and 21.6% to 31.2%, 28.9%, 27.7%, and 27.1%, respectively, as the condenser pressure is varied from 12 kPa to 2.7 kPa. Similarly, the exergetic efficiencies of these plants increase from 67.2%, 64.9%, 63.8%, and 63.2% to 83.1%, 82.54%, 82.51%, and 82.55%, respectively, for the same change in condenser pressure. This is attributed to an increase in turbine power outputs. As the condenser pressure is lowered, the turbine power outputs increase, hence resulting in higher system energetic and exergetic efficiencies. It is thus recommended to conduct a comprehensive thermodynamic study of geothermal power plants and determine the optimum operating parameters that can be implemented to achieve optimal system performances.

Effect of Geothermal Fluid Mass Flow Rate on Power Outputs.

The geothermal fluid mass flow rate is also an important system parameter that determines the system outputs. For the steady-state analysis presented above, this mass flow rate was assumed to be 1 kg/s. However, the effect of varying geothermal fluid mass flow rate on the total power outputs is depicted in Fig. 13. The power outputs of the single, double, triple, and quadruple power plants are observed to increase from 232.7 kW, 273.6 kW, 282.1 kW, and 284 kW to 6980 kW, 8208 kW, 8464 kW, and 8521 kW, respectively, as the geothermal fluid mass flow rate varies from 1 kg/s to 30 kg/s. However, this mass flow rate varies according to the characteristics of the geothermal well. In some locations, the geothermal wells have been found to provide substantially high flow rates, whereas in some areas they provide lower mass flow rates. Thus, the performance of the geothermal power plants will depend significantly on the type and potential of the well. Hence, it is recommended to conduct a resource analysis on the geothermal wells before building such plants to ensure the wells utilized provide high system outputs and performance.

Conclusions

In this paper, geothermal power plants with single, double, triple, and quadruple flashing stages are investigated. The optimal flashing pressures are determined and the total power outputs as well as the exergy efficiency and energy efficiency are evaluated. There is found to be a higher rise in power outputs when the flashing stages are increased from 1 to 2. However, when the flashing stages are increased from 2 to 3 and 3 to 4, the rise in power outputs is observed to drop significantly. Also, the energetic efficiency as well as exergetic efficiency is found to decrease with the increasing number of flash stages. Hence, double-flash steam power plants are found to be more favorable than triple or quadruple if multiple stages are to be used. The exergy efficiency and energy efficiency of these plants are studied at different flashing pressures, and important inferences are made with regard to the efficiency results and trends obtained.

Nomenclature

• ex =

specific exergy, kJ/kg

•
• h =

specific enthalpy, kJ/kg

•
• P =

pressure, kPa

•
• s =

specific entropy, kJ/kg K

•
• T =

temperature, °C

•
• $m˙$ =

mass flow rate, kg/s

•
• $E˙x$ =

exergy rate, kW

•
• $Q˙$ =

heat rate, kW

•
• $S˙gen$ =

entropy generation, kJ/K

•
• $W˙$ =

work rate, kW

• η =

efficiency

Subscripts

• c =

condenser

•
• cv =

control volume

•
• DF =

double flash

•
• en =

energy

•
• dest =

destruction

•
• ex =

exergy

•
• HX =

heat exchanger

•
• i =

inlet

•
• o =

outlet

•
• P =

pump

•
• QF =

•
• SF =

single flash

•
• T =

turbine

•
• TF =

triple flash

•
• TV =

throttle valve

•
• x =

mass fraction

Acronyms

• C =

condenser

•
• S =

separator

•
• T =

turbine

•
• TV =

throttle valve

2

Worldbank, Fossil Fuel Energy Consumption (% of total). http://data.worldbank.org/indicator/EG.USE.COMM.FO.ZS.

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