Optimization of ORC Power Plants for Geothermal Application in Kenya by Combining Exergy and Pinch Point Analysis

: Geothermal energy is a sustainable renewable source of energy. The installed capacity of geothermal energy in Kenya is 847.4 MWe of the total 2.7 GWe. This paper presents the effect of six different working ﬂuids to optimize the geothermal of 21.5 MWe of reinjected brine at a single-ﬂash power plant in Kenya. Engineering Equation Solver (EES) code was used to design and optimize simple organic Rankine (ORC) and regenerative cycles. The objective was to combine pinch point analysis and exergy analysis for the optimum utilization of geothermal energy by varying the turbine inlet pressure, pinch point, and reinjection temperature. The turbine inlet pressures, and pinch points were varied to obtain optimum pressures for higher net power output and exergy efﬁciencies. As the pressure increased, the efﬁciencies and net power generated increase to optimal at turbine inlet pressures between 2000 and 3000 kPa. By maintaining a condenser temperature at 46.7 ◦ C, the turbine outlet pressures were 557.5 kPa for isobutene, 627.4 kPa for isobutane, 543.7 kPa for butene, 438.9 kPa for trans-2-butene, 412.3 kPa for R236ea, and 622.9 kPa for R142b. For the pinch point of 10 ◦ C, the working ﬂuid with a lower net power is trans-2-butene at 5936 kW for a ﬂow rate of 138.8 kg/s and the highest reinjection at 89.05 ◦ C. On the other hand, R236ae had a ﬂow rate of 398.2 kg/s, a higher power output of 7273 kW, and the lowest reinjection temperature of 73.47 ◦ C for a 5 ◦ C pinch point. In the pinch point consideration, the suitable ﬂuid will depend on the best reinjection temperatures. The pinch point affects the heat transfer rates and effectiveness in the heat exchangers. The best pinch point is 10 ◦ C, since the reinjection temperatures are the highest between 83 and 89 ◦ C. The analysis showed that for unlimited reinjection temperatures, basic ORC is suitable. The regenerative cycle would be best suited where reinjection temperature is constrained by brine geochemistry.


Introduction
Geothermal energy utilization is mainly power conversion technologies as flash or binary cycles [1][2][3][4]. The high grade and most applicable form of the energy is power generation with the classification of geothermal power plants as dry steam, single flash, binary, hybrid, and back pressure [4,5]. Other uses of geothermal energy are ground source heat pumps, district heating as in Iceland, and greenhouse heating (Kenya and Japan) [6][7][8][9]. In Kenya, most of the geothermal power plants developed in the Olkaria geothermal complex are single flash [10][11][12][13][14]. This paper optimizes the geothermal energy available in Olkaria II geothermal power plant in Kenya. Geothermal resources with temperatures below 150 • C are utilized for binary power plants [15][16][17][18]. Shallow geothermal systems (<200 m) are designed for ground heat source pumps to allow repeated operational and avoid soil thermal depletion [9].
In Kenya, the energy sources are mainly hydropower and thermal power plants at 35.12% and 34.93% of installed generation capacity, respectively. Of the total installed In Kenya, the energy sources are mainly hydropower and thermal power plants at 35.12% and 34.93% of installed generation capacity, respectively. Of the total installed capacity of 2.712 GWe, geothermal is ranked third with an installed capacity of 847. 4 MWe which translates to 31.24% [19,20].
The areas developed are Olkaria and Eburru geothermal fields with Menengai caldera at advanced exploration stages [21,22]. Figure 1 shows the distribution of the geothermal resources in Kenya mainly associated with quaternary volcanic complexes in the GEARS [21]. The rock types in Olkaria are pyroclastic occurring between depths of 0 and 100 m and consist of tuffs, pumice, volcanic glass, obsidian, and rhyolitic fragments [22]. The reservoir is estimated to be in the trachyte formation with intrusion indicating the heat source in Olkaria at depths of 900-3000 m [23]. The alteration and oxidation signify a permeable geothermal system.  [21].
Energy conversion systems use the geothermal resource for electricity generation in a power plant or for heating as in-ground source heat pumps. For in-ground heating, a closed geothermal loop exchanges heat with the ground within a specified volume where soil or groundwater provides heat to warm buildings or receive excess heat [24]. Energy conversion systems use the geothermal resource for electricity generation in a power plant or for heating as in-ground source heat pumps. For in-ground heating, a closed geothermal loop exchanges heat with the ground within a specified volume where soil or groundwater provides heat to warm buildings or receive excess heat [24]. Thermodynamic principles mainly govern geothermal power plants' operations and design configurations. binary (ORC) [25,26]. In single-flash power plants, pressurized two-phase fluid undergoes the flashing process once by lowering the pressure below the saturation pressure of the fluid temperature in one separator. The power generated and efficiencies are low for SF units. To increase the efficiencies or power generated from the geothermal resource, double or triple flashings are performed by adding one and two more flashing stages, respectively [1,25,27]. After flashing the brine, the high-quality steam is sent to the steam turbine to generate electricity. The dry-steam case directs steam to the turbine from the steam field. Unlike the flash units, the dry-steam type does not have a flasher/separator and brine to be reinjected. The third type of power plant is binary units using lowertemperature resources. In binary power plants, the geothermal brine is passed through the heat exchanger to heat working fluid in a closed circuit of turbine, evaporator, condenser, pump, and preheater. In a geothermal system, an optimum reinjection strategy should be considered depending on the geochemistry of the brine. Reinjection temperatures should be high enough to avoid silica scaling. The brine has been reinjected at temperatures of above 70 • C [28] or 80 • C [29].
The brine source can be the geothermal fields of an abandoned oil well. In Nevada, 92 • C fluid at a flow rate of 26 kg/s generates 216 kW from oil wells [30]. The Huaibei oil field has the first ORC system in China with 110 • C of geothermal fluid [30]. Binary power plants are cost-effective and require low enthalpy resources [31]. The lowest temperature difference between hot fluid and cold fluid is referred to as the pinch point [32,33]. Heat exchanger designers mainly define the values of pinch points.
The first binary power plant reported used ethyl chloride (C 2 H 5 Cl) as a working fluid [25] and heat supplied with two-phase brine at 130 • C from a single well with an estimated capacity of 250 kWe and 12.4% efficiency [25]. The heat source temperature may vary from as low as 50 to 250 • C [34]. Binary power plants constitute over 35% of the geothermal units as of December 2014, with an average rating of 6 MW per unit [25]. Generally, binary power plants utilize a different range of geothermal brine temperatures [35]. The main advantage of adding a binary plant to existing single flash is the elimination of exploration and drilling costs, which are the most expensive and risky part of geothermal development. ORC units are also simple in construction; system components are available, high in flexibility, and safe [36]. The ORC technique is characterized by its robustness, compact design, the ability for automation, and comparatively high efficiency with the exclusion of blade corrosion [37]. Binary units are more complex than flash units and designed to maximize the extraction of available energy (exergy) from geothermal brine [1]. Exergy applied in the classification of 18 underperforming geothermal power plants in Japan as either high-exergy or medium exergy power plant [38].
The investigation of pinch point position in the heat exchangers showed they are located at the bubble point and dew point in the evaporator and condenser, respectively, and they are influenced by the heat source temperature [39]. The application of a minimum pinch point in different working fluids ranking performance indicated a net power improvement of 13.6% [33]. Pinch point optimization in an evaporator using R600a working fluid showed that the pinch point temperature difference is related to the total investment cost of the evaporator [32]. Optimization based on exergy recovery and exergy destruction perspectives found that the range of pinch points in the evaporator is between 8 and 20 • C [32]. An optimal pinch point in the heat exchangers lowers the cost per unit exergy in isobutane ORC using a heat source at 150 • C [40]. In evaluating power generation from hot springs of 60-140 • C, using different working fluids applied a pinch point of 5 • C to obtain 19 kW power output, and the evaporator accounted for 44% of exergy destruction [41]. The selection of an optimal pinch point in the evaporator depends on the manufacturers' experience, while in studies and analysis, it ranged between 3 and 11 [18,32,40,[42][43][44][45][46]. In a binary power plant using R600a working fluid, the results showed that the optimal pinch point values (in the range of 5-12 • C) are closely related to the investment cost of the evaporator [32]. Thermodynamic optimization of a flash-binary power plant using an ammonia-water mixture used a pinch point of 10 • C in the evaporator [47,48]. An increase in pinch points led to a decrease in the heat transfer rate and lower working fluid mass flow rates [47]. A constant pinch point of 10 • C was considered for all the working fluids in a comparison of pure and zeotropic working fluids [33]. Past researchers have considered different working fluids and pinch point optimization in binary power plants in various geothermal fields. The studies have considered pinch point optimization. The pinch point values were in ranges or had the same fixed values for different working fluids. Graphical plots were used to select optimum pinch points to analyze exchangers. This research includes the most effective pinch point in a preheater and evaporator and the relation of the exergy's concept with sustainability index as a function of utilization efficiency in the Olkaria geothermal field. The energy and mass balance equations calculate the brine exit temperature from the preheater.
This paper describes and optimizes binary power plants by employing the energy and exergy, pinch point, and sustainability index for six different working fluids. The objective is to optimize two power configurations (basic/simple ORC and regenerative ORC). The main parameters varied were turbine inlet pressure and pinch point in the heat exchangers.

Thermodynamic and Energy Analysis
In a thermo-exergy analysis of the system, each component in the system is studied as a steady state. The effects of kinetic and potential energies are neglected in the analysis [49]. The general steady-state energy and mass balance equations for any components are as shown in Equations (1) and (2) [36].
Geothermal binary units contribute 73% of ORC cycles [37]. Heat exchangers (evaporator and preheater) play a significant role in binary units because they are in contact with the heat source (hot brine) [47,50]. The energy efficiency of the system is calculated as follows: ( Binary plants have efficiencies between 6.362 and 15.35% [51].

Exergy Analysis
Thermodynamics is an intersection of three fields: energy, exergy, and entropy [52]. Entropy considers the effects of irreversibility in a system resulting from exergy destruction. Exergy is the available energy that is available from a system in equilibrium with the surrounding environment [36,53,54]. Exergy is the quality of energy in the heat stream that can be converted to useful work [2,26].
Exergy aims to maximize/optimize the available energy for better utilization from an optimum usage view perspective [55,56]. Exergy analysis is used to identify the system's inefficiency in terms of exergy destruction for the components with respect to its surrounding [52,55,57,58]. Exergy models show imperfections in thermodynamic processes and help to make thermodynamic models more efficient [54,59].
A reservoir temperature of 250 • C and a sink of 40 • C in Nisyros Island, Greece, established exergy efficiencies of 38.7% and 49% for single-flash and double-flash cycles, respectively [55]; assessment of the second law of thermodynamics for binary units utilizing low-temperature geothermal brine for the proposed plant in Nisyros shows 40% efficiency [55]. Exergy represents the upper limit of the amount of work a system can deliver in line with the laws of thermodynamics [60]. The difference between the available exergy and actual work varies from component to environment, and the difference brings a challenge to the improvement of the system to increase efficiency and reduce wastage [54,60]. Equation (4) shows the general expression for specific exergy involving environmental thermal interaction [25,43,55,61].
where i is for all incoming streams and j is for all outgoing streams with the exergy loss, and ∆ . E is always positive [25]. Exergy losses are subdivided into working fluid pump, turbine, evaporator, and condenser losses. For a control volume, the general exergy balance [61], the exergy output is always less than the total exergy input into the system [2]. The exergy equations are used to determine efficiencies for various components in power plants. Exergy destruction for each component is calculated using Equation (9) [36].

Modeling and Analysis
Olkaria II single flash units generate 105 MW from three condensing turbo-generating units of each 35 MWe [12]. Two-phase fluid is separated in the separator at 462.25 kPa, 156.4 • C into brine and steam. The steam quality is 0.52, and the flow rate of 227.4 kg/s, while the brine flow rate is 206.9 kg/s. The brine reinjected at this state has energy and exergy that can generate power using a binary unit. The brine exergy at the separator exit is 21.5 MW of 196.6 MW exergy. Other parameters are the condenser (temperature, 44.97 • C, pressure, 699.7 kPa, condensate flow rate, 2372 kg/s, cooling water flow rate, 2194 kg/s) [12]. Two ORC cycle configurations for six different working fluids in this study are optimized by multi-objectively constraining parameters.

System Description
The proposed units are a basic binary power plant with an evaporator and preheater, and a regenerative cycle with an evaporator ( Figure 2) [1,50]. The addition of the binary power plant will increase the power output and efficiencies of the available geothermal energy in Olkaria II [37]. The main parameters known are the flow rate ( . m) and temperature of the brine. The thermodynamic properties of states are obtained from EES code. For any thermodynamic system, the energy, mass, and exergy balance equations hold.
Upon flashing the brine from the steam field, the brine destined for reinjection is utilized for the proposed basic binary for different working fluids. For the simple ORC, Figure 2a, the brine (State A) from the separator enters the ORC evaporator at 156.7 • C. Working fluid enters the preheater and evaporator at States 4 and 5, respectively, and it is changed to saturated or super-heated vapor (State 1). For an optimization pressure, P 1 , the vapor expands isentropically in the turbine coupled to a generator. The condenser temperature, T 2 , is set at 46.5 • C for both cycles [50]. At State 3, the sub-cooled fluid is pumped to the preheater and evaporator to complete the closed-loop of ORC. The turbines' and pumps' isentropic efficiencies are 85% and 75%, respectively. In the other unit of Figure  Upon flashing the brine from the steam field, the brine destined for reinjection is utilized for the proposed basic binary for different working fluids. For the simple ORC, Figure 2a, the brine (State A) from the separator enters the ORC evaporator at 156.7 °C . Working fluid enters the preheater and evaporator at States 4 and 5, respectively, and it is changed to saturated or super-heated vapor (State 1). For an optimization pressure, P1, the vapor expands isentropically in the turbine coupled to a generator. The condenser temperature, T2, is set at 46.5 °C for both cycles [50]. At State 3, the sub-cooled fluid is pumped to the preheater and evaporator to complete the closed-loop of ORC. The turbines' and pumps' isentropic efficiencies are 85% and 75%, respectively. In the other unit of Figure 2b, the geothermal brine passes only through the evaporator (States A and B). The working fluid enters the evaporator at State 6 and is vaporized at State 1. The main difference in the system's configurations is the regenerator in States 2-3 and 5-6 replacing the preheater as in the simple ORC case. After the condenser, the working fluid is pressurized in State 4, passed through the regenerator, and in State 6, the cycle in the evaporator is completed.
For both models, a water-cooled surface condenser is used to condense the working fluid. The thermodynamic analysis focused on the ORC cycle. A cooling tower will be considered in another article to compare cooling systems (air-cooled and water-cooled). In this paper, the cooling towers are assumed to be similar, and their impact is on the economic part of the power plant. For the exergy analysis, the local temperature at Olkaria is 20 °C and the ambient pressure is 86 kPa [62]. Olkaria has an elevation of about 2100 m.a.s.l. For the modeled binary power plants, six different working fluids were selected and analyzed. The fluids investigated have critical temperatures less than the heat source temperature of 156 °C . The assumptions made in the system analysis include the system operating under steady conditions [49], well-insulated and counter flow heat exchangers, the brine having thermophysical properties of IAPWS [63], the turbine and pumps being adiabatic, and a dead state and cooling water temperature of 20 °C.
The parameters optimized were the turbine inlet pressure, the pinch point in the heat exchangers, and the reinjection temperatures. For the turbine inlet pressure, the values were between 1000 kPa and lower than the critical pressures for each fluid. On varying the turbine pressure, exergy efficiencies and work net generated plots were used to identify the optimum operating pressures. The pinch point temperatures varied from 5 to 15 °C . The pinch points affected the net power generated, working fluid flow rates and For both models, a water-cooled surface condenser is used to condense the working fluid. The thermodynamic analysis focused on the ORC cycle. A cooling tower will be considered in another article to compare cooling systems (air-cooled and water-cooled). In this paper, the cooling towers are assumed to be similar, and their impact is on the economic part of the power plant. For the exergy analysis, the local temperature at Olkaria is 20 • C and the ambient pressure is 86 kPa [62]. Olkaria has an elevation of about 2100 m.a.s.l. For the modeled binary power plants, six different working fluids were selected and analyzed. The fluids investigated have critical temperatures less than the heat source temperature of 156 • C. The assumptions made in the system analysis include the system operating under steady conditions [49], well-insulated and counter flow heat exchangers, the brine having thermophysical properties of IAPWS [63], the turbine and pumps being adiabatic, and a dead state and cooling water temperature of 20 • C.
The parameters optimized were the turbine inlet pressure, the pinch point in the heat exchangers, and the reinjection temperatures. For the turbine inlet pressure, the values were between 1000 kPa and lower than the critical pressures for each fluid. On varying the turbine pressure, exergy efficiencies and work net generated plots were used to identify the optimum operating pressures. The pinch point temperatures varied from 5 to 15 • C. The pinch points affected the net power generated, working fluid flow rates and efficiencies, and reinjection temperatures. Pinch points of 5, 8, and 10 • C were used to show the effect of pinch point selection on the reinjection temperature, net power generated, and exergy efficiency.

Working Fluid Selection
One of the factors in setting up a binary power plant is working fluid selection. The working fluid in most cases consists of organic compounds, and selecting it depends on the thermodynamic properties [25], including critical temperature, T cr , critical pressure, P cr , health, safety, and environmental safety [27,52]. Table 1 shows some properties of the working fluid [25,37,64,65]. Most of the working fluids are unstable at temperatures higher than 327 • C [65]. For the relative turbine size, a generalized figure of merit, ξ, directly proportional to the turbine size was developed by Milora and Tester [64]. The ξ is expressed as: P c h f g r T cond g gmole 1 2 bar −1 (8) where m is the fluid's molecular weight, P c is the critical pressure, h f g is the reduced latent heat, v sat g is the reduced gas-specific volume evaluated at condensing temperature, T cond , and T.E.A is turbine exhaust area [64]. From Equation (8), it can be correlated that the lower the condenser temperature, the smaller the turbine translating to lower plant cost. The selection of working fluid will ultimately dictate the size of the turbine [43]. The isobutane turbine exit area is much larger compared to propane, as shown in Table 1. Most ORC cycles operate as sub-critical cycles and utilize hydrocarbons [34]. Supercritical thermal efficiency usually exceeds subcritical cycle efficiency. Using isobutane with 147 • C turbine temperature, 47 • C condensing temperature, 85% turbine isentropic efficiency, and 80% feed pump isentropic efficiency has the following results at different pressures: 4000 kPa (supercritical); η th = 12.3% and 3000 kPa (supercritical); η th = 11.0% [25]. Most plants utilize hydrocarbons because of the low levels of global warming potential and low toxicity, and there is no effect on the ozone layer. Working fluids are classified as wet, isentropic, or dry [66], depending on the shape of the T-s diagram on the vapor line [67]. The type of the working fluid will influence the binary geothermal layout [53]. Dry fluid types have better performances, but the superheat will have to be wasted in the condenser. The temperature of the brine/source dictates the fluid to be selected. In renewable energy, sustainable development requires the efficient use of available resources. The sustainability index is defined as shown in Equation (9) [36] as a function of exergy efficiency [58]. The energy and exergy efficiencies are employed in the calculating the energy and exergy of a thermodynamic system [56].
Chlorofluorocarbons have good thermodynamic properties but catalyze the ozone layer. Suitable alternatives for CFCs are hydrofluorocarbons (HFCs) with proper precautions to avoid environmental damages and harming human health [37]. From the list of working fluids in Table 1, the fluids considered for the binary plant are trans-2butene, isobutane, butene, and isobutene hydrocarbons and refrigerants R236ea and R142b. Thermodynamic parameters of the fluids were obtained using EES code. The different working fluids analyzed in this paper agreed with the constraining energy and mass balance equations [25].

Heat Exchangers
This section will discuss analysis of the evaporator and preheater. Shell and plate types of heat exchangers have a high rate of heat transfer coefficient [36]. The pinch point temperature difference (∆T pp ) affects heat exchangers' thermodynamic and economic performance [68]. The pinch point for the heat exchangers was varied from 5 to 15 • C.
The heat exchanger(s) heat transfer area is calculated as: .
where A is the heat exchanger surface area, . Q EV/PH is the heat transfer rate in the heat exchanger (evaporator/preheater), ∆TLMTD is given by Equations (13) and (14) for the evaporator and preheater, respectively, as shown in Figure 3; and U is the overall heat transfer.

Results and Discussion
This paper combined exergy and pinch point analyses to optimize two binary of the geothermal power plant. At the steady-state conditions, energy, mass, and balance equations apply at each state. In the study, eight working fluids were se

Results and Discussion
This paper combined exergy and pinch point analyses to optimize two binary cycles of the geothermal power plant. At the steady-state conditions, energy, mass, and exergy balance equations apply at each state. In the study, eight working fluids were selected based on the validity of the energy and mass balance equations in the heat exchangers (evaporator and preheater) with the same three pinch points (5 • C, 8 • C, and 1 • C).
The input temperature required varies for each working fluid. The brine reinjection temperature depends on the pinch point selection. The pinch point factor affects the effectiveness of the heat exchangers and the calculation of reinjection temperatures. The pinch point also affects the mass flow rate of the working fluid, the net power output generated from the plant, and the reinjection temperature. Results show that low pinch point values correspond to lower reinjection temperatures. The optimum pressures were identified using exergy efficiency, net power generated, reinjection temperature, and pinch point temperature plots. Figures 4-6 show the effects of varying turbine inlet pressure on net power generated, efficiencies, and reinjection temperatures, respectively. As the pressure increases, the efficiencies and net power generated work increased to optimal values as presented in Figure 4a and Table 2 at 1955 kPa for isobutene, 2378 kPa for isobutane, 1888 kPa for butene, 1563 kPa for trans-2-butene, 1845 kPa for R236ea, and 2302 kPa for R142b for the simple ORC cycle. In the analysis, the condenser temperature and pinch point were fixed while varying turbine inlet pressure.

Fluid P 1 (kPa) P 4 (kPa) P cr (kPa) T C ( • C) W net (kW) Sum exd (kW) η th (%) η u (%) η u2 (%) SI (−)
.  Referring to Figure 4, the optimum turbine inlet pressures for the simple ORC are less than in the case of the regenerative cycle. Figure 4b shows the effect of turbine inlet pressure on net power for different working fluids for the regenerative cycle. At the condenser temperature of 46.7 °C , the turbine outlet pressures were 557.5 kPa for isobutene, 627.4 kPa for isobutane, 543.7 kPa for butene, 438.9 kPa for trans-2-butene, 412.3 kPa for R236ea, and 622.9 kPa for R142b, as listed in Table 2. The inlet turbine pressure is the main parameter for identifying the optimal operating pressures in binary power plants [63,69]. Figure 5 illustrates the effect of turbine inlet pressure on exergy efficiencies, while  Referring to Figure 4, the optimum turbine inlet pressures for the simple ORC are less than in the case of the regenerative cycle. Figure 4b shows the effect of turbine inlet pressure on net power for different working fluids for the regenerative cycle. At the condenser temperature of 46.7 • C, the turbine outlet pressures were 557.5 kPa for isobutene, 627.4 kPa for isobutane, 543.7 kPa for butene, 438.9 kPa for trans-2-butene, 412.3 kPa for R236ea, and 622.9 kPa for R142b, as listed in Table 2. The inlet turbine pressure is the main parameter for identifying the optimal operating pressures in binary power plants [63,69]. Figure 5 illustrates the effect of turbine inlet pressure on exergy efficiencies, while other parameters (pinch point and condenser temperature) are kept constant. Increasing the turbine inlet pressure will decrease the exergy difference between the inlet and outlet brine, thus reducing the mass flow rate of the working fluid; consequently, exergy efficiency decreases. Referring to Figure 4, the optimum turbine inlet pressures for the simple ORC are less than in the case of the regenerative cycle. Figure 4b shows the effect of turbine inlet pressure on net power for different working fluids for the regenerative cycle. At the condenser temperature of 46.7 °C , the turbine outlet pressures were 557.5 kPa for isobutene, 627.4 kPa for isobutane, 543.7 kPa for butene, 438.9 kPa for trans-2-butene, 412.3 kPa for R236ea, and 622.9 kPa for R142b, as listed in Table 2. The inlet turbine pressure is the main parameter for identifying the optimal operating pressures in binary power plants [63,69]. Figure 5 illustrates the effect of turbine inlet pressure on exergy efficiencies, while other parameters (pinch point and condenser temperature) are kept constant. Increasing the turbine inlet pressure will decrease the exergy difference between the inlet and outlet brine, thus reducing the mass flow rate of the working fluid; consequently, exergy efficiency decreases.   Figure 6 shows that the turbine pressure varies with the type of working fluid and cycle configuration. The trends illustrated are due to different values of critical temperature and pressure. Figure 5a shows that the optimum turbine inlet pressures for simple ORC are lower than for the regenerative ORC cycle (Figure 5b). A simple ORC has higher efficiencies between 20 and 35% due to more heat being recovered in the preheater than in the regenerative ORC. In the regenerative cycle, the reinjection temperature was fixed, unlike in simple ORC, where it was simulated using EES code. The exergy efficiencies for the regenerative cycle were between 15% and 27%.

m (kg/s)
An increase in the turbine inlet pressure led to changes in the enthalpy drop between the turbine inlet and outlet pressures. With the constant condenser temperature, varying pressure, P 1, there will be optimum pressures yielding the maximum power generated and exergy efficiencies. Figure 6 shows the effect of varying the turbine inlet pressure on the reinjection temperature of the brine. For temperatures above 89 • C, most of the working fluids are suitable. The limiting factor will be the geothermal water geochemistry. Once the optimum reinjection temperature has been selected, the design parameter that was checked was the pinch point.
exergy efficiencies. Figure 6 shows the effect of varying the turbine inlet pressure on the re temperature of the brine. For temperatures above 89 °C , most of the working f suitable. The limiting factor will be the geothermal water geochemistry. O optimum reinjection temperature has been selected, the design parameter t checked was the pinch point. By increasing pressures, the amount of vapor decreases with increasing tem and specific enthalpy [70]. The effect of turbine inlet pressure is related to the load. As the turbine inlet pressure increases, the heat transfer between brine working fluid decreases, and the pump power consumption increases, decrea total power output [71,72].
In this study, exergy and pinch point analysis combined to optimize the geo brine in Kenya. Figure 7 shows the effects of varying pinch points between 5 and the net power output and reinjection temperature. As the pinch point tem increases, the net power generated decreases, but Tc's reinjection temperature in (a) (b) Figure 6. Variation of turbine inlet pressure with reinjection temperatures of brine for the simple ORC. The highest reinjection temperature was noted to be for trans-2-butene at 89.05.
By increasing pressures, the amount of vapor decreases with increasing temperature and specific enthalpy [70]. The effect of turbine inlet pressure is related to the parasitic load. As the turbine inlet pressure increases, the heat transfer between brine and the working fluid decreases, and the pump power consumption increases, decreasing the total power output [71,72].
In this study, exergy and pinch point analysis combined to optimize the geothermal brine in Kenya. Figure 7 shows the effects of varying pinch points between 5 and 15 • C on the net power output and reinjection temperature. As the pinch point temperature increases, the net power generated decreases, but Tc's reinjection temperature increases.
the turbine inlet and outlet pressures. With the constant condenser temperature, varying pressure, P1, there will be optimum pressures yielding the maximum power generated and exergy efficiencies. Figure 6 shows the effect of varying the turbine inlet pressure on the reinjection temperature of the brine. For temperatures above 89 °C , most of the working fluids are suitable. The limiting factor will be the geothermal water geochemistry. Once the optimum reinjection temperature has been selected, the design parameter that was checked was the pinch point. Figure 6. Variation of turbine inlet pressure with reinjection temperatures of brine for the simple ORC. The highest reinjection temperature was noted to be for trans-2-butene at 89.05.
By increasing pressures, the amount of vapor decreases with increasing temperature and specific enthalpy [70]. The effect of turbine inlet pressure is related to the parasitic load. As the turbine inlet pressure increases, the heat transfer between brine and the working fluid decreases, and the pump power consumption increases, decreasing the total power output [71,72].
In this study, exergy and pinch point analysis combined to optimize the geothermal brine in Kenya. Figure 7 shows the effects of varying pinch points between 5 and 15 °C on the net power output and reinjection temperature. As the pinch point temperature increases, the net power generated decreases, but Tc's reinjection temperature increases. From Figure 7, pinch point selection is a crucial parameter that weighs between net power generated and brine reinjection. The effects of pinch point temperature difference on net power output of the considered cycles are shown in Figure 7. Lower values of power and higher reinjection temperatures are obtained at a higher pinch point difference because of the reduced mass flow rate of the working fluid. The reduction in the flow rates of the working fluid will reduce the heat exchangers' duty and give higher reinjection temperatures.
The reinjection temperatures in this study are above 80 • C for pinch points above 8 • C. Higher pinch points above 8 • C should be considered in the design of heat exchangers because of higher reinjection temperatures as compared to 5 • C.
The combination of exergy and pinch point optimization shows the analysis and optimization call for critical analysis to include other thermodynamic parameters. Table 2 shows that R236ea has the lowest reinjection temperature, 73.47 • C, as in the constrained energy and mass balance equations. At the optimum turbine pressure, the highest second utilization efficiency is 44.93% with isobutane, and the lowest value is with trans-2-butene at 42.33%. The main factor in efficiency calculation is the reinjection temperature. At high reinjection temperatures, the exergy available is reduced. Table 3 shows the effects of the 8 • C pinch point chosen for the analysis. Tc's reinjection temperatures are between 79 and 86 • C. The net power generated for the 8 • C pinch point is lower than for 5 • C. The lower pinch point has lower mass flow rates, thus generating less power. The sustainability index is a function of exergy and is between 1.71 and 1.78.  Table 4 shows the power plant results operating at optimum turbine pressure and a pinch point of 10 • C. Higher reinjection temperatures are noted for the higher value of the pinch point. A pinch point of 10 • C shows higher reinjection temperature values. From Table 4, the reinjection temperatures are between 82.94 and 89.05 • C.  4 show that the net power generated is less than the exergy destruction. For a pinch point of 10 • C, the working fluid with a lower net power is trans-2-butene at 5936 kW for a flow rate of 138.8 kg/s and the highest reinjection among other fluids at 89.05 • C (Table 4). R236ae having a flow rate of 398.2 kg/s, on the other hand, has a higher power output of 7273 kW and the lowest reinjection temperature of 73.47 • C for a 5 • C pinch point ( Table 2).
Tables 5-7 shows the results of a regenerative cycle operating at optimum turbine inlet pressures for pinch points of 10, 5, and 8 • C, respectively. As in the case of simple ORC, increasing the pinch point lowers the net power output because of the reduced mass flow rates of the working fluids. From Table 5, the energy efficiencies are between 8.75 and 11.46%. The mass flow rates contribute to the net power generated. The mass flow rates of working fluids are 151.7 kg/s, 167.8 kg/s, 150.9 kg/s, 140.6 kg/s, 355.3 kg/s, and 273 kg/s for isobutene, isobutane, butene trans-2-butene, R236ea, and R142b, respectively. The highest net power generated is 7057 kW using trans-2-butene, while the lowest is 5388 kW using R142b. The combination of exergy and pinch point optimization shows the analysis and optimization call for critical analysis to include other thermodynamic parameters. The main factor in efficiency calculation is the reinjection temperature.
From Tables 2-7, the effect of pinch point is seen to affect the net output power. The tables indicate that an increase in pinch point decreases the net output power. After increasing the pinch point, the working fluid mass flow rate decreases because of the lower heat absorption in the heat exchangers.  The sustainability index is a function of exergy and is between 1.36 and 1.55. Exergy destruction for the regenerative cycle is less than in the simple ORC. The regenerative cycle exergy destruction in the preheater is excluded unlike in the case of simple ORC. The heat exchangers contribute most of the exergy destruction in the ORC.
To design a geothermal binary unit, the following parameters should be considered in design and optimization: the available geothermal temperature ranges, limit of reinjection temperature, turbine inlet pressure, and pinch point based on the manufacturer's specifications.

Conclusions
This study shows that the selection of working fluid for ORC depends on many parameters. The main parameters are the turbine inlet pressure, efficiencies, maximum power generated, reinjection temperature of geothermal fluid, sustainability index, pinch point, and total exergy destroyed. Most studies have been on optimization based on other parameters by applying a fixed pinch point for different working fluids, cases not supported by graphical representation by heat transfer diagrams, and energy and mass balance equations. It is worthwhile to combine pinch point analysis and the exergy optimization of binary power plants. The results show that the optimum and practical pinch point is 8 • C for reinjection temperatures above 80 • C.
Exergy efficiency and net power generated plots identify the optimum pressure. The turbine inlet pressure affects the efficiencies, net power generated, and reinjection temperatures. Depending on the objective function and the cycle configurations, the working fluid selection is a multi-criteria process. For the six working fluids investigated, based on the reinjection temperatures and exergy efficiency, a suitable fluid would be trans-2-butene. The ORC cycle has a higher net output power compared to the regenerative cycle. The first and second-law efficiencies correspond to the simple ORC with a preheater. Selection of the suitable fluid is a multi-objective criterion, it can be based on pinch point difference, exergy efficiency, and reinjection temperature.
According to the optimum design conditions at fixed condenser temperature, a simple ORC cycle had the highest net power output. The optimum pressures for the simple ORC are less than 2000 kPa, whereas for the regenerative cycle, they are about 3000 kPa. The analysis showed that for unlimited reinjection temperatures, basic ORC is suitable. The regenerative cycle would be best suited where the reinjection temperature is constrained by brine geochemistry. Pinch points in heat exchangers affect the efficiencies/effectiveness, net power output, reinjection, heat transfer rates, and working fluid flow rates.