Comparison of Thermodynamic Performances in Three Geothermal Power Plants Using Flash Steam

Farsi, Aida; Rosen, Marc A.

doi:10.1115/1.4054038

Abstract

Three geothermal systems, including single-flash, double-flash, and double-flash connected turbine flash geothermal power plants, are compared in terms of electrical power production and exergy efficiency. In the double-flash connected turbine (double-T) geothermal electrical power production systems, the outlet stream from the first steam turbine is recovered in the mixing chamber and combined with the vapor product of the second separator. The thermodynamic model for the single-flash, double-flash, and double-T geothermal systems is developed using energy and exergy balances for each component of the systems. From the thermodynamic model, the optimum flash chambers pressures, at which the electrical power production is a maximum, can be determined. It is found that, for an input geothermal source temperature of 230 °C and an input geothermal water mass flowrate of 230 kg/s, the optimum pressures for the first flash chamber are 300 kPa, 350 kPa, and 350 kPa for the single-flash, double-flash, and double-T geothermal systems, respectively. The electrical power produced in these systems at their corresponding optimum flashing pressures, respectively, are 16,000 kW, 19,500 kW, and 20,600 kW. Also, for the single-flash, double-flash, and double-T geothermal systems, the exergy efficiency at the optimum flash chamber pressures are found to be 44.2%, 47.1%, and 48.5%, respectively.

Introduction

The worldwide energy demand is mainly satisfied by fossil fuels. However, these energy sources are finite and cause environmental problems. The need for energy is continually increasing due to global population growth and industrialization, increasing consumption rates of fossil fuels. With continuing consumption of fossil fuels, easily accessible ones will become scarcer and more difficult to extract. It is, therefore, important to develop alternative energy resources like renewable energies to continue to meet global energy demand with low or minimum environmental impacts.

Geothermal resources are promising options for electrical power production, particularly in regions with large geothermal resources. Thermal energy can be extracted from geothermal resources and used for diverse purposes like heating, cooling, and electrical power production. Geothermal energy resources are relatively environmentally benign and, unlike other renewable energy resources (e.g., solar, wind), this source is capable of continuous generation of thermal energy. Various geothermal system configurations exist, depending on the method of energy transfer from the geothermal fluid to the energy system. High-temperature geothermal power plants are typically flash steam, dry steam, or binary cycles. The flash steam configuration uses a separator to produce steam from the extracted geothermal water in a power cycle. In the dry steam configuration, steam from the geothermal source is directly used in the power cycle. In a binary cycle, a heat exchanger is used to transfer heat from the high-temperature geothermal fluid to the working fluid in the power plant. In recent years, numerous studies of geothermal power plant systems have been reported. Selected recent studies are now described.

Colorado-Garrido et al. [1] applied energy and exergy methods to real single and double-flash geothermal power plants located in the Mexicali Valley, Mexico. They calculated the exergy destruction rates in each component of the single and double-flash cycles. It was found for the single-flash geothermal system that the condenser has the highest exergy destruction rate, while for the double-flash system the highest exergy destruction rate is associated with the condenser followed by the low-pressure steam turbine. Furthermore, Rudiyanto et al. [2] examined the Dieng geothermal power plant in Indonesia, which has an electrical power production capacity of 400 MW. In this plant, the geothermal water source temperature is between 240 °C and 333 °C. The authors performed energy and exergy analysis to identify the sources of irreversibilities in the geothermal power plant. The exergy efficiency of the system was found to be 38.2%. An optimization study identified the optimum turbine pressure as 5.5 bar. It was further found that the irreversibilities in the cycle increase with turbine pressure. Koroneos et al. [3] investigated a geothermal binary power plant in Nisyros Islan, Greece from an exergy viewpoint. They identified the inefficiencies by evaluating the exergy destruction and loss within the system and determined the exergy efficiency of the geothermal binary power plant to be 41%.

There have been also many studies in which multiple sources of renewable energy are combined to drive an energy system. For example, Kurşun [4] used a photovoltaic system in a geothermal-based multi-generation system. Also, Bonyadi et al. [5] proposed a power plant that operates on solar and geothermal energy resources. Energy, exergy, and economic assessments were carried out for the system. It was reported that the proposed system is capable of 60% more electrical power production during the summer. Senturk Acar and Arslan [6] studied a hybrid geothermal-solar powered organic Rankine cycle with a capacity of 305,700 kWh, from energy and exergy perspectives. The authors considered design parameters for the Simav geothermal field and showed that through integration of solar energy, the exergy efficiency of the system is reduced. It was noted that the exergy efficiency of the hybrid solar-geothermal power plant increases as solar collector area decreases. Ehyaei et al. [7] carried out energy, exergy, and economic analyses of a novel geothermal electrical power-cooling combined system, which comprised an organic Rankine cycle coupled with a Li-Br absorption chiller. A multi-objective optimization, performed using a particle swarm optimization, determined that the optimum electrical power and cooling cost is 0.0033 $/kWh while the exergy efficiency is 6.8%.

In flash steam geothermal electrical power production systems, the pressures of the flash chambers significantly affect the system performance and exergy efficiency. In a single-flash geothermal system, the electrical power is produced from only one flash chamber, which is the source of the generated vapor. This vapor is used in the steam turbine for electricity production. In multi-stage flash geothermal systems, more than one flashing process occurs in the flash chambers. The vapor flows generated in each flash chamber are sent to a steam turbine, generating more electrical power compared with a comparable single-flash geothermal system. The selection of flash chamber pressure is important, as it affects notably the rate of electricity production by the geothermal system. In addition, the configurations of steam turbines in double- and multi-stage flash geothermal power plants affect the system power production and efficiency. The turbines can be connected or operate independently. When the turbines are connected, the outlet vapor from the higher pressure turbine is the inlet vapor of the other turbine. For instance, in a double-flash geothermal system in which the turbines are connected, the vapor outlet from the first turbine is combined with the generated vapor in the second flash chamber, and the combined mixture is sent to the second turbine.

Ozgener et al. [8] conducted an exergy analysis of a geothermal plant using actual operating parameters. The energy and exergy efficiencies of the system were both found to be 42.9% and the exergy losses are associated with the reinjection of the geo-fluid. Zhao et al. [9] determined optimum temperatures of 150 °C and 100 °C for single- and double-flash geothermal power plant systems. Siddiqui and Dincer [10] investigated the thermodynamic performance of single to quadruple flash geothermal power plants. They noted that, as the number of flash chambers increases, the energy and exergy efficiencies of the geothermal power plant both decrease. The authors reported exergy efficiencies of 72.6%, 70.9%, 70.2%, and 69.8%, respectively, for the single, double, triple, and quadruple flash geothermal power plants. Salehi et al. [11] optimized a double-flash geothermal power plant integrated with absorption heat transformation and seawater desalination systems. The objective functions were selected to be minimizing product unit cost, as well as maximizing electric power generation and the production rate of freshwater. Note also that, with a decrease in the pressure of the flash chamber, the product unit cost declines.

Many advances in sustainable energy and geothermal technologies have been reported in recent years. The concept of energy is applied by Jalili et al. [12] to a geothermal power plant. Studies have been also undertaken on high-temperature geothermal energy [13–21] and ambient ground energy sources [22–25].

Although investigations have been carried out on various geothermal electrical power production systems, there is still a knowledge gap related to the comparison of single-flash, double-flash, and double-flash connected turbine geothermal systems in terms of electrical power production and exergy efficiency. It is also important to investigate the configurations of turbines in geothermal systems with more than one flash chamber. This research addresses these knowledge gaps by providing a comparative study of single-flash, double-flash, and double-flash connected turbine (double-T) geothermal power production systems. In this study, the systems are first modeled in Engineering Equation Solver (EES) software based on the exergy method. The thermodynamic properties at each state point that all three systems considered are obtained from the property package available in EES. Then, the optimal flash chamber pressures are identified at which the maximum electrical power production is attained. The effects of first and second flash chamber pressures on the produced electrical power are illustrated and compared for the systems. Finally, the exergy efficiency variations with the flash chamber pressure are attained and compared for the examined systems.

Descriptions of Systems

Figure 1 depicts a single-flash geothermal system. It consists of an expansion valve, a flash chamber, a steam turbine, and a condenser. The high-temperature geothermal heat source is extracted from the production well and then passes through an expansion valve, where its pressure is reduced during an isenthalpic process. Then, the geothermal water enters the flash chamber, where it flashes; the vapor part is transferred to the steam turbine and the liquid part is rejected to the injection well. The vapor part expands in the steam turbine and electrical power is generated. The turbine outlet stream enters the condenser and is completely condensed.

Fig. 1

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Single-flash geothermal electrical power generation system

In the double-flash chamber geothermal system (see Fig. 2), the liquid geothermal water outlet from the flash chamber is further used for additional production of electrical power. This stream is passed through a second expansion valve and then a second flash chamber to permit the generation of additional vapor. This vapor is used in the second steam turbine to produce electrical power.

Fig. 2

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Double-flash geothermal electrical power generation system

In the third configuration, shown in Fig. 3, the outlet stream from the first steam turbine is combined with the vapor generated in the second flash chamber before the combined fluid enters the second steam turbine. In the present article, this system is referred to as a double-flash connected turbine (double-T) geothermal system. In the double-T geothermal system, the outlet stream from the first steam turbine is recovered for use in the second steam turbine. The uniform combined stream exits the mixing chamber and expands in the second steam turbine.

Fig. 3

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Double-flash connected turbine (double-T) geothermal electrical power generation system

Figures 4(a), 4(b), and 4(c) illustrate entropy-temperature diagrams for the considered systems (single-flash, double-flash, and double-T geothermal systems) at a specific operating condition. In Fig. 4(a), for example, the saturated liquid water is drawn from the production well and enters the expansion valve (point 2). The saturated mixture is flashed in the flash chamber. The steam exiting the flash chamber is considered to be dry saturated (i.e., x₄ = 1) and drives the steam turbine (process 4–5) to produce electrical power.

Fig. 4

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Temperature-entropy diagrams for a (a) single-flash geothermal power plant, (b) double-flash geothermal power plant, and (c) double-flash connected turbine (double-T) geothermal power plant

Analysis

The geothermal systems described in the Descriptions of systems section are now analyzed using exergy methods. The thermodynamic properties at each state point are determined from property packages in the EES software. The input design parameters of the systems are listed in Table 1.

Table 1

Input design parameters for thermodynamic analysis of single-flash, double-flash, and double-T geothermal systems

Parameter	Value
Environment temperature, T_o	25 °C
Environment pressure, P_o	101 kPa
Turbine isentropic efficiency	68%
Geothermal water temperature from production well, T₁	230 °C
Geothermal water mass flowrate from production well, ${\dot{m}}_{1}$	230 kg/s
Quality of geo-fluid at production well, x₁	0
Single-flash geothermal system
Flash chamber pressure (equivalent to geothermal water pressure at expansion valve outlet, P₂)	0.4 P₁
Condenser pressure, P₅	10 kPa
Double-flash geothermal system
First flash chamber pressure, P₂	0.4 P₁ (P₁ is geothermal water source input pressure)
Second flash chamber pressure, P₇	0.65 P₄
First condenser pressure, P₅	10 kPa
Second condenser pressure, P₁₀	10 kPa
Double-T geothermal system
First flash chamber pressure, P₂	0.4 P₁
Second flash chamber pressure, P₇	0.65 P₄
Condenser pressure, P₁₀	10 kPa

Parameter	Value
Environment temperature, T_o	25 °C
Environment pressure, P_o	101 kPa
Turbine isentropic efficiency	68%
Geothermal water temperature from production well, T₁	230 °C
Geothermal water mass flowrate from production well, ${\dot{m}}_{1}$	230 kg/s
Quality of geo-fluid at production well, x₁	0
Single-flash geothermal system
Flash chamber pressure (equivalent to geothermal water pressure at expansion valve outlet, P₂)	0.4 P₁
Condenser pressure, P₅	10 kPa
Double-flash geothermal system
First flash chamber pressure, P₂	0.4 P₁ (P₁ is geothermal water source input pressure)
Second flash chamber pressure, P₇	0.65 P₄
First condenser pressure, P₅	10 kPa
Second condenser pressure, P₁₀	10 kPa
Double-T geothermal system
First flash chamber pressure, P₂	0.4 P₁
Second flash chamber pressure, P₇	0.65 P₄
Condenser pressure, P₁₀	10 kPa

In the thermodynamic analysis of the single-flash, double-flash, and double-T geothermal systems, the following assumptions are considered:

steady-state operation;
negligible values of kinetic and potential energy;
negligible pressure drops and heat losses in geothermal steam turbines;
disregardable startup periods;
adiabatic behavior for the steam turbine and flash chambers;
isenthalpic behavior for the expansion valves;
isobaric behavior for the condensers.

General rate balance expressions for mass, energy, and exergy, respectively, for an open system in a control volume can be expressed under steady-state conditions as

\sum_{i n} \dot{m} = \sum_{o u t} \dot{m}

(1)

\dot{Q} + \sum_{i n} \dot{m} h = \dot{W} + \sum_{o u t} \dot{m} h

(2)

\dot{E} x^{\dot{Q}} - \dot{E} x^{\dot{W}} + \sum_{i n} \dot{m} e x - \sum_{o u t} \dot{m} e x - \dot{E} x_{D} = 0

(3)

where

\dot{m}

, h, and ex, respectively, denote mass flowrate, specific enthalpy, and specific exergy; and

\dot{Q}

⁠,

\dot{W}

⁠, and

\dot{E} x_{D}

⁠, respectively, denote heat transfer rate, work rate, and exergy destruction rate. The terms

\dot{E} x^{\dot{W}}

and

\dot{E} x^{\dot{Q}}

⁠, respectively, are the exergy rates associated with work and heat, which can be written as

\dot{E} x^{\dot{W}} = \dot{W}

(4)

\dot{E} x^{\dot{Q}} = (1 - \frac{T_{0}}{T}) \dot{Q}

(5)

where T is the absolute temperature at which the heat transfer process occurs. Equations – can be written for each component of the systems. Table 2 provides energy and exergy balance equations for the components of the single-flash, double-flash, and double-T geothermal systems.

Table 2

Energy and exergy rate balance equations for components of the single-flash, double-flash, and double-T geothermal systems shown in Figs. 1, 2, and 3

System	Energy rate balance	Exergy rate balance
Single-flash geothermal system
Expansion valve (ev)	${\dot{m}}_{1} h_{1} - {\dot{m}}_{2} h_{2} = 0$	${\dot{m}}_{1} e x_{1} - {\dot{m}}_{2} e x_{2} - \dot{E} x_{D, e v} = 0$
Flash chamber (fc)	${\dot{m}}_{2} h_{2} - {\dot{m}}_{3} h_{3} - {\dot{m}}_{4} h_{4} = 0$	${\dot{m}}_{2} e x_{2} - {\dot{m}}_{3} e x_{3} - {\dot{m}}_{4} e x_{4} - \dot{E} x_{D, f c} = 0$
Steam turbine (st)	${\dot{m}}_{3} h_{3} - {\dot{m}}_{5} h_{5} - {\dot{W}}_{s t} = 0$	${\dot{m}}_{3} e x_{3} - {\dot{m}}_{5} e x_{5} - {\dot{W}}_{s t} - \dot{E} x_{D e s, s t} = 0$
Condenser (c)	${\dot{m}}_{5} h_{5} - {\dot{m}}_{6} h_{6} - {\dot{Q}}_{c} = 0$	${\dot{m}}_{5} e x_{5} - {\dot{m}}_{6} e x_{6} - (1 - \frac{T_{0}}{T_{c}}) {\dot{Q}}_{c} - \dot{E} x_{D, c} = 0$
Double-flash geothermal system
Expansion valve 1 (ev₁)	${\dot{m}}_{1} h_{1} - {\dot{m}}_{2} h_{2} = 0$	${\dot{m}}_{1} e x_{1} - {\dot{m}}_{2} e x_{2} - \dot{E} x_{D, e v 1} = 0$
Flash chamber 1 (fc₁)	${\dot{m}}_{2} h_{2} - {\dot{m}}_{3} h_{3} - {\dot{m}}_{4} h_{4} = 0$	${\dot{m}}_{2} e x_{2} - {\dot{m}}_{3} e x_{3} - {\dot{m}}_{4} e x_{4} - \dot{E} x_{D, f c 1} = 0$
Steam turbine 1 (st₁)	${\dot{m}}_{3} h_{3} - {\dot{m}}_{5} h_{5} - {\dot{W}}_{s t, 1} = 0$	${\dot{m}}_{3} e x_{3} - {\dot{m}}_{5} e x_{5} - {\dot{W}}_{s t, 1} - \dot{E} x_{D, s t 1} = 0$
Condenser 1 (c₁)	${\dot{m}}_{5} h_{5} - {\dot{m}}_{6} h_{6} - {\dot{Q}}_{c 1} = 0$	${\dot{m}}_{5} e x_{5} - {\dot{m}}_{6} e x_{6} - (1 - \frac{T_{0}}{T_{c 1}}) {\dot{Q}}_{c 1} - \dot{E} x_{D, c 1} = 0$
Expansion valve 2 (ev₂)	${\dot{m}}_{4} h_{4} - {\dot{m}}_{7} h_{7} = 0$	${\dot{m}}_{4} e x_{4} - {\dot{m}}_{7} e x_{7} - \dot{E} x_{D, e v 2} = 0$
Flash chamber 2 (fc₂)	${\dot{m}}_{7} h_{7} - {\dot{m}}_{8} h_{8} - {\dot{m}}_{9} h_{9} = 0$	${\dot{m}}_{7} e x_{7} - {\dot{m}}_{8} e x_{8} - {\dot{m}}_{9} e x_{9} - \dot{E} x_{D, f c 2} = 0$
Steam turbine 2 (st₂)	${\dot{m}}_{8} h_{8} - {\dot{m}}_{10} h_{10} - {\dot{W}}_{s t, 2} = 0$	${\dot{m}}_{8} e x_{8} - {\dot{m}}_{10} e x_{10} - {\dot{W}}_{s t, 2} - \dot{E} x_{D, s t 2} = 0$
Condenser 2 (c₂)	${\dot{m}}_{10} h_{10} - {\dot{m}}_{11} h_{11} - {\dot{Q}}_{c 2} = 0$	${\dot{m}}_{10} e x_{10} - {\dot{m}}_{11} e x_{11} - (1 - \frac{T_{0}}{T_{c 2}}) {\dot{Q}}_{c 2} - \dot{E} x_{D, c 2} = 0$
Double-T geothermal system
Expansion valve 1 (ev₁)	${\dot{m}}_{1} h_{1} - {\dot{m}}_{2} h_{2} = 0$	${\dot{m}}_{1} e x_{1} - {\dot{m}}_{2} e x_{2} - \dot{E} x_{D, e v 1} = 0$
Flash chamber 1 (fc₁)	${\dot{m}}_{2} h_{2} - {\dot{m}}_{3} h_{3} - {\dot{m}}_{4} h_{4} = 0$	${\dot{m}}_{2} e x_{2} - {\dot{m}}_{3} e x_{3} - {\dot{m}}_{4} e x_{4} - \dot{E} x_{D, f c 1} = 0$
Steam turbine 1 (st₁)	${\dot{m}}_{3} h_{3} - {\dot{m}}_{5} h_{5} - {\dot{W}}_{s t, 1} = 0$	${\dot{m}}_{3} e x_{3} - {\dot{m}}_{5} e x_{5} - {\dot{W}}_{s t, 1} - \dot{E} x_{D, s t 1} = 0$
Expansion valve 2 (ev₂)	${\dot{m}}_{4} h_{4} - {\dot{m}}_{7} h_{7} = 0$	${\dot{m}}_{4} e x_{4} - {\dot{m}}_{7} e x_{7} - \dot{E} x_{D, e v 2} = 0$
Flash chamber 2 (fc₂)	${\dot{m}}_{7} h_{7} - {\dot{m}}_{8} h_{8} - {\dot{m}}_{9} h_{9} = 0$	${\dot{m}}_{7} e x_{7} - {\dot{m}}_{8} e x_{8} - {\dot{m}}_{9} e x_{9} - \dot{E} x_{D, f c 2} = 0$
Mixing chamber (mc)	${\dot{m}}_{8} h_{8} + {\dot{m}}_{5} h_{5} - {\dot{m}}_{12} h_{12} = 0$	${\dot{m}}_{8} e x_{8} + {\dot{m}}_{5} e x_{5} - {\dot{m}}_{12} e x_{12} - \dot{E} x_{D, m c} = 0$
Steam turbine 2 (st₂)	${\dot{m}}_{8} h_{8} - {\dot{m}}_{10} h_{10} - {\dot{W}}_{s t, 2} = 0$	${\dot{m}}_{8} e x_{8} - {\dot{m}}_{10} e x_{10} - {\dot{W}}_{s t, 2} - \dot{E} x_{D, s t 2} = 0$
Condenser (c)	${\dot{m}}_{10} h_{10} - {\dot{m}}_{11} h_{11} - {\dot{Q}}_{c} = 0$	${\dot{m}}_{10} e x_{10} - {\dot{m}}_{11} e x_{11} - (1 - \frac{T_{0}}{T_{c}}) {\dot{Q}}_{c} - \dot{E} x_{D, c} = 0$

System	Energy rate balance	Exergy rate balance
Single-flash geothermal system
Expansion valve (ev)	${\dot{m}}_{1} h_{1} - {\dot{m}}_{2} h_{2} = 0$	${\dot{m}}_{1} e x_{1} - {\dot{m}}_{2} e x_{2} - \dot{E} x_{D, e v} = 0$
Flash chamber (fc)	${\dot{m}}_{2} h_{2} - {\dot{m}}_{3} h_{3} - {\dot{m}}_{4} h_{4} = 0$	${\dot{m}}_{2} e x_{2} - {\dot{m}}_{3} e x_{3} - {\dot{m}}_{4} e x_{4} - \dot{E} x_{D, f c} = 0$
Steam turbine (st)	${\dot{m}}_{3} h_{3} - {\dot{m}}_{5} h_{5} - {\dot{W}}_{s t} = 0$	${\dot{m}}_{3} e x_{3} - {\dot{m}}_{5} e x_{5} - {\dot{W}}_{s t} - \dot{E} x_{D e s, s t} = 0$
Condenser (c)	${\dot{m}}_{5} h_{5} - {\dot{m}}_{6} h_{6} - {\dot{Q}}_{c} = 0$	${\dot{m}}_{5} e x_{5} - {\dot{m}}_{6} e x_{6} - (1 - \frac{T_{0}}{T_{c}}) {\dot{Q}}_{c} - \dot{E} x_{D, c} = 0$
Double-flash geothermal system
Expansion valve 1 (ev₁)	${\dot{m}}_{1} h_{1} - {\dot{m}}_{2} h_{2} = 0$	${\dot{m}}_{1} e x_{1} - {\dot{m}}_{2} e x_{2} - \dot{E} x_{D, e v 1} = 0$
Flash chamber 1 (fc₁)	${\dot{m}}_{2} h_{2} - {\dot{m}}_{3} h_{3} - {\dot{m}}_{4} h_{4} = 0$	${\dot{m}}_{2} e x_{2} - {\dot{m}}_{3} e x_{3} - {\dot{m}}_{4} e x_{4} - \dot{E} x_{D, f c 1} = 0$
Steam turbine 1 (st₁)	${\dot{m}}_{3} h_{3} - {\dot{m}}_{5} h_{5} - {\dot{W}}_{s t, 1} = 0$	${\dot{m}}_{3} e x_{3} - {\dot{m}}_{5} e x_{5} - {\dot{W}}_{s t, 1} - \dot{E} x_{D, s t 1} = 0$
Condenser 1 (c₁)	${\dot{m}}_{5} h_{5} - {\dot{m}}_{6} h_{6} - {\dot{Q}}_{c 1} = 0$	${\dot{m}}_{5} e x_{5} - {\dot{m}}_{6} e x_{6} - (1 - \frac{T_{0}}{T_{c 1}}) {\dot{Q}}_{c 1} - \dot{E} x_{D, c 1} = 0$
Expansion valve 2 (ev₂)	${\dot{m}}_{4} h_{4} - {\dot{m}}_{7} h_{7} = 0$	${\dot{m}}_{4} e x_{4} - {\dot{m}}_{7} e x_{7} - \dot{E} x_{D, e v 2} = 0$
Flash chamber 2 (fc₂)	${\dot{m}}_{7} h_{7} - {\dot{m}}_{8} h_{8} - {\dot{m}}_{9} h_{9} = 0$	${\dot{m}}_{7} e x_{7} - {\dot{m}}_{8} e x_{8} - {\dot{m}}_{9} e x_{9} - \dot{E} x_{D, f c 2} = 0$
Steam turbine 2 (st₂)	${\dot{m}}_{8} h_{8} - {\dot{m}}_{10} h_{10} - {\dot{W}}_{s t, 2} = 0$	${\dot{m}}_{8} e x_{8} - {\dot{m}}_{10} e x_{10} - {\dot{W}}_{s t, 2} - \dot{E} x_{D, s t 2} = 0$
Condenser 2 (c₂)	${\dot{m}}_{10} h_{10} - {\dot{m}}_{11} h_{11} - {\dot{Q}}_{c 2} = 0$	${\dot{m}}_{10} e x_{10} - {\dot{m}}_{11} e x_{11} - (1 - \frac{T_{0}}{T_{c 2}}) {\dot{Q}}_{c 2} - \dot{E} x_{D, c 2} = 0$
Double-T geothermal system
Expansion valve 1 (ev₁)	${\dot{m}}_{1} h_{1} - {\dot{m}}_{2} h_{2} = 0$	${\dot{m}}_{1} e x_{1} - {\dot{m}}_{2} e x_{2} - \dot{E} x_{D, e v 1} = 0$
Flash chamber 1 (fc₁)	${\dot{m}}_{2} h_{2} - {\dot{m}}_{3} h_{3} - {\dot{m}}_{4} h_{4} = 0$	${\dot{m}}_{2} e x_{2} - {\dot{m}}_{3} e x_{3} - {\dot{m}}_{4} e x_{4} - \dot{E} x_{D, f c 1} = 0$
Steam turbine 1 (st₁)	${\dot{m}}_{3} h_{3} - {\dot{m}}_{5} h_{5} - {\dot{W}}_{s t, 1} = 0$	${\dot{m}}_{3} e x_{3} - {\dot{m}}_{5} e x_{5} - {\dot{W}}_{s t, 1} - \dot{E} x_{D, s t 1} = 0$
Expansion valve 2 (ev₂)	${\dot{m}}_{4} h_{4} - {\dot{m}}_{7} h_{7} = 0$	${\dot{m}}_{4} e x_{4} - {\dot{m}}_{7} e x_{7} - \dot{E} x_{D, e v 2} = 0$
Flash chamber 2 (fc₂)	${\dot{m}}_{7} h_{7} - {\dot{m}}_{8} h_{8} - {\dot{m}}_{9} h_{9} = 0$	${\dot{m}}_{7} e x_{7} - {\dot{m}}_{8} e x_{8} - {\dot{m}}_{9} e x_{9} - \dot{E} x_{D, f c 2} = 0$
Mixing chamber (mc)	${\dot{m}}_{8} h_{8} + {\dot{m}}_{5} h_{5} - {\dot{m}}_{12} h_{12} = 0$	${\dot{m}}_{8} e x_{8} + {\dot{m}}_{5} e x_{5} - {\dot{m}}_{12} e x_{12} - \dot{E} x_{D, m c} = 0$
Steam turbine 2 (st₂)	${\dot{m}}_{8} h_{8} - {\dot{m}}_{10} h_{10} - {\dot{W}}_{s t, 2} = 0$	${\dot{m}}_{8} e x_{8} - {\dot{m}}_{10} e x_{10} - {\dot{W}}_{s t, 2} - \dot{E} x_{D, s t 2} = 0$
Condenser (c)	${\dot{m}}_{10} h_{10} - {\dot{m}}_{11} h_{11} - {\dot{Q}}_{c} = 0$	${\dot{m}}_{10} e x_{10} - {\dot{m}}_{11} e x_{11} - (1 - \frac{T_{0}}{T_{c}}) {\dot{Q}}_{c} - \dot{E} x_{D, c} = 0$

In contrast to the energy efficiency, which is the ratio of useful energy output to input energy, the exergy efficiency reflects the extent to which a process is reversible. In general, the exergy efficiency can be defined as the ratio of exergy rate of useful process outputs

(\dot{E} x_{u s e f u l})

to the exergy rate of the process inputs

(\dot{E} x_{i n})

⁠. So, the general exergy efficiency for an energy system can be written, respectively, as

η_{e x} = \frac{\dot{E} x_{u s e f u l}}{\dot{E} x_{i n}}

(6)

In this study, the useful process output from each geothermal system is the electrical power produced from the system $({\dot{W}}_{T})$ and the exergy rate of the process input is the geothermal water source input to the systems. So, the exergy efficiencies for the single-flash, double-flash, and double-T geothermal systems can be expressed, respectively, as

η_{e x, s i n g l e} = \frac{{\dot{W}}_{s t}}{{\dot{m}}_{1} e x_{1} - {\dot{m}}_{6} e x_{6}}

(7)

η_{e x, D o u b l e} = \frac{{\dot{W}}_{s t, 1} + {\dot{W}}_{s t, 2}}{{\dot{m}}_{1} e x_{1} - {\dot{m}}_{6} e x_{6} - {\dot{m}}_{9} e x_{9} - {\dot{m}}_{11} e x_{11}}

(8)

η_{e x, D o u b l e, T} = \frac{{\dot{W}}_{s t, 1} + {\dot{W}}_{s t, 2}}{{\dot{m}}_{1} e x_{1} - {\dot{m}}_{9} e x_{9} - {\dot{m}}_{11} e x_{11}}

(9)

In the Results and discussion section, the optimal flashing pressures that provide the maximum electrical power for the single-flash, double-flash, and double-T geothermal systems are first analyzed. Then, the exergetic performance and produced electrical power for these three systems are compared and discussed.

Results and Discussion

A thermodynamic model using energy and exergy rate balances is developed for each component of the single-flash, double-flash, and double-T geothermal systems. Then, the developed model is simulated in EES software using the thermodynamic properties of the water as a working fluid at the state points. By solving simultaneously the thermodynamic equations in EES, the thermodynamic properties for all state points can be determined. Tables 3–5 tabulate the input and evaluated thermodynamic properties at each state point for the single-flash, double-flash, and double-T geothermal systems. In the parametric study conducted in this paper, the effects of pressures of flash chambers, geothermal water input temperature, and mass flowrate are investigated. Other design parameters listed in Table 1 (e.g., isentropic efficiencies of turbines) remain constant at a specified value in this analysis.

Table 3

Thermodynamic properties at state points of the single-flash geothermal system shown in Fig. 1

State no.	T (°C)	P (kPa)	h (kJ/kg)	s (kJ/kg · K)	ex (kJ/kg)	x (quality)	$\dot{m} (kg / s)$
1	230	2797	990.1	2.61	212.5	0	230
2	184.8	1119	990.1	2.635	205	0.11	230
3	184.8	1119	2781	6.546	822.8	1	23.7
4	184.8	1119	784.4	2.186	134	0	206.3
5	45.81	10	2299	7.257	127.7	0.88	23.7
6	45.81	10	191.8	0.6492	2.409	0	23.7

State no.	T (°C)	P (kPa)	h (kJ/kg)	s (kJ/kg · K)	ex (kJ/kg)	x (quality)	$\dot{m} (kg / s)$
1	230	2797	990.1	2.61	212.5	0	230
2	184.8	1119	990.1	2.635	205	0.11	230
3	184.8	1119	2781	6.546	822.8	1	23.7
4	184.8	1119	784.4	2.186	134	0	206.3
5	45.81	10	2299	7.257	127.7	0.88	23.7
6	45.81	10	191.8	0.6492	2.409	0	23.7

Table 4

Thermodynamic properties at state points of the double-flash geothermal system shown in Fig. 2

State no.	T (°C)	P (kPa)	h (kJ/kg)	s (kJ/kg · K)	ex (kJ/kg)	x (quality)	$\dot{m} (kg / s)$
1	230	2797	990.1	2.61	212.5	0	230
2	184.8	1119	990.1	2.635	205	0.11	230
3	184.8	1119	2781	6.546	822.8	1	23.7
4	184.8	1119	784.4	2.186	134	0	206.3
5	45.81	10	2299	7.257	127.7	0.88	23.7
6	45.81	10	191.8	0.6492	2.409	0	23.7
7	166.5	727.3	784.4	2.19	132.6	0.04	206.3
8	166.5	727.3	2764	6.694	761.5	1	8.07
9	166.5	727.3	703.7	2.007	107	0	198.2
10	45.81	10	2326	7.341	129.3	0.89	8.07
11	45.81	10	191.8	0.6492	2.409	0	8.07

State no.	T (°C)	P (kPa)	h (kJ/kg)	s (kJ/kg · K)	ex (kJ/kg)	x (quality)	$\dot{m} (kg / s)$
1	230	2797	990.1	2.61	212.5	0	230
2	184.8	1119	990.1	2.635	205	0.11	230
3	184.8	1119	2781	6.546	822.8	1	23.7
4	184.8	1119	784.4	2.186	134	0	206.3
5	45.81	10	2299	7.257	127.7	0.88	23.7
6	45.81	10	191.8	0.6492	2.409	0	23.7
7	166.5	727.3	784.4	2.19	132.6	0.04	206.3
8	166.5	727.3	2764	6.694	761.5	1	8.07
9	166.5	727.3	703.7	2.007	107	0	198.2
10	45.81	10	2326	7.341	129.3	0.89	8.07
11	45.81	10	191.8	0.6492	2.409	0	8.07

Table 5

Thermodynamic properties at state points of the double-T geothermal system shown in Fig. 3

State no.	T (°C)	P (kPa)	h (kJ/kg)	s (kJ/kg · K)	ex (kJ/kg)	x (quality)	$\dot{m} (kg / s)$
1	230	2797	990.1	2.61	212.5	0	230
2	184.8	1119	990.1	2.635	205	0.11	230
3	184.8	1119	2781	6.546	822.8	1	23.7
4	184.8	1119	784.4	2.186	134	0	206.3
5	45.81	10	2299	7.257	127.7	0.88	23.7
7	166.5	727.3	784.4	2.19	132.6	0.04	206.3
8	166.5	727.3	2764	6.694	761.5	1	8.07
9	166.5	727.3	703.7	2.007	107	0	198.2
10	45.81	10	2326	7.341	129.3	0.89	32.8
11	45.81	10	191.8	0.6492	2.409	0	32.8
12	166.5	727.3	2764	6.694	761.5	1	32.8

State no.	T (°C)	P (kPa)	h (kJ/kg)	s (kJ/kg · K)	ex (kJ/kg)	x (quality)	$\dot{m} (kg / s)$
1	230	2797	990.1	2.61	212.5	0	230
2	184.8	1119	990.1	2.635	205	0.11	230
3	184.8	1119	2781	6.546	822.8	1	23.7
4	184.8	1119	784.4	2.186	134	0	206.3
5	45.81	10	2299	7.257	127.7	0.88	23.7
7	166.5	727.3	784.4	2.19	132.6	0.04	206.3
8	166.5	727.3	2764	6.694	761.5	1	8.07
9	166.5	727.3	703.7	2.007	107	0	198.2
10	45.81	10	2326	7.341	129.3	0.89	32.8
11	45.81	10	191.8	0.6492	2.409	0	32.8
12	166.5	727.3	2764	6.694	761.5	1	32.8

Figure 5 compares the electrical power output variations with the pressure of the second flash chamber in a double-flash geothermal power plant for the present study and Siddiqui and Dincer [10]. The geothermal input pressure and first flash chamber pressure are considered as 10,000 kPa and 1029 kPa, respectively. It is seen that the optimum pressure of the second flash chamber in which the maximum total electrical power is attained is observed to be 135 kPa in both the present article and Siddiqui and Dincer [10].

Fig. 5

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Variation of total electrical power output and electrical power produced from the second turbine with the pressure of the second flash chamber in a double-flash geothermal power plant for the present study and Siddiqui and Dincer [10]

Figure 6 shows the variation of electrical power production with the pressure of the flash chamber for the single-flash geothermal power system at several geothermal source temperatures. It can be seen for each inlet geothermal source temperature that there is an optimum flash chamber pressure at which the electrical power produced from the turbine is maximum. For inlet geothermal temperatures of 230 °C, 250 °C, and 270 °C, the maximum powers are produced at flash chamber pressures of 300 kPa, 410 kPa, and 590 kPa, respectively. It is clear that, as inlet geothermal temperature increases, the optimum pressure in terms of the maximum electrical power output increases as well.

Fig. 6

View large Download slide

Variations in electrical power produced by steam turbine with flash chamber pressure at several geothermal water temperatures in the single-flash geothermal power plant

The variations in total electrical power output from the double-flash and double-T (connected turbines) geothermal systems with the pressure of the first flash chamber are presented in Figs. 7 and 8 for several inlet geothermal source temperatures. In both the double-flash and double-T geothermal systems, the maximum power outputs are attained at the optimum pressures of the first flash chamber. Comparing Figs. 7 and 8, it is seen that the electrical power produced in the double-T geothermal system is higher than that of the double-flash geothermal system. At inlet geothermal temperatures of 230 °C, 250 °C, and 270 °C, respectively, the maximum electrical power outputs for the double-flash geothermal system are 17,500 kW, 21,500 kW, and 26,400 kW, and for the double-T geothermal system are 17,900 kW, 22,000 kW, and 26,400 kW. Note that the optimum pressures at which the power production outputs are maximum are identical for both double-flash and double-T geothermal systems.

Fig. 7

View large Download slide

Variations in total electrical power produced by steam turbines with first flash chamber pressure for several geothermal water temperatures in the double-flash geothermal power plant

Fig. 8

View large Download slide

Variations in total electrical power produced by steam turbines with first flash chamber pressure for several geothermal water temperatures in the double-flash connected turbine (double-T) geothermal power plant

Figures 9 and 10 show the effects of the second flash chamber pressure on the total electrical power produced by the double-flash and double-T geothermal systems for three geothermal source temperatures. Like first flash chamber pressure, the second flash chamber pressure has a significant effect on the total electrical power produced in both the double-flash and double-T geothermal systems. The double-T geothermal system yields a relatively higher electrical power compared with the double-flash geothermal system. For both double-flash and double-T geothermal systems, the optimum pressures at which the maximum electrical powers are produced are 150 kPa, 200 kPa, and 240 kPa at the corresponding geothermal temperatures of 230 °C, 250 °C, and 270 °C, respectively. From Figs. 6–10, it can be concluded that, with an increase in the geothermal water source temperature, the electrical power produced from the geothermal power plant increases. As the temperature of the geothermal source increases, the steam ratio in the two-phase geothermal fluid coming from the source increases. The temperature of the ground naturally increases with depth and varies based on the geographic location. Therefore, it is important to perform a resource analysis to determine the geothermal fluid characteristics before the design and construction of any geothermal power plants.

Fig. 9

View large Download slide

Variations in total electrical power produced by steam turbines with second flash chamber pressure for several geothermal water temperatures in the double-flash geothermal power plant

Fig. 10

View large Download slide

Variations in total electrical power produced by steam turbines with second flash chamber pressure for several geothermal water temperatures in the double-flash connected turbine (double-T) geothermal power plant

Figure 11 shows the effect of geothermal mass flowrate on the electrical power production by the steam turbines for the single-flash, double-flash, and double-T geothermal power plants. For the steady-state analyses carried out in this paper, the total mass flowrate of geothermal water supply to the power plants is 230 kg/s. The electrical power output generated from the steam turbines of the single-flash, double-flash, and double-T geothermal power plants is observed to increase. For instance, in the double-T geothermal power plants, the electrical power output from the first and second turbines increases from 861 kW to 1436 kW and from 9081 kW and 15,135 kW, respectively, as the geothermal fluid mass flowrate rises from 150 kg/s to 250 kg/s. The geothermal water input mass flowrate varies according to the characteristics of the geothermal well. In some locations, geothermal wells have been observed to supply low flowrates, whereas in other areas they provide higher mass flowrates. Therefore, the type and potential of the well significantly affect the performance of the geothermal power plants. Thus, it is necessary to perform a resource analysis on the geothermal wells before building such geothermal power plants to ensure the wells utilized provide good system electrical power outputs and performance.

Fig. 11

View large Download slide

Variations in electrical power produced by steam turbines with geothermal water supply mass flowrate for single-flash, double-flash, and double-T geothermal power plants

In Fig. 12, the variations in total electrical power generation with the first flash chamber pressure are compared for the single-flash, double-flash, and double-T geothermal systems. It is observed that the total electrical power production outputs for the double and double-T geothermal systems are higher than that for the single-flash geothermal system. The maximum electrical power for the single-flash geothermal system is seen to be attained at relatively lower optimum pressures than for the double and double-T systems. The maximum electrical power generated for the double and double-T systems are 8.8% and 10.7% higher than that for the single-flash geothermal system.

Fig. 12

View large Download slide

Variations in total electrical power produced by steam turbines with first flash chamber pressure for single-flash, double-flash, and double-T geothermal power plants

Figure 13 compares the variations in the exergy efficiency and total electrical power production with the pressure of the second flash chamber for double and double-T geothermal systems. The exergy efficiencies of both systems are found to rise rapidly with the second flash chamber pressure until 200 kPa, and for any higher flashing pressures, this rise is slower. Furthermore, the electrical power production and exergy efficiency are higher for the double-T geothermal system compared with the double-flash geothermal system.

Fig. 13

View large Download slide

Variations in exergy efficiency and total electrical power produced by steam turbines with second flash chamber pressure for the double-flash and double-T geothermal power plants

Figure 14 compares the exergy efficiencies of the single-flash, double-flash, and double-T geothermal systems as the pressure of the first flash chamber varies. It is observed that the three systems exhibit almost the same exergitic performances. It can be concluded that, although the electrical power production in the single-flash geothermal system is lower than that of the double and double-T geothermal systems, the exergy destruction rates for the double and double-T systems are higher, resulting in almost the same exergy efficiencies for all three systems. This observation is consistent with the exergy efficiency equations (Eqs. (7)–(9)) where the denominator (which is the exergy rate of the process input) for double-flash and double-T geothermal systems is higher than for the single-flash geothermal system. Therefore, in Eqs. (7)–(9), both numerator (electrical power output) and denominator (exergy rate of the process input) for the double-flash and double-T geothermal power systems are higher than for the single-flash geothermal system, resulting in almost the same exergy efficiencies for all three systems. For relatively high operating pressures of the first flash chamber (>2200 kPa), the exergy efficiency for the single-flash geothermal system exceeds those of the double and double-T geothermal systems.

Fig. 14

View large Download slide

Variations in exergy efficiency with the first flash chamber pressure for single-flash, double-flash, and double-T geothermal power plants

Conclusions

The electrical power production and exergy efficiency are compared for three configurations of geothermal power plants. The examined systems are single-flash, double-flash, and double-flash connected turbine (double-T) geothermal electrical power production systems. The systems are thermodynamically modeled and assessed using energy and exergy methods and simulated in EES software. The simulation results indicate the optimum values for the flash chamber pressures at which the electrical power production is a maximum. At an input geothermal source temperature of 230 °C, the optimum pressures for the first flash chamber are 300 kPa, 350 kPa, and 350 kPa for single-flash, double-flash, and double-T geothermal systems, respectively. The optimum values for the flash chamber pressures increase as the input geothermal source temperature increases. The optimum pressure for the second flash chamber is found to be 150 kPa for both the double-flash and double-T geothermal systems. For relatively low-operating pressures of the first flash chamber (<2200 kPa), the highest values of electricity production rate and exergy efficiency are associated with the double-T geothermal system followed by the double-flash and single-flash geothermal systems. However, for relatively high-operating pressures of the first flash chamber (>2200 kPa), the exergy efficiency for the single-flash geothermal system exceeds that of the double and double-T geothermal systems.

Conflict of Interest

There are no conflicts of interest. This article does not include research in which human participants were involved. This article does not include any research in which animal participants were involved.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. No data, models, or code were generated or used for this paper.

Nomenclature

h =: specific enthalpy (kJ/kg)
s =: specific entropy (kJ/kg · K)
x =: quality
P =: pressure (kPa)
T =: temperature (°C, K)
$\dot{m}$ =: mass flowrate (kg/s)
$\dot{Q}$ =: heat transfer rate (kW)
$\dot{W}$ =: work rate (kW)
ex =: specific exergy (kJ/kg)
$\dot{E} x$ =: exergy rate (kW)
$\dot{E} x_{D}$ =: exergy destruction rate (kW)

Greek Symbol

η =: efficiency

Subscripts

0 =: reference state
c =: condenser
ev =: expansion valve
ex =: exergy
fc =: flash chamber
mc =: mixing chamber
st =: steam turbine

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Comparison of Thermodynamic Performances in Three Geothermal Power Plants Using Flash Steam

Abstract

Introduction

Descriptions of Systems

Analysis

Results and Discussion

Conclusions

Conflict of Interest

Data Availability Statement

Nomenclature

Greek Symbol

Subscripts

References

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Comparison of Thermodynamic Performances in Three Geothermal Power Plants Using Flash Steam

Abstract

Introduction

Descriptions of Systems

Analysis

Results and Discussion

Conclusions

Conflict of Interest

Data Availability Statement

Nomenclature

Greek Symbol

Subscripts

References

Get Email Alerts

Cited By

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