The schematic of a single-flash geothermal power plant with state numbers is given in Fig. P10–69. Geothermal resource exists as saturated liquid at 230°C. The geothermal liquid is withdrawn from the production well at a rate of 230 kg/s and is flashed to a pressure of 500 kPa by an essentially isenthalpic flashing process where the resulting vapor is separated from the liquid in a separator and is directed to the turbine. The steam leaves the turbine at 10 kPa with a moisture content of 5 percent and enters the condenser where it is condensed; it is routed to a reinjection well along with the liquid coming off the separator. Determine (a) the power output of the turbine and the thermal efficiency of the plant, (b) the exergy of the geothermal liquid at the exit of the flash chamber, and the exergy destructions and the second-law efficiencies for (c) the turbine and (d) the entire plant.
FIGURE P10–69
(a)
The temperature of the steam after the flashing process and the power output from the turbine if the pressure of the steam at the exit of flash chamber is
Answer to Problem 69P
The power output turbine is
The thermal efficiency of the plant is
Explanation of Solution
Draw schematic diagram of single flash geothermal power plant as shown in Figure 1.
Write the general energy rate balance equation.
Here, the rate of total energy in is
Consider the system operates at steady state. Hence, the rate of change in net energy of the system becomes zero.
The Equation (I) is reduced as follows.
Refer Figure 1.
The flash chamber is nothing but the expansion valve. At expansion valve, the enthalpy kept constant.
Express the energy balance equation for the flash chamber.
Express the energy balance equation for the separator.
Express the energy balance equation for the turbine.
At state 1:
The geothermal water is extracted at the state of saturated liquid at the temperature of
The enthalpy and entropy at state 1 is as follows.
Refer Table A-4, “Saturated water-Temperature table”
The enthalpy
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
At state 2:
The exit pressure of the flash chamber is
The geothermal steam is flashed at constant enthalpy. The exit steam of the flash chamber is at the quality of
Here, the fluid enthalpy is
Refer Table A-5, “Saturated water-Pressure table”.
Obtain the following corresponding to the pressure of
The entropy
Write the formula for mass flow rate of vapor at entering the turbine.
Here, the mass flow rate is
At state 3:
There is no pressure drop in the separator. The separator separates vapor and liquid form the flashed steam, and the separated vapor alone sent to the turbine.
The enthalpy
Refer Table A-5, “Saturated water-Pressure table”.
The enthalpy
At state 4:
The steam is at the state of saturated mixture at the pressure of
The quality at state 4 is as follows.
The enthalpy
Refer Table A-5, “Saturated water-Pressure table”.
Obtain the following corresponding to the pressure of
At state 6:
The saturated water only exits at the bottom of the separator. The enthalpy
Refer Table A-5, “Saturated water-Pressure table”.
The enthalpy
Write the formula for net energy input of the plant.
Write the formula for thermal efficiency.
Consider, the surrounding temperature is
The surrounding enthalpy
Refer Table A-4, “Saturated water-Temperature table”.
The enthalpy
Conclusion:
Substitute
Substitute
Substitute
Substitute
Equation (VII).
Substitute
Substitute
Equation (III).
Thus, the power output turbine is
Substitute
Equation (IX).
Substitute
Thus, the thermal efficiency of the plant is
(b)
The exergy of the geothermal liquid at the exit of the flash chamber, and the exergy destructions.
Answer to Problem 69P
The exergy of the geothermal liquid at the exit of the flash chamber, and the exergy destruction is
Explanation of Solution
Write the formula for exergy of the steam at their respective process state.
Here, the enthalpy is
Write the formula for rate of exergy destruction at the exit of flash chamber (state 6).
Here, the rate of exergy destruction at state 6 is
Conclusion:
For process state 1:
Substitute
For process state 2:
Substitute
For process state 3:
Substitute
For process state 4:
Substitute
For process state 6:
Substitute
The mass flow rate of water at the bottom exit of separator (state 6) is expressed as follows.
Substitute
Thus, the exergy of the geothermal liquid at the exit of the flash chamber, and the exergy destruction is
(c)
The exergy destruction and second law of efficiency for the turbine.
Answer to Problem 69P
The exergy destruction and second law of efficiency for the turbine is
Explanation of Solution
Write the formula for rate of exergy destruction of the turbine.
Write the formula for second law of efficiency of the turbine.
Conclusion:
Substitute
Substitute
Thus, the exergy destruction and second law of efficiency for the turbine is
(d)
The exergy destruction and second law of efficiency for the entire plant.
Answer to Problem 69P
The exergy destruction and second law of efficiency for the plant is
Explanation of Solution
Write the formula for rate of exergy input of the plant.
Write the formula for rate of exergy destruction of the plant.
Write the formula for second law of efficiency of the plant.
Conclusion:
Substitute
Substitute
Substitute
Thus, the exergy destruction and second law of efficiency for the plant is
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Chapter 10 Solutions
Thermodynamics: An Engineering Approach
- 3. The schematic of a single-flash geothermal power plant with state numbers is given in the fiure below. Geothermal resource exists as saturated liquid at 230°C. The geothermal liquid is withdrawn from the production well at a rate of 230 kg/s and is flashed to a pressure of 500 kPa by an essentially isenthalpic flashing process where the resulting vapor is separated from the liquid in a separator and is directed to the turbine. The steam leaves the turbine at 10 kPa with a moisture content of 5 percent and enters the condenser where it is condensed; it is routed to a reinjection well along with the liquid coming off the separator. Determine (a) the power output of the turbine and the thermal efficiency of the plant, Answers: (a) 10.8 MW, 0.053, Separator Flash chamber Production well Steam turbine Condenser Ⓒ-1 Reinjection wellarrow_forwardSteam is generated at 5.15 Mpa and 525C and condensation occurs at 0.127 Mpa. Considering that a Rankine cycle occurs between the same limits, determine the QA, QR, Wnet, cycle efficiency, engine efficiency and heat rate. What mass flow rate is required for a net output of 25000 kW?arrow_forwardThe production well of a typical geothermal power plant is at 230°C saturated liquid and ground water flow rate of 230kg/s with separator pressure of 0.5MPaa while its condenser pressure is at 0.01MPa. the turbine and generator efficiencies are 83% and 87% , respectively. Sketch the T-s diagram of the system. Determine the amount of mass flowing into the reinjection well from the separator, generator output, heat rejection in the condenser and overall plant efficiency.arrow_forward
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- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning