Question

(30 points) We are designing a geothermal flash steam power plant that pumps water from underground geothermal reservoirs at 180 °C at 5 MPa to a tank at 150 °C. Some of the water flashes to produce saturated steam that is sent to a turbine and a water stream that is returned to the well. The output of the turbine is at 0.1 MPA. Assume that the system is well insulated. Determine: a. The flowrate of steam leaving the flash tank if the feed to the tank from geothermal reservoirs is 10 kg/s. b. If the output from the turbine is a saturated vapor, is this process reversible or irreversible? c. What is the work generated by the turbine. Tout fromversiblefon by th

Answer 1

T _{​​​​​​1} =  180°C

P ₁ = 5 MPa

Turbine output = 0.1 MPa

A) feed of flash tank = 10 Kg/s

Fraction of it forms saturated steam and rest leaves of it water

From perry handbook steam tables

Properties of water at 180°C and 5 Mpa

H = 765.219 KJ/kg

s = 2.1340 KJ/kg K

U = 758.599 KJ/kg

Output of turbine is 0.1 MPa

Properties of saturated steam at 0.1 MPa

T - 99.6°C

H = 2674.9 KJ/kg

s= 7.3588 KJ/kg K

U = 2505.5 KJ/kg

Enthaply of water at feed of flash drum

= 10(765.219) = 7652.19 KJ/s

Enthaply of saturated steam = 2674.9 KJ/kg

mass of steam produced

7652.19 = m (2674.9)

m = 2.860 Kg/s

Flowrate of stream leaving flash tank = 2.860 Kg/s

B ) output from the turbine is saturated vapor

For reversible process

∆s_T = 0

∆s_system = s_water - s_steam = 2.1340-7.3588 = -5. 224

∆s_surrounding =( H/T) _water - (H/T) _steam

s_water = (765.219/(180+273)) = 1.689 KJ/kg K

s_steam = (2674.9)/(273+99.6) ) = 7.17 KJ/kg K

∆S_surrounding = 7.17-1.689+5.48 KJ/kg K

∆S_T = -5. 22 + 5.48 = 0.22

∆S_T>0 , hence the process strictly speaking is irreversible but it is close to reversibility

C) The process is well insulated hence adiabatic

at adiabatic conditions Q= 0

∆U = W

∆U = m_{​​​​​​w}u₁ - m _su₂

m_w = 10 kg/S

m_s = 2.860 Kg/s

u₁ = 758.99 KJ/kg

u₂ = 2505.5 KJ/kg

∆U = 10(758.99) -(2.860) (2505.5) = 424.17 KJ

∆U = W = 424.17 KJ

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