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Thermal Efficiency of  Steam Turbine Cycle NPP with PWR

Author: Valery Ochkov (http://twt.mpei.ac.ru/ochkov/v_ochkov.htm)

Introduction
 

This application calculates the thermal efficiency of a steam turbine cycle in a Nuclear Power Plant (NPP) with a Pressure Water reactor (PWR).

 

Pressurized water flows from the nuclear reactor (NPP primary circuit) to the steam generator (SG) and transfers heat to the boiling water of the second circuit. Saturated steam is supplied from the steam generator to the high pressure cylinder (HPC) of the steam turbine. Part of the live steam from the steam generator enters the superheater. Before being superheated, the exhaust steam from the HPC is partially dried in the separator (S), where some water is separated from the wet steam, and then returned to the circuit with bypass of the low pressure cylinder (LPC) of the steam turbine.

 

The thermal circuit of an NPP introduces a risk factor not found in fossil fuel power plant. In an NPP, If saturated steam is supplied to a turbine, whose outlet pressure is 5-4 kPa, moisture in the last stages of the  turbine will be unacceptably high; this may lead to steam turbine failure.

Water Properties
 

Start
 
> 

restart; with(ThermophysicalData); with(Units[Standard])

 

Water/steam Proterties
 

Specific enthalpy of water or steam as function of pressure and temperature

> 

wspTSP := proc (P) options operator, arrow; Property(temperature, pressure = P, Q = 1, water) end proc

Specific enthalpy of steam on the saturated line as function of temperature

> 

wspHSST := proc (T) options operator, arrow; Property(enthalpy, temperature = T, Q = 1, water) end proc

Specific entropy of steam on the saturated line as function of temperature

> 

wspSSST := proc (T) options operator, arrow; Property(entropy, temperature = T, Q = 1, water) end proc

Specific enthalpy of water on the saturated line as function of temperature

> 

wspHSWT := proc (T) options operator, arrow; Property(enthalpy, temperature = T, Q = 0, water) end proc

Specific entropy of water on the saturated line as function of pressure

> 

wspSSWP := proc (P) options operator, arrow; Property(entropy, pressure = P, Q = 0, water) end proc

Specific enthalpy of water on the saturated line as function of pressure

> 

wspHSWP := proc (P) options operator, arrow; Property(enthalpy, pressure = P, Q = 0, water) end proc

Vapor fraction of steam as function of pressure and specific enthalpy

> 

wspXSPH := proc (P, H) options operator, arrow; Property(Q, pressure = P, enthalpy = H, water) end proc

Specific enthalpy of water or steam as function of pressure and temperature

> 

wspHPT := proc (P, T) options operator, arrow; Property(enthalpy, pressure = P, temperature = T, water) end proc

Specific entropy of water or steam as function of pressure and temperature

> 

wspSPT := proc (P, T) options operator, arrow; Property(entropy, pressure = P, temperature = T, water) end proc

Specific volume of water or steam as function of pressure and temperature

> 

wspXPS := proc (P, S) options operator, arrow; Property(Q, pressure = P, entropy = S, water) end proc

Specific enthalpy of water or steam as function of temperature and vapor fraction

> 

wspHSTX := proc (T, X) options operator, arrow; Property(enthalpy, temperature = T, Q = X, water) end proc

Temperature of water or steam as function of pressure and specific entropy

> 

wspTPS := proc (P, S) options operator, arrow; Property(temperature, pressure = P, entropy = S, water) end proc

Specific enthalpy of water or steam as function of pressure and specific entropy

> 

wspHPS := proc (P, S) options operator, arrow; Property(enthalpy, pressure = P, entropy = S, water) end proc

Temperature of water or steam as function of pressure and specific enthalpy

> 

wspTPH := proc (P, H) options operator, arrow; Property(temperature, pressure = P, enthalpy = H, water) end proc

Functions for processes steam expansion and water compression
 
> 

wspHEXPANSIONPPEFF := proc (p0, p1, eff) local t0, h0, s0, s1, t1, x1, h1; t0 := wspTSP(p0); h0 := wspHSST(t0); s0 := wspSSST(t0); s1 := s0; t1 := wspTSP(p1); x1 := wspXPS(p1, s1); h1 := wspHSTX(t1, x1); return h0-(h0-h1)*eff end proc
> 

wspHEXPANSIONPTPEFF := proc (p0, t0, p1, eff) local h0, s0, s1, t1, x1, h1; h0 := wspHPT(p0, t0); s0 := wspSPT(p0, t0); s1 := s0; t1 := wspTPS(p1, s1); if Property(PhaseString, pressure = p1, entropy = s1, water) = "twophase" then x1 := wspXPS(p1, s1); h1 := wspHSTX(t1, x1) else h1 := wspHPT(p1, t1) end if; return h0-(h0-h1)*eff end proc
> 

wspHCOMPRESSIONPPEFF := proc (p0, p1, eff) local h0, s0, s1, h1; h0 := wspHSWP(p0); s0 := wspSSWP(p0); s1 := s0; h1 := wspHPS(p1, s1); return h0+(h1-h0)/eff end proc
> 

wspHCOMPRESSIONPTPEFF := proc (p0, t0, p1, eff) local h0, s0, s1, h1; h0 := wspHPT(p0, t0); s0 := wspSPT(p0, t0); s1 := s0; h1 := wspHPS(p1, s1); return h0+(h1-h0)/eff end proc

Input Data
 
> 

p_1 := 6.2*Unit('MPa'); p_2 := .5*Unit('MPa'); p_4 := 4*Unit('kPa'); t_3 := 250*Unit('degC'); p_10 := (1+0.5e-1)*p_1; `η_i_HPC` := .89; `η_i_LPC` := .86; `η_i_p` := .8

 

Calculations
 

Steam parameters at the inlet to the HPC

> 

t_1 := wspTSP(p_1); t_1-273.15*Unit('K')

277.7328922*Units:-Unit(`°C`)

 (4.1)
> 

h_1 := wspHSST(t_1)

2782.370471*Units:-Unit(kJ/kg)

 (4.2)

Specific enthalpy water from Superheater (SH)

> 

hw_1 := wspHSWT(t_1)

1225.057924*Units:-Unit(kJ/kg)

 (4.3)

Steam parameters on the inlet to the separator (S)

> 

t_2 := wspTSP(p_2); t_2-273.15*Unit('K')

151.8310791*Units:-Unit(`°C`)

 (4.4)
> 

hw_2 := wspHSWT(t_2)

640.0851269*Units:-Unit(kJ/kg)

 (4.5)
> 

s_2 := s_1
> 

h_2 := wspHEXPANSIONPPEFF(p_1, p_2, `η_i_HPC`)

2394.007108*Units:-Unit(kJ/kg)

 (4.6)
> 

x_2 := wspXSPH(p_2, h_2)

.8320218824

 (4.7)

The parameters at the inlet to the LPC

> 

p_3 := p_2
> 

h_3 := wspHPT(p_3, t_3)

2961.035156*Units:-Unit(kJ/kg)

 (4.8)

Parameters at the end of the expansion process of steam in the LPC

> 

t_4 := wspTSP(p_4); t_4-273.15*Unit('K')

28.9603790*Units:-Unit(`°C`)

 (4.9)
> 

h_4 := wspHEXPANSIONPTPEFF(p_3, t_3, p_4, `η_i_LPC`)

2298.679010*Units:-Unit(kJ/kg)

 (4.10)
> 

x_4 := wspXSPH(p_4, h_4)

.8951644538

 (4.11)

Parameters on the outlet of the condenser (C)

> 

h_5 := wspHSWP(p_4)

121.3879295*Units:-Unit(kJ/kg)

 (4.12)

The share of steam extraction in the separator (S)

> 

`α_SH` := solve(h_1*`α_SH`+h_2 = (1-x_2)*hw_2+`α_SH`*hw_1+x_2*h_3, `α_SH`)

.1137595862

 (4.13)

 

> 

p_5 := p_4

Specific enthalpy water at the outlet of the condenser pump 1 (CP1)

> 

h_6 := wspHCOMPRESSIONPPEFF(p_5, p_2, `η_i_p`)

122.0104042*Units:-Unit(kJ/kg)

 (4.14)

 

Specific enthalpy water at the inlet of the condenser pump 2 (CP2)

> 

h_7 := solve(x_2*h_5+(1-x_2)*hw_2 = h_7, h_7)

208.5177083*Units:-Unit(kJ/kg)

 (4.15)

 

Water temperature at the inlet of the condenser pump 2 (CP2)

> 

t_7 := wspTPH(p_2, h_7); t_7-273.15*Unit('K')

49.7022831*Units:-Unit(`°C`)

 (4.16)

 

Specific enthalpy water at the outlet of the condenser pump 2 (CP2)

> 

h_8 := wspHCOMPRESSIONPTPEFF(p_2, t_7, p_1, `η_i_p`)

215.7180628*Units:-Unit(kJ/kg)

 (4.17)

Water temperature at the outlet of the condenser pump 2 (CP2)

> 

t_8 := wspTPH(p_1, h_8); t_8-273.15*Unit('K')

50.2510776*Units:-Unit(`°C`)

 (4.18)

 

Specific enthalpy water at the inlet of the feed pump (FP)

> 

h_9 := solve(hw_1*`α_SH`+h_8 = (1+`α_SH`)*h_9, h_9)

318.8122013*Units:-Unit(kJ/kg)

 (4.19)

Water temperature at the inlet of the feed pump (FP)

> 

t_9 := wspTPH(p_1, h_9); t_9-273.15*Unit('K')

74.9548161*Units:-Unit(`°C`)

 (4.20)

Specific enthalpy of feed water

> 

h_10 := wspHCOMPRESSIONPTPEFF(p_1, t_9, p_10, `η_i_p`)

319.2085704*Units:-Unit(kJ/kg)

 (4.21)

Specific pumps work

> 

w_p := x_2*(h_6-h_5)+h_8-h_7+(1+`α_SH`)*(h_10-h_9)

8.159726957*Units:-Unit(kJ/kg)

 (4.22)

Specific work of the HPC

> 

w_HPC := h_1-h_2

388.3633630*Units:-Unit(kJ/kg)

 (4.23)

Specific work of the LPC

> 

w_LPC := x_2*(h_3-h_4)

551.0948074*Units:-Unit(kJ/kg)

 (4.24)

Specific heat of the Steam Generator (SG)

> 

q_SG := (1+`α_SH`)*(h_1-h_7)

2866.653188*Units:-Unit(kJ/kg)

 (4.25)

Answer
 

Hence the thermal efficiency

> 

`η_T` := (w_HPC+w_LPC-w_p)/q_SG

.3248730775

 (5.1)