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Thermal Efficiency of  Steam Turbine Cycle with 2 Pre-heaters

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

Introduction
 

This application calculates the thermal efficiency of a steam turbine cycle with two pre-heaters

Water Properties
 
> 

restart; with(ThermophysicalData)


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 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:

Vapor fraction of steam as function of pressure and specific entropy

> 

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:


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

> 

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

 

Specific entropy of water at 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 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 entropy

> 

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


Functions for processes steam expansion and water compression

 

> 

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:

 

Input Data
 
> 

t_0 := 540*Unit('degC'):

 

Calculations
 

Heat balance of  in H-1 and H-2 pre-heaters:

> 

equ1 := (1-`α_1`-`α_2`)*h_p1out+`α_1`*h_1 = (1-`α_2`)*h_p2in:
> 

equ2 := (1-`α_2`)*h_p2out+`α_2`*h_2 = h_p3in:

 

Specific enthalpy of steam in the inlet of the turbine

> 

h_0 := wspHPT(p_0, t_0)

3445.023934*Units:-Unit(kJ/kg)

 (4.1)

Specific enthalpy of steam in the inlet of the pre-heater 2

> 

h_2 := wspHEXPANSIONPTPEFF(p_0, t_0, p_2, `η_i_t`)

3276.108250*Units:-Unit(kJ/kg)

 (4.2)

Specific enthalpy of steam in the inlet of the pre-heater 1

> 

h_1 := wspHEXPANSIONPTPEFF(p_0, t_0, p_1, `η_i_t`)

3079.291235*Units:-Unit(kJ/kg)

 (4.3)

Specific enthalpy of wet steam in the outlet of the turbine

> 

h_cond := wspHEXPANSIONPTPEFF(p_0, t_0, p_cond, `η_i_t`)

2200.287725*Units:-Unit(kJ/kg)

 (4.4)

Specific enthalpy of water in the inlet of the pump 1

> 

h_p1in := wspHSWP(p_cond)

121.3879295*Units:-Unit(kJ/kg)

 (4.5)

Specific enthalpy of water in the outlet of the pump 1

> 

h_p1out := wspHCOMPRESSIONPPEFF(p_cond, p_1, `η_i_p`)

125.3963306*Units:-Unit(kJ/kg)

 (4.6)

``Specific enthalpy of water in the inlet of the pump 2

> 

h_p2in := wspHSWP(p_1)

1008.344614*Units:-Unit(kJ/kg)

 (4.7)

Specific enthalpy of water in the outlet of the pump 2

> 

h_p2out := wspHCOMPRESSIONPPEFF(p_1, p_2, `η_i_p`)

1014.823021*Units:-Unit(kJ/kg)

 (4.8)

NULL

NULLSpecific enthalpy of water in the inlet of the pump 3

> 

h_p3in := wspHSWP(p_2)

1267.659283*Units:-Unit(kJ/kg)

 (4.9)

NULLSpecific enthalpy of water in the outlet of the pump 3 (feed water for the boiler)

> 

h_p3out := wspHCOMPRESSIONPPEFF(p_2, p_0, `η_i_p`)

1278.430043*Units:-Unit(kJ/kg)

 (4.10)

Solution of the system of equations (see above) of the heat balance in H-1 and H-2 pre-heaters:

> 

res := solve({equ1, equ2}, {`α_1`, `α_2`})

{`α_1` = .2654884807, `α_2` = .1118108670}

 (4.11)

Specific work of the turbine

> 

w_t := eval(h_0-h_2+(1-`α_2`)*(h_2-h_1)+(1-`α_1`-`α_2`)*(h_1-h_cond), res)

891.0824770*Units:-Unit(kJ/kg)

 (4.12)

Specific work of pumps

> 

w_p := eval((1-`α_1`-`α_2`)*(h_p1out-h_p1in)+(1-`α_2`)*(h_p2out-h_p2in)+h_p3out-h_p3in, res)

19.02084468*Units:-Unit(kJ/kg)

 (4.13)

Specific heat of the boiler

> 

q_b := h_0-h_p3out

2166.593891*Units:-Unit(kJ/kg)

 (4.14)

Hence the thermal efficiency

 

> 

`η_T` := eval((w_t-w_p)/q_b, res)

.4025035037

 (4.15)