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Efficiency of  a Turbine Cycle cycle with supercritical CO2 as working fluid

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

 

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restart

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with(ThermophysicalData):

Calculation of the thermal efficiency a cycle with supercritical CO2 as working fluid. This cycle is used for recycling waste heat (in flue gas) from industrial plants - to generate electricity

Input data:

> 

t__1 := (300+273.15)*Unit('K'); 1; p__1 := 31*Unit('MPa'); 1; p__2 := 5*Unit('MPa')

573.15*Units:-Unit('K')

31*Units:-Unit('MPa')

5*Units:-Unit('MPa')

(1)

Inernal*efficiency*of*the*turbine:

> 

eta__oi_t := .83

.83

(2)

Inernal*efficiency*of*the*turbine:

> 

eta__oi_p := .82

.82

(3)

Temperature difference between the recuperator and the condencer

> 

Delta__r_c := 10*Unit('K')

10*Units:-Unit(K)

(4)

Specific entropy of  live CO2 vapor (the turbine inlet - the point #1):

> 

s__1 := Property(entropy, pressure = p__1, temperature = t__1, CO2)

2.182861756*Units:-Unit(kJ/(kg*K))

(5)

Specific enthalpy  of live CO2 vapor (the turbine inlet - the point #1):

> 

h__1 := ThermophysicalData:-Property(enthalpy, pressure = p__1, temperature = t__1, CO2)

708.7281650*Units:-Unit(kJ/kg)

(6)

Specific entropy of working fluid in the outlet of the turbine (an ideal process of the vapor extension)

> 

s__2is := s__1:

Temperature of working fluid in the outlet of the turbine (an ideal process of the vapor extension)

> 

t__2is := ThermophysicalData:-Property(temperature, pressure = p__2, entropy = s__2is, CO2); -1; t__2is-273.15*Unit('K')

115.1907621*Units:-Unit(`°C`)

(7)

Specific enthalpy of working fluid in the outlet of the turbine (an ideal process of the vapor extension)

> 

h__2is := ThermophysicalData:-Property(enthalpy, pressure = p__2, temperature = t__2is, CO2)

558.5276468*Units:-Unit(kJ/kg)

(8)

Specific isentropic work of the tubine (an ideal process of the vapor extension)

> 

l__t_is := h__1-h__2is

150.2005182*Units:-Unit(kJ/kg)

(9)

Specific actual work of tubine

> 

l__t := eta__oi_t*l__t_is

124.6664301*Units:-Unit(kJ/kg)

(10)

Specific enthalpy of working fluid in the point 2

> 

h__2 := h__1-l__t

584.0617349*Units:-Unit(kJ/kg)

(11)

Temperature of working fluid in point 2

> 

t__2 := ThermophysicalData:-Property(temperature, pressure = p__2, enthalpy = h__2, CO2); -1; t__2-273.15*Unit('K')

138.4644771*Units:-Unit(`°C`)

(12)

 

> 

s__2 := ThermophysicalData:-Property(entropy, pressure = p__2, temperature = t__2, CO2)

2.246723820*Units:-Unit(kJ/(kg*K))

(13)

 

> 

p__4 := p__2:

Temperature of working fluid in point 4

> 

t__4 := ThermophysicalData:-Property(temperature, pressure = p__4, Q = 1, CO2); -1; t__4-273.15*Unit('K')

14.2839238*Units:-Unit(`°C`)

(14)

Specific entropy of working fluid in point 4

> 

s__4 := ThermophysicalData:-Property(entropy, pressure = p__4, Q = 0, CO2)

1.128864818*Units:-Unit(kJ/(kg*K))

(15)

Specific enthalpy of working fluid in point 4

> 

h__4 := ThermophysicalData:-Property(enthalpy, pressure = p__4, Q = 0, CO2)

237.8660784*Units:-Unit(kJ/kg)

(16)

Specific entropy of working fluid in point 5 (an ideal process of the vapor extension)

> 

s__5is := s__4:

Pressure in point 5

> 

p__5 := p__1:

Temperature of working fluid in point 5 (an ideal process of the liquid compression)

> 

t__5is := ThermophysicalData:-Property(temperature, pressure = p__5, entropy = s__5is, CO2); -1; t__5is-273.15*Unit('K')

38.7611956*Units:-Unit(`°C`)

(17)

Specific enthalpy of working fluid in point 5 (an ideal process of the liquid compression)

> 

h__5is := ThermophysicalData:-Property(enthalpy, pressure = p__5, temperature = t__5is, CO2)

267.4215357*Units:-Unit(kJ/kg)

(18)

Specific isentropic work of the pump

> 

l__p_is := h__5is-h__4

29.55545730*Units:-Unit(kJ/kg)

(19)

Specific actual work of pump

> 

l__p := l__p_is/eta__oi_p

36.04324061*Units:-Unit(kJ/kg)

(20)

Specific enthalpy of working fluid in point 5

> 

h__5 := h__4+l__p

273.9093190*Units:-Unit(kJ/kg)

(21)

Temperature of working fluid in point 5

> 

t__5 := ThermophysicalData:-Property(temperature, pressure = p__5, enthalpy = h__5, CO2); -1; t__5-273.15*Unit('K')

42.1059041*Units:-Unit(`°C`)

(22)

Specific entropy of working fluid in point 5

> 

s__5 := ThermophysicalData:-Property(entropy, pressure = p__5, temperature = t__5, CO2)

1.149554101*Units:-Unit(kJ/(kg*K))

(23)

Pressure in point 3

> 

p__3 := p__2:

Temperature in point 3

> 

t__3 := t__5+Delta__r_c; -1; t__3-273.15*Unit('K')

52.1059041*Units:-Unit(`°C`)

(24)

Specific enthalpy of working fluid in point 3

> 

h__3 := ThermophysicalData:-Property(enthalpy, pressure = p__3, temperature = t__3, CO2)

483.9663596*Units:-Unit(kJ/kg)

(25)

Specific entropy of working fluid in point 3

> 

s__3 := ThermophysicalData:-Property(entropy, pressure = p__3, temperature = t__3, CO2)

1.972805998*Units:-Unit(kJ/(kg*K))

(26)

Heat of the recuperator

> 

q__2_3 := h__2-h__3

100.0953753*Units:-Unit(kJ/kg)

(27)

Specific enthalpy of working fluid in point 6

> 

h__6 := h__5+q__2_3

374.0046943*Units:-Unit(kJ/kg)

(28)

Pressure in point 6

> 

p__6 := p__5

31*Units:-Unit(MPa)

(29)

Temperature in point 6

> 

t__6 := ThermophysicalData:-Property(temperature, pressure = p__6, enthalpy = h__6, CO2); -1; t__6-273.15*Unit('K')

92.1519688*Units:-Unit(K)

(30)

Specific entropy of working fluid in point 6

> 

s__6 := ThermophysicalData:-Property(entropy, pressure = p__6, temperature = t__6, CO2)

1.444068952*Units:-Unit(kJ/(kg*K))

(31)

Waste heat

> 

q__w := h__1-h__6

334.7234707*Units:-Unit(kJ/kg)

(32)

Thermal efficiency

> 

eta__t_is := (l__t_is-l__p_is)/q__w

.3604320326

(33)

Internal efficiency

> 

eta__t := (l__t-l__p)/q__w

.2647653877

(34)

Author: Valery Ochkov``NULL

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