//EQUATIONS
//Units: SI, Temperatures in Celsius, pressures in bar
//Project file: D:\_classement\_Thopt\THERMOPTIM_Pro_282\proj\PWR_Extract.prj
//Date and Time: 2024-08-11 14:00:47

//Flow rate unit: t/s

//PROCESSES

//Process: extraction
//Equation: 1
m_dot_extraction = 0.2 // Given value

//Process: liq_HP_turb
//Equation: 2
//m_dot_liq_HP_turb = 0.14070175729 // Given value

//Process: condenser
//Equation: 3
m_dot_condenser = m_dot_LPturbine // Upstream process - LP turbine
// Comment = mDeltaH not set
//Equation: 4
Q_dot_condenser = m_dot_condenser*(h_D - h_C) // Upstream point - C - Downstream point - D - DeltaH/flow

//Process: superheating
//Equation: 5
m_dot_superheating = m_dot_superheatingvalve // Upstream process - superheating valve
// Comment = isobaricExchange
//Equation: 6
p_K = p_F // Upstream point - F - Downstream point - K
// Comment = //Exchange process connected to a heat exchanger

//Process: steam superheating
// Comment = isobaricExchange
//Equation: 7
p_I = p_I0 // Upstream point - I0 - Downstream point - I
// Comment = //Exchange process connected to a heat exchanger

//Process: generator
//Equation: 8
m_dot_generator = m_dot_economizer // Upstream process - economizer
// Comment = mDeltaH not set
//Equation: 9
Q_dot_generator = m_dot_generator*(h_A - h_N) // Upstream point - N - Downstream point - A - DeltaH/flow

//Process: economizer
// Comment = mDeltaH not set
//Equation: 10
Q_dot_economizer = m_dot_economizer*(h_N - h_M) // Upstream point - M - Downstream point - N - DeltaH/flow


//Process: HP valve
// Comment = Isenthalpic throttling
//Equation: 11
p_B = 50.0// Given outlet pressure
//Equation: 12
xl_B = 0.// Saturated liquid quality
//Equation: 13
Tl_B = T_B- 0.01// Saturated liquid temperature
//Equation: 14
xv_B = 1.// Saturated vapor quality
//Equation: 15
Tv_B = T_B+ 0.01// Saturated vapor temperature
//Equation: 16
hl_B = hsat_Px("water",p_B,xl_B)// Saturated liquid enthalpy
//Equation: 17
hv_B = hsat_Px("water",p_B,xv_B)// Saturated vapor enthalpy
//Equation: 18
x_B = (h_A - hl_B)/(hv_B - hl_B)// Quality
//Equation: 19
T_B = Tsat_P("water",p_B) // Downstream point - B
//Equation: 20
h_B = hsat_Px("water",p_B,x_B) // Enthalpy

//Process: HP turbine
//Equation: 21
m_dot_HPturbine = m_dot_HPvalve // Upstream process - HP valve
//Equation: 22
s_B = s_Ph("water",p_B,h_B) // Upstream point - B - Downstream point - G
// Comment = Polytropic reference
//Equation: 23
ds_G = -(1 - etaT_HPturbine)*8.314/M_B*ln(p_G/p_B) // Upstream point - B - Downstream point - G
//Equation: 24
s_G = s_B + ds_G // Entropy - G
//Equation: 25
M_B = 18.01528 // Molar mass - G
//Equation: 26
etaT_HPturbine = 0.91// Polytropic efficiency
// Comment = Polytropic coefficient: k = -Math.log(aval.p/amont.p)/Math.log(aval.V/amont.V)
//Equation: 27
xl_G = 0.// Saturated liquid quality
//Equation: 28
Tl_G = T_G- 0.01// Saturated liquid temperature
//Equation: 29
xv_G = 1.// Saturated vapor quality
//Equation: 30
Tv_G = T_G+ 0.01// Saturated vapor temperature
//Equation: 31
sl_G = s_PT("water",p_G,Tl_G)// Saturated liquid entropy
//Equation: 32
sv_G = s_PT("water",p_G,Tv_G)// Saturated vapor entropy
//Equation: 33
x_G = (s_G - sl_G)/(sv_G - sl_G)// Quality
//Equation: 34
T_G = Tsat_P("water",p_G) // Downstream point - G
//Equation: 35
h_G = hsat_Px("water",p_G,x_G) // Enthalpy
// Comment = Given outlet pressure
//Equation: 36
p_G = 15.0// Outlet pressure
//Equation: 37
W_dot_HPturbine = m_dot_HPturbine*(h_G - h_B) // DeltaH 

//Process: superheating valve
// Comment = Isenthalpic throttling
//Equation: 38
p_F = 51.5// Given outlet pressure
//Equation: 39
xl_F = 0.// Saturated liquid quality
//Equation: 40
Tl_F = T_F- 0.01// Saturated liquid temperature
//Equation: 41
xv_F = 1.// Saturated vapor quality
//Equation: 42
Tv_F = T_F+ 0.01// Saturated vapor temperature
//Equation: 43
hl_F = hsat_Px("water",p_F,xl_F)// Saturated liquid enthalpy
//Equation: 44
hv_F = hsat_Px("water",p_F,xv_F)// Saturated vapor enthalpy
//Equation: 45
x_F = (h_A - hl_F)/(hv_F - hl_F)// Quality
//Equation: 46
T_F = Tsat_P("water",p_F) // Downstream point - F
//Equation: 47
h_F = hsat_Px("water",p_F,x_F) // Enthalpy

//Process: LP turbine
//Equation: 48
m_dot_LPturbine = m_dot_steamsuperheating // Upstream process - steam superheating
//Equation: 49
s_I = s_Ph("water",p_I,h_I) // Upstream point - I - Downstream point - C
// Comment = Isentropic reference
//Equation: 50
hs_C = h_Ps("water",p_C,s_I) // Downstream point - C
//Equation: 51
etaT_LPturbine = 0.85// Isentropic efficiency
//Equation: 52
h_C = h_I - etaT_LPturbine*(h_I - hs_C) // Upstream point - I - Downstream point - C
//Equation: 53
xl_C = 0.// Saturated liquid quality
//Equation: 54
Tl_C = T_C- 0.01// Saturated liquid temperature
//Equation: 55
xv_C = 1.// Saturated vapor quality
//Equation: 56
Tv_C = T_C+ 0.01// Saturated vapor temperature
//Equation: 57
hl_C = hsat_Px("water",p_C,xl_C)// Saturated liquid enthalpy
//Equation: 58
hv_C = hsat_Px("water",p_C,xv_C)// Saturated vapor enthalpy
//Equation: 59
x_C = (h_C - hl_C)/(hv_C - hl_C)// Quality
//Equation: 60
T_C = Tsat_P("water",p_C) // Downstream point - C
//Equation: 61
s_C = s_Ph("water",p_C,h_C) // Entropy
// Comment = Given outlet pressure
//Equation: 62
p_C = 0.07// Outlet pressure
//Equation: 63
W_dot_LPturbine = m_dot_LPturbine*(h_C - h_I) // DeltaH 

//Process: extraction pump
//Equation: 64
m_dot_extractionpump = m_dot_condenser // Upstream process - condenser
// Comment = Isentropic reference
//Equation: 65
s_D = s_Ph("water",p_D,h_D) // Upstream point - D - Downstream point - L
//Equation: 66
hs_L = h_Ps("water",p_L,s_D) // Downstream point - L
//Equation: 67
etaT_extractionpump = 0.9// Isentropic efficiency
//Equation: 68
v_L = v_Ph("water",p_L,h_L) // Downstream point volume - 
//Equation: 69
h_L = h_D + v_L*(p_L - p_D)/100. // Liquid compression
//Equation: 70
T_L = T_Ph("water",p_L,h_L) // Downstream point - L
// Comment = Given outlet pressure
//Equation: 71
p_L = 15.0// Outlet pressure
//Equation: 72
W_dot_extractionpump = m_dot_extractionpump*(h_L - h_D) // DeltaH 

//Process: LP tank throttling
//Equation: 73
m_dot_LPtankthrottling = m_dot_extractionpump // Upstream process - extraction pump
// Comment = Isenthalpic throttling
//Equation: 74
p_L2 = 11.0// Given outlet pressure
//Equation: 75
xl_L2 = 0.// Saturated liquid quality
//Equation: 76
Tl_L2 = T_L2- 0.01// Saturated liquid temperature
//Equation: 77
xv_L2 = 1.// Saturated vapor quality
//Equation: 78
Tv_L2 = T_L2+ 0.01// Saturated vapor temperature
//Equation: 79
hl_L2 = hsat_Px("water",p_L2,xl_L2)// Saturated liquid enthalpy
//Equation: 80
hv_L2 = hsat_Px("water",p_L2,xv_L2)// Saturated vapor enthalpy
//Equation: 81
x_L2 = (h_L - hl_L2)/(hv_L2 - hl_L2)// Quality
//Equation: 82
h_L2 = h_L // Enthalpy
//Equation: 83
s_L2 = s_Ph("water",p_L2,h_L2) // Enthalpy
//Equation: 84
T_L2 = T_Ph("water",p_L2,h_L2) // Downstream point - L2

//Process: liquid compression
// Comment = Isentropic reference
//Equation: 85
s_P = s_Ph("water",p_P,h_P) // Upstream point - P - Downstream point - E
//Equation: 86
hs_E = h_Ps("water",p_E,s_P) // Downstream point - E
//Equation: 87
etaT_liquidcompression = 0.9// Isentropic efficiency
//Equation: 88
v_E = v_Ph("water",p_E,h_E) // Downstream point volume - 
//Equation: 89
h_E = h_P + v_E*(p_E - p_P)/100. // Liquid compression
//Equation: 90
T_E = T_Ph("water",p_E,h_E) // Downstream point - E
// Comment = Given outlet pressure
//Equation: 91
p_E = 70.0// Outlet pressure
//Equation: 92
W_dot_liquidcompression = m_dot_liquidcompression*(h_E - h_P) // DeltaH 

//Process: throttling superheating-tank
//Equation: 93
m_dot_throttlingsuperheatingtank = m_dot_superheating // Upstream process - superheating
// Comment = Isenthalpic throttling
//Equation: 94
p_K2 = 11.0// Given outlet pressure
//Equation: 95
xl_K2 = 0.// Saturated liquid quality
//Equation: 96
Tl_K2 = T_K2- 0.01// Saturated liquid temperature
//Equation: 97
xv_K2 = 1.// Saturated vapor quality
//Equation: 98
Tv_K2 = T_K2+ 0.01// Saturated vapor temperature
//Equation: 99
hl_K2 = hsat_Px("water",p_K2,xl_K2)// Saturated liquid enthalpy
//Equation: 100
hv_K2 = hsat_Px("water",p_K2,xv_K2)// Saturated vapor enthalpy
//Equation: 101
x_K2 = (h_K - hl_K2)/(hv_K2 - hl_K2)// Quality
//Equation: 102
T_K2 = Tsat_P("water",p_K2) // Downstream point - K2
//Equation: 103
h_K2 = hsat_Px("water",p_K2,x_K2) // Enthalpy

//Process: IP turbine
//Equation: 104
//s_G = s_Ph("water",p_G,h_G) // Upstream point - G - Downstream point - H
// Comment = Polytropic reference
//Equation: 105
ds_H = -(1 - etaT_IPturbine)*8.314/M_G*ln(p_H/p_G) // Upstream point - G - Downstream point - H
//Equation: 106
s_H = s_G + ds_H // Entropy - H
//Equation: 107
M_G = 18.01528 // Molar mass - H
//Equation: 108
etaT_IPturbine = 0.91// Polytropic efficiency
// Comment = Polytropic coefficient: k = -Math.log(aval.p/amont.p)/Math.log(aval.V/amont.V)
//Equation: 109
xl_H = 0.// Saturated liquid quality
//Equation: 110
Tl_H = T_H- 0.01// Saturated liquid temperature
//Equation: 111
xv_H = 1.// Saturated vapor quality
//Equation: 112
Tv_H = T_H+ 0.01// Saturated vapor temperature
//Equation: 113
sl_H = s_PT("water",p_H,Tl_H)// Saturated liquid entropy
//Equation: 114
sv_H = s_PT("water",p_H,Tv_H)// Saturated vapor entropy
//Equation: 115
x_H = (s_H - sl_H)/(sv_H - sl_H)// Quality
//Equation: 116
T_H = Tsat_P("water",p_H) // Downstream point - H
//Equation: 117
h_H = hsat_Px("water",p_H,x_H) // Enthalpy
// Comment = Given outlet pressure
//Equation: 118
p_H = 9.0// Outlet pressure
//Equation: 119
W_dot_IPturbine = m_dot_IPturbine*(h_H - h_G) // DeltaH 

//NODES

//Node: SG outlet
// Comment = Divider
//Equation: 120
m_dot_generator =  m_dot_HPvalve +  m_dot_superheatingvalve // Upstream process - generator

//Node: drier
// Comment = Separator
//Equation: 121
m_dot_liq_HP_turb = m_dot_IPturbine*(1. - x_H) // liquid process - liq_HP_turb
//Equation: 122
m_dot_steamsuperheating = m_dot_IPturbine*x_H // vapor process - steam superheating
// Comment = Isobaric separator
//Equation: 123
p_I0 = p_H// outlet pressure
//Equation: 124
p_J = p_H// outlet pressure

//Node: feed water tank
// Comment = Mixer
//Equation: 125
m_dot_liquidcompression =  m_dot_LPtankthrottling +  m_dot_liq_HP_turb +  m_dot_throttlingsuperheatingtank // Downstream process - liquid compression
//Equation: 126
h_P = ( m_dot_LPtankthrottling*h_L2 +  m_dot_liq_HP_turb*h_J +  m_dot_throttlingsuperheatingtank*h_K2)/m_dot_liquidcompression // Downstream point - P

//Node: extraction
// Comment = Divider
//Equation: 127
m_dot_HPturbine =  m_dot_extraction +  m_dot_IPturbine // Upstream process - HP turbine

//Node: preheating
// Comment = Mixer
//Equation: 128
//m_dot_economizer =  m_dot_liquidcompression +  m_dot_extraction // Downstream process - economizer
//Equation: 129
h_M = ( m_dot_liquidcompression*h_E +  m_dot_extraction*h_G)/m_dot_economizer // Downstream point - M

//HEAT EXCHANGERS

//Heat exchanger: MSR
//Equation: 130
mCp_steamsuperheating = (h_I - h_I0)/(T_I - T_I0)*m_dot_steamsuperheating // mCpf =deltaH/deltaT - steam superheating
//Equation: 131
mCp_superheating = (h_K - h_F)*m_dot_superheating/(T_K - T_F) // mCpc =-deltaH/deltaT - superheating
// Comment = mCpc>mCpf
//Equation: 132
UA_MSR = NTU_MSR *mCp_steamsuperheating // Cold fluid - steam superheating
//Equation: 133
R_MSR = mCp_steamsuperheating /mCp_superheating // Hot fluid - superheating - Cold fluid - steam superheating
//Equation: 134
T_I = T_I0 + epsilon_MSR*(T_F - T_I0) // Hot fluid outlet temperature
//Equation: 135
h_I =  h_PT("water",p_I,T_I)// Enthalpy
//Equation: 136
h_K = - m_dot_steamsuperheating /m_dot_superheating*(h_I - h_I0) + h_F // Hot fluid - superheating - Cold fluid - steam superheating
//Equation: 137
//T_K =  T_Ph("water",p_K,h_K)// Hot fluid outlet temperature
// Comment = epsilon given value
//Equation: 138
epsilon_MSR = 0.8949974956232079 // Given value
//Equation: 139
argLn_MSR = (1 - epsilon_MSR*R_MSR)/(1 - epsilon_MSR)
//Equation: 140
NTU_MSR = 1/(1 - R_MSR)*ln(argLn_MSR) // Counterflow heat exchanger
//Equation: 141
Q_dot_superheating = m_dot_superheating*(h_K - h_F) // DeltaH hot fluid
//Equation: 142
Q_dot_steamsuperheating = m_dot_steamsuperheating*(h_I - h_I0) // DeltaH cold fluid


//Number of equations: 142

//POINTS WITH SATURATION TEMPERATURE SET


//Point N

//Outlet point of process economizer
//Equation: 143
p_N = 65.0// P (bar)
//Equation: 144
x_N = 0.0// Quality
//Equation: 145
dTsat_N = 0.0// Deviation from Tsat
//Equation: 146
T_N = Tsat_P("water",p_N)+dTsat_N// set Tsat (Celsius)
//Equation: 147
h_N = hsat_Px("water",p_N,x_N)// Enthalpy


//Point A

//Outlet point of process generator
//Equation: 148
p_A = 56.0// P (bar)
//Equation: 149
x_A = 1.0// Quality
//Equation: 150
dTsat_A = 0.0// Deviation from Tsat
//Equation: 151
T_A = Tsat_P("water",p_A)+dTsat_A// set Tsat (Celsius)
//Equation: 152
h_A = hsat_Px("water",p_A,x_A)// Enthalpy


//Point K

//Outlet point of process superheating
//Equation: 153
x_K = 0.0// Quality
//Equation: 154
dTsat_K = -0.1// Deviation from Tsat
//Equation: 155
T_K = Tsat_P("water",p_K)+dTsat_K// set Tsat (Celsius)
//Equation: 156
//h_K = hsat_Px("water",p_K,x_K)// Enthalpy


//Point J

//Outlet point of process liq_HP_turb
//Equation: 157
//p_J = 9.0// P (bar)
//Equation: 158
x_J = 0.0// Quality
//Equation: 159
dTsat_J = 0.0// Deviation from Tsat
//Equation: 160
T_J = Tsat_P("water",p_J)+dTsat_J// set Tsat (Celsius)
//Equation: 161
h_J = hsat_Px("water",p_J,x_J)// Enthalpy


//Point D

//Outlet point of process condenser
//Equation: 162
p_D = 0.07// P (bar)
//Equation: 163
x_D = 0.0// Quality
//Equation: 164
dTsat_D = 0.0// Deviation from Tsat
//Equation: 165
T_D = Tsat_P("water",p_D)+dTsat_D// set Tsat (Celsius)
//Equation: 166
h_D = hsat_Px("water",p_D,x_D)// Enthalpy


//Point I0
//Equation: 167
//p_I0 = 9.0// P (bar)
//Equation: 168
x_I0 = 1.0// Quality
//Equation: 169
dTsat_I0 = 0.0// Deviation from Tsat
//Equation: 170
T_I0 = Tsat_P("water",p_I0)+dTsat_I0// set Tsat (Celsius)
//Equation: 171
h_I0 = hsat_Px("water",p_I0,x_I0)// Enthalpy


//OTHER POINTS WITH PRESSURE SET


//SET FLOW RATES

//Equation: 172
//m_dot_extraction = 0.2// Given flow
//Equation: 173
m_dot_economizer = 1.4000000003// Given flow 
//Equation: 174
m_dot_superheatingvalve = 0.11// Given flow 

//OVERALL BALANCE

//Equation: 175
usefulEnergy = W_dot_HPturbine + W_dot_LPturbine + W_dot_extractionpump + W_dot_liquidcompression + W_dot_IPturbine
//Equation: 176
purchasedEnergy = Q_dot_generator + Q_dot_economizer
//Equation: 177
eta0 = usefulEnergy/purchasedEnergy
//Equation: 178
eta = abs(eta0)
//m_dot_IPturbine
p_P = 11
//m_dot_HPvalve