//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 = enthalpy(Water;P = p_B;X = xl_B)// Saturated liquid enthalpy
//Equation: 17
hv_B = enthalpy(Water;P = p_B;X = xv_B)// Saturated vapor enthalpy
//Equation: 18
x_B = (h_A - hl_B)/(hv_B - hl_B)// Quality
//Equation: 19
T_B = t_sat(Water;P = p_B) // Downstream point - B
//Equation: 20
h_B = enthalpy(Water;P = p_B;X = x_B) // Enthalpy
 
//Process: HP turbine
//Equation: 21
m_dot_HPturbine = m_dot_HPvalve // Upstream process - HP valve
//Equation: 22
s_B = entropy(Water;P = p_B;H = 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 = entropy(Water;T = Tl_G;P = p_G)// Saturated liquid entropy
//Equation: 32
sv_G = entropy(Water;T = Tv_G;P = p_G)// Saturated vapor entropy
//Equation: 33
x_G = (s_G - sl_G)/(sv_G - sl_G)// Quality
//Equation: 34
T_G = t_sat(Water;P = p_G) // Downstream point - G
//Equation: 35
h_G = enthalpy(Water;P = p_G;X = 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 = enthalpy(Water;P = p_F;X = xl_F)// Saturated liquid enthalpy
//Equation: 44
hv_F = enthalpy(Water;P = p_F;X = xv_F)// Saturated vapor enthalpy
//Equation: 45
x_F = (h_A - hl_F)/(hv_F - hl_F)// Quality
//Equation: 46
T_F = t_sat(Water;P = p_F) // Downstream point - F
//Equation: 47
h_F = enthalpy(Water;P = p_F;X = x_F) // Enthalpy
 
//Process: LP turbine
//Equation: 48
m_dot_LPturbine = m_dot_steamsuperheating // Upstream process - steam superheating
//Equation: 49
s_I = entropy(Water;P = p_I;H = h_I) // Upstream point - I - Downstream point - C
// Comment = Isentropic reference
//Equation: 50
hs_C = enthalpy(Water;P = p_C;S = 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 = enthalpy(Water;P = p_C;X = xl_C)// Saturated liquid enthalpy
//Equation: 58
hv_C = enthalpy(Water;P = p_C;X = xv_C)// Saturated vapor enthalpy
//Equation: 59
x_C = (h_C - hl_C)/(hv_C - hl_C)// Quality
//Equation: 60
T_C = t_sat(Water;P = p_C) // Downstream point - C
//Equation: 61
s_C = entropy(Water;P = p_C;H = 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 = entropy(Water;P = p_D;H = h_D) // Upstream point - D - Downstream point - L
//Equation: 66
hs_L = enthalpy(Water;P = p_L;S = s_D) // Downstream point - L
//Equation: 67
etaT_extractionpump = 0,9// Isentropic efficiency
//Equation: 68
v_L = volume(Water;P = p_L;H = h_L) // Downstream point volume - 
//Equation: 69
h_L = h_D + v_L*(p_L - p_D)/100, // Liquid compression
//Equation: 70
T_L = temperature(Water;P = p_L;H = 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 = enthalpy(Water;P = p_L2;X = xl_L2)// Saturated liquid enthalpy
//Equation: 80
hv_L2 = enthalpy(Water;P = p_L2;X = 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 = entropy(Water;P = p_L2;H = h_L2) // Enthalpy
//Equation: 84
T_L2 = temperature(Water;P = p_L2;H = h_L2) // Downstream point - L2
 
//Process: liquid compression
// Comment = Isentropic reference
//Equation: 85
s_P = entropy(Water;P = p_P;H = h_P) // Upstream point - P - Downstream point - E
//Equation: 86
hs_E = enthalpy(Water;P = p_E;S = s_P) // Downstream point - E
//Equation: 87
etaT_liquidcompression = 0,9// Isentropic efficiency
//Equation: 88
v_E = volume(Water;P = p_E;H = h_E) // Downstream point volume - 
//Equation: 89
h_E = h_P + v_E*(p_E - p_P)/100, // Liquid compression
//Equation: 90
T_E = temperature(Water;P = p_E;H = 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_throttlsuperheattank = 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 = enthalpy(Water;P = p_K2;X = xl_K2)// Saturated liquid enthalpy
//Equation: 100
hv_K2 = enthalpy(Water;P = p_K2;X = xv_K2)// Saturated vapor enthalpy
//Equation: 101
x_K2 = (h_K - hl_K2)/(hv_K2 - hl_K2)// Quality
//Equation: 102
T_K2 = t_sat(Water;P = p_K2) // Downstream point - K2
//Equation: 103
h_K2 = enthalpy(Water;P = p_K2;X = x_K2) // Enthalpy
 
//Process: IP turbine
//Equation: 104
//s_G = entropy(water;P = p_G;H = 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 = entropy(Water;T = Tl_H;P = p_H)// Saturated liquid entropy
//Equation: 114
sv_H = entropy(Water;T = Tv_H;P = p_H)// Saturated vapor entropy
//Equation: 115
x_H = (s_H - sl_H)/(sv_H - sl_H)// Quality
//Equation: 116
T_H = t_sat(Water;P = p_H) // Downstream point - H
//Equation: 117
h_H = enthalpy(Water;P = p_H;X = 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_throttlsuperheattank // Downstream process - liquid compression
//Equation: 126
h_P = ( m_dot_LPtankthrottling*h_L2 +  m_dot_liq_HP_turb*h_J +  m_dot_throttlsuperheattank*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 =  enthalpy(Water;P = p_I;T = 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 =  temperature(water;P = p_K;H = 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 = t_sat(Water;P = p_N)+dTsat_N// set Tsat (Celsius)
//Equation: 147
h_N = enthalpy(Water;P = p_N;X = 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 = t_sat(Water;P = p_A)+dTsat_A// set Tsat (Celsius)
//Equation: 152
h_A = enthalpy(Water;P = p_A;X = 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 = t_sat(Water;P = p_K)+dTsat_K// set Tsat (Celsius)
//Equation: 156
//h_K = enthalpy(water;P = p_K;X = 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 = t_sat(Water;P = p_J)+dTsat_J// set Tsat (Celsius)
//Equation: 161
h_J = enthalpy(Water;P = p_J;X = 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 = t_sat(Water;P = p_D)+dTsat_D// set Tsat (Celsius)
//Equation: 166
h_D = enthalpy(Water;P = p_D;X = 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 = t_sat(Water;P = p_I0)+dTsat_I0// set Tsat (Celsius)
//Equation: 171
h_I0 = enthalpy(Water;P = p_I0;X = 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