Rankine Cycle + HRSG #554

PabloMBarral · 2024-10-16T00:23:55Z

PabloMBarral
Oct 16, 2024

Issue with NaN Results in TESPy Model

Hi, community. Hope you're all great.

Together with a student (I'm his tutor), we are developing a model of a HRSG and a small Rankine Cycle. The process data is from real pieces of equipment.

The (ackward) truth is that we are stuck. We cannot find why the system shows NaN in the results.
TPP - PFD (2).pdf

The process fluid diagram is attached. It contains the connections' numbers (almost every connection is represented, with the small exception of a valve inside the steam turbine and the gas path).

I’m fully aware that debugging is really a pain in the foot, and that this code is still a work-in-progress in terms of style. I am posting to ask for help, and I’ll continue improving readiness and clarity.

Thanks in advance! 🙏

PS: Apologies for the bad English and the Spanish-English messy mixture

Python Code

def export(__file__, results):

    import os

    path = os.path.dirname(os.path.abspath(__file__))

    text_file = os.path.join(path, 'results.txt')

    formatted_text = results.to_string(index=False, justify='left')

    with open(text_file, 'w') as file:
        file.write(formatted_text)

from tespy.networks import Network

from tespy.components import (
                            CycleCloser, 
                            Turbine,
                            Pump,
                            Valve,
                            Source,
                            Sink,                              
                            Splitter,
                            Merge,
                            SimpleHeatExchanger,
                            HeatExchanger,                              
                            Drum,
                            )

from tespy.connections import Bus

from tespy.tools import ExergyAnalysis

my_plant = Network()

my_plant.set_attr(
                T_unit='C',
                p_unit='bar', 
                h_unit='kJ / kg', 
                m_unit='t / h', 
                s_unit='kJ / kgK', 
                iterinfo=False
                )

powergen = Bus("electrical power output")
my_plant.add_busses(powergen)

pamb = 1.013 # bar(a)
Tamb = 17 # C

cc = CycleCloser('cycle closer HPDRUM to ST')

st_ext = Turbine('extraction st', eta_s=0.9)
st_cond = Turbine('cond st', eta_s=0.9)

att_pump = Pump('att_pump', eta_s=0.7)
cond_pump = Pump('cond_pump', eta_s=0.7)
sg_pump = Pump('steam generator pump', eta_s=0.7)
lp_pump=Pump('low pressure pump', eta_s=0.7)

cond_st_cv = Valve('cond st cv', pr=0.85)

water_inlet_1 = Source('Process condensate return')
water_inlet_2 = Source('Water makeup')

turbine_exhaust = Source('Hot gases source')

wst = Sink('LPDRUM saturated steam waste')
wst_2 = Sink('HPDRUM saturated liquid waste')
process_steam = Sink('process IP steam')
gases_outlet = Sink('hot gases outlet')

sp_1 = Splitter('st inner splitter')
sp_2 = Splitter('condensate header')
sp_3 = Splitter('HPEC1 splitter')
sp_4 = Splitter('HPDRUM outlet')
bd_1 = Splitter('LPDRUM splitter to waste')
bd_2= Splitter('HPDRUM splitter to waste')

me_1 = Merge('Attemper')
me_3 = Merge('Water from reposition & condensate mixture', num_in=3)
me_4 = Merge('merge at the inlet of sweet water condenser in SG')
me_5 = Merge('attemp HPS2')

HE = HeatExchanger('heat exchanger', pr1=0.9, pr2=0.9)

LPEV1 = HeatExchanger('LPEV1', pr2=1)

LPDRUM = Drum('LP Drum')

HPEC1 = HeatExchanger('HPEC1', pr1=1, pr2=1)
HPEC2 = HeatExchanger('HPEC2',pr1=1, pr2=1)
HPEC3 = HeatExchanger('HPEC3',pr1=1, pr2=1)

HPEV1 = HeatExchanger('HPEV1', pr2=1)

HPS1 = HeatExchanger('HPS1', pr1=1, pr2=1)
HPS2 = HeatExchanger('HPS2', pr1=1, pr2=1)

HPDRUM = Drum('HP Drum')

condenser = SimpleHeatExchanger('condenser', pr=1)
HE_cond = HeatExchanger('sweet water condenser', pr1=1, pr2=1)

powergen.add_comps(
                    {"comp": st_ext, "char": 0.97, "base": "component"},
                    {"comp": st_cond, "char": 0.97, "base": "component"},
                    {"comp": att_pump, "char": 0.97, "base": "bus"},
                    {"comp": cond_pump, "char": 0.97, "base": "bus"},
                    {"comp": sg_pump, "char": 0.97, "base": "bus"},
                    )

from tespy.connections import (Connection, Ref)

N = 50
c = [None] * N
names = [None] * N

# caudal_vapor_sobrecalentado = 2*102.3 # t/h 
c[0] = Connection(cc, 'out1', st_ext, 'in1', label='1')
c[0].set_attr(
                #m=caudal_vapor_sobrecalentado, 
                fluid={'water': 1}
              )
names[0] = 'hp steam'

c[1] = Connection(st_ext, 'out1', sp_1, 'in1', label='2')
names[1] = 'extraction st outlet'

caudal_extraccion_turbina = 160 # t/h
c[2] = Connection(sp_1, 'out2', me_1, 'in2', label='3')
c[2].set_attr(m=caudal_extraccion_turbina)
names[2] = 'Steam from TV to attemp'

c[3] = Connection(sp_1, 'out1', cond_st_cv, 'in1', label='4')
names[3] = 'cond st cv inlet'

c[4] = Connection(cond_st_cv, 'out1', st_cond, 'in1', label='5')
names[4] = 'cond st inlet'

c[5] = Connection(st_cond, 'out1', condenser, 'in1', label='6')
names[5] = 'condenser inlet'

c[6] = Connection(condenser, 'out1', sp_2, 'in1', label='7')
c[6].set_attr(x=0, T=Tamb + 18)
names[6] = 'condenser outlet'

c[7] = Connection(sp_2, 'out1', cond_pump, 'in1', label='8')
names[7] = 'cond pump inlet'

c[8] = Connection(sp_2, 'out2', att_pump, 'in1', label='9')
names[8] = 'att pump inlet'

c[9] = Connection(att_pump,'out1', me_1,'in1',label='10')
names[9] = 'att pump outlet'

presion_vapor_proceso = 13 # bar(a)
grado_sobrecalentamiento = 10 # C
c[10] = Connection(me_1, 'out1',process_steam,'in1',label='11')
c[10].set_attr(
                Td_bp=grado_sobrecalentamiento, 
                p=presion_vapor_proceso
                )
names[10] = 'process steam'

c[11] = Connection(cond_pump,'out1', me_3, 'in1', label='12')
c[11].set_attr(p=pamb)
names[11] = 'cond pump outlet'

retorno_condensado = 0.75 # dim
c[12] = Connection(water_inlet_1, 'out1', me_3, 'in2', label='13')
c[12].set_attr( m=Ref(c[10], retorno_condensado, 0), fluid={'water': 1})
names[12] = 'Condensate return from process'

c[13] = Connection(water_inlet_2,'out1',me_3,'in3',label='14')
c[13].set_attr(T=Tamb)
names[13] = 'Water makeup'

c[14] = Connection(me_3,'out1', lp_pump,'in1', label='15')
names[14] = 'Water mixture feed to low pressure pump'

c[15] = Connection(lp_pump,'out1', HE,'in2', label='16')
c[15].set_attr(p=2.3, T=55)
names[15] = 'Water mixture feed to heat exchanger'

c[16] = Connection(HE,'out2', LPDRUM,'in1',label='17')
c[16].set_attr(T=100)
names[16] = 'heated water feed to LPDRUM'

c[17] = Connection(HE,'out1', sg_pump,'in1', label='18')
names[17] = 'Cooled water feed to HP pump'

c[18] = Connection(sg_pump, 'out1', sp_3,'in1', label='19')
c[18].set_attr(p=88.52)
names[18] = 'pressurized water to HPEC1'

c[19] = Connection(sp_3, 'out1', me_4, 'in2', label='20')
c[19].set_attr(m=0) 
names[19] = 'pressurized water to sg condenser'

c[20] = Connection(sp_3, 'out2', HPEC1, 'in1', label='21')
names[20] = 'pressurized water to HPEC1'

c[21] = Connection(HPEC1, 'out1', HPEC2, 'in1', label='22')
c[21].set_attr(T=116.1)
names[21] = 'pressurized water to HPEC2'

c[22] = Connection(HPEC2, 'out1', me_4, 'in1', label='23')
c[22].set_attr(T=230.9)
names[22] = 'outlet of HPEC2 to merge with cold flow'

c[23] = Connection(me_4, 'out1', HE_cond, 'in1', label='24')
names[23] = 'outlet of merge to sweet water condenser'

c[24] = Connection(HE_cond, 'out1', HPEC3, 'in1', label='25')
names[24] = 'outlet of sweet water condenser to HPEC3'

c[25] = Connection(HPEC3, 'out1', HPDRUM, 'in1', label='26')
c[25].set_attr(T=289.9)
names[25] = 'outlet of HPEC3 to HP drum'

c[26] = Connection(HPDRUM, 'out1', bd_2, 'in1', label='27')
names[26] = 'saturated liquid outlet of HPDRUM to Splitter'

c[27] = Connection(bd_2, 'out1', HPEV1, 'in1', label='28')
names[27] = 'saturated liquid outlet of HPDRUM to HPEV1'

c[28] = Connection(bd_2, 'out2', wst_2, 'in1', label='29')
names[28] = 'saturated liquid outlet of HPDRUM to waste'
c[28].set_attr(m=2)

c[29] = Connection(HPEV1, 'out1', HPDRUM, 'in2', label='30')
c[29].set_attr(x=0.05)
names[29] = 'saturated steam outlet of HPEV1 to HPDRUM'

c[30] = Connection(HPDRUM, 'out2', sp_4 , 'in1', label='31')
names[30] = 'saturated steam outlet of HPDRUM' 

c[31] = Connection(sp_4, 'out1', HPS1, 'in1', label='32')
names[31] = 'saturated steam inlet to HPS1' 

c[32] = Connection(HPS1, 'out1', me_5, 'in1', label='33')
c[32].set_attr(T=528.6)
names[32] = 'Steam outlet of HPS1 to attemp' 

c[33] = Connection(sp_4, 'out2', HE_cond, 'in2', label='34')
names[33] = 'Steam derivation of HPDRUM to sweet water condenser'

c[34] = Connection(HE_cond, 'out2', me_5, 'in2', label='35')
c[34].set_attr(x=0)
names[34] = 'Sweet water condenser outlet to attemp'

c[35] = Connection(me_5, 'out1', HPS2, 'in1', label='36')
c[35].set_attr(T=428.8)
names[35] = 'Attemp outlet to HPS2'

c[36] = Connection(HPS2, 'out1', cc, 'in1', label='37')
temperatura_vapor_sobrecalentado = 480 # C
c[36].set_attr(T=temperatura_vapor_sobrecalentado)
names[36] = 'Superheated steam to steam turbine'

c[37] = Connection(LPDRUM,'out1', bd_1,'in1', label='38')
names[37] = 'Saturated liquid outlet of LPDRUM to LPEV1'

c[38] = Connection(bd_1, 'out1', HE, 'in1', label='39')
names[38] = 'LPDRUM saturated liquid outlet to HE'

c[39] = Connection(bd_1, 'out2', LPEV1, 'in1', label='40')
names[39] = 'Saturated liquid inlet to LPEV1'

c[40] = Connection(LPEV1, 'out1', LPDRUM, 'in2', label='41')
c[40].set_attr(x=0.05)
names[40] = 'Saturated steam inlet to LPDRUM'

c[41] = Connection(LPDRUM, 'out2', wst, 'in1', label='42')
names[41] = 'Saturated steam outlet to vent'
c[41].set_attr(m=2*0.05)

c[42] = Connection(turbine_exhaust, 'out1', HPS2, 'in2', label='43')
x_gh_CO2 = 0.061 # dim
x_gh_H2O = 0.07768 # dim
x_gh_N2 = 0.7364 # dim
x_gh_O2 = 0.1126 # dim
x_gh_Ar = 1 - x_gh_CO2 - x_gh_H2O - x_gh_N2 - x_gh_O2
T_gh = 712.9 # C
G_gh = 2*481.98 # t/h
p_gh = pamb # bar(a)
c[42].set_attr(
                m=G_gh,
                T=T_gh,
                p=p_gh, 
                fluid={'O2': x_gh_O2, 'N2': x_gh_N2, 'CO2': x_gh_CO2, 'water': x_gh_H2O, 'Ar': x_gh_Ar}
                )

names[42] = 'Hot gases input to HPS2'

c[43] = Connection(HPS2, 'out2', HPS1, 'in2', label='44') 
names[43] = 'Hot gases input to HPS1'

c[44] = Connection(HPS1, 'out2', HPEV1, 'in2', label='45')
names[44] = 'Hot gases input to HPEV1'

c[45] = Connection(HPEV1, 'out2', HPEC3, 'in2', label='46')
names[45] = 'Hot gases input to HPEC3'

c[46] = Connection(HPEC3, 'out2', HPEC2, 'in2', label='47')
names[46] = 'Hot gases input to HPEC2'

c[47] = Connection(HPEC2, 'out2', LPEV1 , 'in2', label='48')
names[47] = 'Hot gases input to LPEV1'

c[48] = Connection(LPEV1, 'out2', HPEC1 , 'in2', label='49')
names[48] = 'Hot gases input to HPEC1'

c[49] = Connection(HPEC1, 'out2', gases_outlet , 'in1', label='50')
names[49] = 'Hot gases outlet'

for j in range(0,N):
    my_plant.add_conns(c[j])

my_plant.solve(mode='design')
my_plant.print_results()

bus_results = my_plant.results['electrical power output']
df_results_for_conns = my_plant.results['Connection']

df_results_for_conns['denomination'] = names

results = df_results_for_conns[['denomination',
                                'p','p_unit',
                                'T','T_unit',
                                'h','h_unit',
                                's','s_unit',
                                'x',
                                'm','m_unit']]

start_index_for_gases = 42

results_gases = results[start_index_for_gases:]
results_gases = results_gases[['denomination',
                                'p','p_unit',
                                'T','T_unit',
                                'h','h_unit',
                                's','s_unit',
                                'm','m_unit']]

results = results[0:start_index_for_gases]

results = results.drop(results.index[0])

results = results.round(3)
  
export(__file__, results)

Answered by PabloMBarral

Feb 3, 2025

Firstly, there are a lot of guesses in the code. They were read from an Excel file generated with EES, where we had solved the model (with a simple script, we could read the file and generate a .txt with the equations). This was because we originally worked with EES, and we needed to understand which inputs were required. This wasn't simple at all.

As stated, the original idea was to provide all the kA values. Moreover, we intended to provide both the heat exchanger areas (obtained from the manufacturer's data) and some general k values (which were estimated, though I could find the actual values in a past work of mine). Although we still need to compare the results with the manufacturer'…

View full answer

PabloMBarral · 2024-10-16T02:16:57Z

PabloMBarral
Oct 16, 2024
Author

There's some problem with two branches that split and then merge, and the equalization of pressures. One of these branches is the economizer bypass, and the other is the sweet-water condenser (for superheated steam attemperation).

Apart from that, the code assumes that the drum component internally, implicitly equalizes all pressures, as a merge does (or a split). That's why the pr1=1 equation is not indicated in the LPEV1 (or HPEV1).

EDIT: By deleting pr1=1 in the HPEC1 one of these problems should disappear. But when I tried to do so in HE_COND, obviously an equation is missing, and I can't figure which.

Python Code

def export(__file__, results):

    import os

    path = os.path.dirname(os.path.abspath(__file__))

    text_file = os.path.join(path, 'results.txt')

    formatted_text = results.to_string(index=False, justify='left')

    with open(text_file, 'w') as file:
        file.write(formatted_text)

from tespy.networks import Network

from tespy.components import (
                            CycleCloser, 
                            Turbine,
                            Pump,
                            Valve,
                            Source,
                            Sink,                              
                            Splitter,
                            Merge,
                            SimpleHeatExchanger,
                            HeatExchanger,                              
                            Drum,
                            )

from tespy.connections import Bus

from tespy.tools import ExergyAnalysis

my_plant = Network()

my_plant.set_attr(
                T_unit='C',
                p_unit='bar', 
                h_unit='kJ / kg', 
                m_unit='t / h', 
                s_unit='kJ / kgK', 
                iterinfo=False
                )

powergen = Bus("electrical power output")
my_plant.add_busses(powergen)

pamb = 1.013 # bar(a)
Tamb = 17 # C

cc = CycleCloser('cycle closer HPDRUM to ST')

st_ext = Turbine('extraction st', eta_s=0.9)
st_cond = Turbine('cond st', eta_s=0.9)

att_pump = Pump('att_pump', eta_s=0.7)
cond_pump = Pump('cond_pump', eta_s=0.7)
sg_pump = Pump('steam generator pump', eta_s=0.7)
lp_pump=Pump('low pressure pump', eta_s=0.7)

cond_st_cv = Valve('cond st cv', pr=0.85)

water_inlet_1 = Source('Process condensate return')
water_inlet_2 = Source('Water makeup')

turbine_exhaust = Source('Hot gases source')

wst = Sink('LPDRUM saturated steam waste')
wst_2 = Sink('HPDRUM saturated liquid waste')
process_steam = Sink('process IP steam')
gases_outlet = Sink('hot gases outlet')

sp_1 = Splitter('st inner splitter')
sp_2 = Splitter('condensate header')
sp_3 = Splitter('HPEC1 splitter')
sp_4 = Splitter('HPDRUM outlet')
bd_1 = Splitter('LPDRUM splitter to waste')
bd_2= Splitter('HPDRUM splitter to waste')

me_1 = Merge('Attemper')
me_3 = Merge('Water from reposition & condensate mixture', num_in=3)
me_4 = Merge('merge at the inlet of sweet water condenser in SG')
me_5 = Merge('attemp HPS2')

HE = HeatExchanger('heat exchanger', pr1=0.9, pr2=0.9)

LPEV1 = HeatExchanger('LPEV1', pr2=1)

LPDRUM = Drum('LP Drum')

#HPEC1 = HeatExchanger('HPEC1', pr1=1, pr2=1)
HPEC1 = HeatExchanger('HPEC1', pr2=1)
HPEC2 = HeatExchanger('HPEC2',pr1=1, pr2=1)
HPEC3 = HeatExchanger('HPEC3',pr1=1, pr2=1)

HPEV1 = HeatExchanger('HPEV1', pr2=1)

HPS1 = HeatExchanger('HPS1', pr1=1, pr2=1)
HPS2 = HeatExchanger('HPS2', pr1=1, pr2=1)

HPDRUM = Drum('HP Drum')

condenser = SimpleHeatExchanger('condenser', pr=1)

#HE_cond = HeatExchanger('sweet water condenser', pr1=1, pr2=1)
HE_cond = HeatExchanger('sweet water condenser', pr1=1)

powergen.add_comps(
                    {"comp": st_ext, "char": 0.97, "base": "component"},
                    {"comp": st_cond, "char": 0.97, "base": "component"},
                    {"comp": att_pump, "char": 0.97, "base": "bus"},
                    {"comp": cond_pump, "char": 0.97, "base": "bus"},
                    {"comp": sg_pump, "char": 0.97, "base": "bus"},
                    )

from tespy.connections import (Connection, Ref)

N = 50
c = [None] * N
names = [None] * N

# caudal_vapor_sobrecalentado = 2*102.3 # t/h 
c[0] = Connection(cc, 'out1', st_ext, 'in1', label='1')
c[0].set_attr(
                #m=caudal_vapor_sobrecalentado, 
                fluid={'water': 1}
              )
names[0] = 'hp steam'

c[1] = Connection(st_ext, 'out1', sp_1, 'in1', label='2')
names[1] = 'extraction st outlet'

caudal_extraccion_turbina = 160 # t/h
c[2] = Connection(sp_1, 'out2', me_1, 'in2', label='3')
c[2].set_attr(m=caudal_extraccion_turbina)
names[2] = 'Steam from TV to attemp'

c[3] = Connection(sp_1, 'out1', cond_st_cv, 'in1', label='4')
names[3] = 'cond st cv inlet'

c[4] = Connection(cond_st_cv, 'out1', st_cond, 'in1', label='5')
names[4] = 'cond st inlet'

c[5] = Connection(st_cond, 'out1', condenser, 'in1', label='6')
names[5] = 'condenser inlet'

c[6] = Connection(condenser, 'out1', sp_2, 'in1', label='7')
c[6].set_attr(x=0, T=Tamb + 18)
names[6] = 'condenser outlet'

c[7] = Connection(sp_2, 'out1', cond_pump, 'in1', label='8')
names[7] = 'cond pump inlet'

c[8] = Connection(sp_2, 'out2', att_pump, 'in1', label='9')
names[8] = 'att pump inlet'

c[9] = Connection(att_pump,'out1', me_1,'in1',label='10')
names[9] = 'att pump outlet'

presion_vapor_proceso = 13 # bar(a)
grado_sobrecalentamiento = 10 # C
c[10] = Connection(me_1, 'out1',process_steam,'in1',label='11')
c[10].set_attr(
                Td_bp=grado_sobrecalentamiento, 
                p=presion_vapor_proceso
                )
names[10] = 'process steam'

c[11] = Connection(cond_pump,'out1', me_3, 'in1', label='12')
c[11].set_attr(p=pamb)
names[11] = 'cond pump outlet'

retorno_condensado = 0.75 # dim
c[12] = Connection(water_inlet_1, 'out1', me_3, 'in2', label='13')
c[12].set_attr( m=Ref(c[10], retorno_condensado, 0), fluid={'water': 1})
names[12] = 'Condensate return from process'

c[13] = Connection(water_inlet_2,'out1',me_3,'in3',label='14')
c[13].set_attr(T=Tamb)
names[13] = 'Water makeup'

c[14] = Connection(me_3,'out1', lp_pump,'in1', label='15')
names[14] = 'Water mixture feed to low pressure pump'

c[15] = Connection(lp_pump,'out1', HE,'in2', label='16')
c[15].set_attr(p=2.3, T=55)
names[15] = 'Water mixture feed to heat exchanger'

c[16] = Connection(HE,'out2', LPDRUM,'in1',label='17')
c[16].set_attr(T=100)
names[16] = 'heated water feed to LPDRUM'

c[17] = Connection(HE,'out1', sg_pump,'in1', label='18')
names[17] = 'Cooled water feed to HP pump'

c[18] = Connection(sg_pump, 'out1', sp_3,'in1', label='19')
c[18].set_attr(p=88.52)
names[18] = 'pressurized water to HPEC1'

c[19] = Connection(sp_3, 'out1', me_4, 'in2', label='20')
c[19].set_attr(m=0) 
names[19] = 'pressurized water to sg condenser'

c[20] = Connection(sp_3, 'out2', HPEC1, 'in1', label='21')
names[20] = 'pressurized water to HPEC1'

c[21] = Connection(HPEC1, 'out1', HPEC2, 'in1', label='22')
c[21].set_attr(T=116.1)
names[21] = 'pressurized water to HPEC2'

c[22] = Connection(HPEC2, 'out1', me_4, 'in1', label='23')
c[22].set_attr(T=230.9)
names[22] = 'outlet of HPEC2 to merge with cold flow'

c[23] = Connection(me_4, 'out1', HE_cond, 'in1', label='24')
c[23].set_attr(p=88.52)
names[23] = 'outlet of merge to sweet water condenser'

c[24] = Connection(HE_cond, 'out1', HPEC3, 'in1', label='25')
names[24] = 'outlet of sweet water condenser to HPEC3'

c[25] = Connection(HPEC3, 'out1', HPDRUM, 'in1', label='26')
c[25].set_attr(T=289.9)
names[25] = 'outlet of HPEC3 to HP drum'

c[26] = Connection(HPDRUM, 'out1', bd_2, 'in1', label='27')
names[26] = 'saturated liquid outlet of HPDRUM to Splitter'

c[27] = Connection(bd_2, 'out1', HPEV1, 'in1', label='28')
names[27] = 'saturated liquid outlet of HPDRUM to HPEV1'

c[28] = Connection(bd_2, 'out2', wst_2, 'in1', label='29')
names[28] = 'saturated liquid outlet of HPDRUM to waste'
c[28].set_attr(m=2)

c[29] = Connection(HPEV1, 'out1', HPDRUM, 'in2', label='30')
c[29].set_attr(x=0.05)
names[29] = 'saturated steam outlet of HPEV1 to HPDRUM'

c[30] = Connection(HPDRUM, 'out2', sp_4 , 'in1', label='31')
names[30] = 'saturated steam outlet of HPDRUM' 

c[31] = Connection(sp_4, 'out1', HPS1, 'in1', label='32')
names[31] = 'saturated steam inlet to HPS1' 

c[32] = Connection(HPS1, 'out1', me_5, 'in1', label='33')
c[32].set_attr(T=528.6)
names[32] = 'Steam outlet of HPS1 to attemp' 

c[33] = Connection(sp_4, 'out2', HE_cond, 'in2', label='34')
names[33] = 'Steam derivation of HPDRUM to sweet water condenser'

c[34] = Connection(HE_cond, 'out2', me_5, 'in2', label='35')
c[34].set_attr(x=0)
names[34] = 'Sweet water condenser outlet to attemp'

c[35] = Connection(me_5, 'out1', HPS2, 'in1', label='36')
c[35].set_attr(T=428.8)
names[35] = 'Attemp outlet to HPS2'

c[36] = Connection(HPS2, 'out1', cc, 'in1', label='37')
temperatura_vapor_sobrecalentado = 480 # C
c[36].set_attr(T=temperatura_vapor_sobrecalentado)
names[36] = 'Superheated steam to steam turbine'

c[37] = Connection(LPDRUM,'out1', bd_1,'in1', label='38')
names[37] = 'Saturated liquid outlet of LPDRUM to LPEV1'

c[38] = Connection(bd_1, 'out1', HE, 'in1', label='39')
names[38] = 'LPDRUM saturated liquid outlet to HE'

c[39] = Connection(bd_1, 'out2', LPEV1, 'in1', label='40')
names[39] = 'Saturated liquid inlet to LPEV1'

c[40] = Connection(LPEV1, 'out1', LPDRUM, 'in2', label='41')
c[40].set_attr(x=0.05)
names[40] = 'Saturated steam inlet to LPDRUM'

c[41] = Connection(LPDRUM, 'out2', wst, 'in1', label='42')
names[41] = 'Saturated steam outlet to vent'
c[41].set_attr(m=2*0.05)

c[42] = Connection(turbine_exhaust, 'out1', HPS2, 'in2', label='43')
x_gh_CO2 = 0.061 # dim
x_gh_H2O = 0.07768 # dim
x_gh_N2 = 0.7364 # dim
x_gh_O2 = 0.1126 # dim
x_gh_Ar = 1 - x_gh_CO2 - x_gh_H2O - x_gh_N2 - x_gh_O2
T_gh = 712.9 # C
G_gh = 2*481.98 # t/h
p_gh = pamb # bar(a)
c[42].set_attr(
                m=G_gh,
                T=T_gh,
                p=p_gh, 
                fluid={'O2': x_gh_O2, 'N2': x_gh_N2, 'CO2': x_gh_CO2, 'water': x_gh_H2O, 'Ar': x_gh_Ar}
                )

names[42] = 'Hot gases input to HPS2'

c[43] = Connection(HPS2, 'out2', HPS1, 'in2', label='44') 
names[43] = 'Hot gases input to HPS1'

c[44] = Connection(HPS1, 'out2', HPEV1, 'in2', label='45')
names[44] = 'Hot gases input to HPEV1'

c[45] = Connection(HPEV1, 'out2', HPEC3, 'in2', label='46')
names[45] = 'Hot gases input to HPEC3'

c[46] = Connection(HPEC3, 'out2', HPEC2, 'in2', label='47')
names[46] = 'Hot gases input to HPEC2'

c[47] = Connection(HPEC2, 'out2', LPEV1 , 'in2', label='48')
names[47] = 'Hot gases input to LPEV1'

c[48] = Connection(LPEV1, 'out2', HPEC1 , 'in2', label='49')
names[48] = 'Hot gases input to HPEC1'

c[49] = Connection(HPEC1, 'out2', gases_outlet , 'in1', label='50')
names[49] = 'Hot gases outlet'

for j in range(0,N):
    my_plant.add_conns(c[j])

my_plant.solve(mode='design')
my_plant.print_results()

bus_results = my_plant.results['electrical power output']
df_results_for_conns = my_plant.results['Connection']

df_results_for_conns['denomination'] = names

results = df_results_for_conns[['denomination',
                                'p','p_unit',
                                'T','T_unit',
                                'h','h_unit',
                                's','s_unit',
                                'x',
                                'm','m_unit']]

start_index_for_gases = 42

results_gases = results[start_index_for_gases:]
results_gases = results_gases[['denomination',
                                'p','p_unit',
                                'T','T_unit',
                                'h','h_unit',
                                's','s_unit',
                                'm','m_unit']]

results = results[0:start_index_for_gases]

results = results.drop(results.index[0])

results = results.round(3)
  
export(__file__, results)

9 replies

fwitte Oct 20, 2024
Maintainer

It was really odd that we had to define the mass flow for the steam extraction instead of the process steam. I’ll double-check this with the latest version if the model still behaves in that way.

This again seems to be an issue with starting values. With the converged solution of step 1 you can fix the mass flow 11 instead of mass flow 3. Btw.: Note, that I changed the numbering on the connections in the pull request.

As complete beginners, it wasn’t entirely clear which equations are implicitly defined in the components. However, we can’t complain—the forum is extremely active, and we may not be the primary target audience for this library. Compared to EES (I'm proficient in that tool), we noticed that while EES offers more control, it also requires more time for coding. I believe that with tespy more complex models can be developed in less time.

Maybe this is not clear enough from the documentation and from the examples then? Are there particular components you are referring to?

Besides, it tasted unrealistic to me that the condensate pump, makeup pump and process condensate pump all had the same discharge pressure (caused by the merge component). I know that this is a mixing chamber, as we find in thermodynamic problems, but it might be a good idea a component that does energy balance but with no requirement for pressure. But some bad choices could lead to unreal solutions and entropy destruction (with small inlet pressure and high outlet pressure).

This would be a MergeWithPressureloss?

From a UX, it might be a good idea to mimic the merge component with a new component named tank (silly comment, not that important, is just if you need to explain someone else the code). The same happens with a steam header and a splitter. Just pure UX.

You mean a new class Tank which integrates the capabilities of a merge connected to a splitter?

HRSGs transfer heat to the ambient due to the casing. This wasn't modelled, the heat exchanger component wasn't prepared for this. Obviously, there's a way: simple heat exchangers between the tube bundles modelling this effect.

We could introduce a new component: DiabaticHeatExchanger. This component could be modeled using something like a kA factor describing the heat transfer coefficient to the ambient while using the mean temperature of the shell side fluid and the ambient temperature or a heat loss directly proportional to the total amount of heat transferred.

Perhaps, with some skill, optimization of pinch and approach could be developed.

I think that would not be too hard, the API to connect tespy with pygmo is available. Once you have a stable model, optimization should be quite straight-forward.

Data was set with a modeller mind. A future iteration should include stating kA data, for example.

Those could be calculated based on a design case. I guess those information are nowhere specified, but deriving them with the help of the model is fine in my opinion.

Stating x=0.05 of steam leaving evaporators might be realistic, but this data was completely made up. From the BOP engineer is hard to predict the value, and it's really not needed at all. Again, a UX comment.

You could also fix a certain mass flow here, e.g. in relation to the primary mass flow.

LP drum isn't really a drum. Hopefully, we had a small vent which is used to remove O2 and CO2. The net steam production is zero. All produced steam is used to heat the liquid to deaerate.

Then it would just be naming the component in a different way? The fact that we have two-phase fluid (just very near to liquid) is still correct, or?

PabloMBarral Oct 22, 2024
Author

Hi,
I've tested the solution, and unfortunately, the results are not realistic.

First, I believe it would be better to add a (control) valve in the branch that goes from HP EC1 to the merge after HP EC2. The pressure ratio (pr) for that valve would be a calculated parameter. This way, the model has the flexibility to select a different pressure ratio for the economizer stages. Without this valve, the only valid value for the pressure ratio would be pr1 = 1, which limits the model's functionality. The idea is to be able to model the boiler capacity to underperform by bypassing the economizer last stages.

A similar issue occurs with the sweetwater condenser from HP COND to the merge after HP SH1. Otherwise, the head loss in HPSH1 must be set to one, which is highly unrealistic.

I acknowledge that these are flaws in the original model I provided.

Results:
| | 3.612e+02 | 8.852e+01 | 3.338e+03 | 4.800e+02 |
361.2 t/h; 88.52 bar(a); 3338 kJ/kg; 480°C

This is with G_gh = 2 × 481.98 t/h (which corresponds to c[42]). However, the main steam production of 361.2 t/h remains unchanged despite variations in the flue gas flow.

This behavior is incorrect. It gets worse: when G_gh = 481.98 t/h, the model returns NaN values for the flue gas connections.

The expected result is around 75 t/h when G_gh = 482 t/h and T_gh = 560°C. The HRSG should produce up to 110 t/h when T_gh is approximately 750°C (I am recalling this from memory and should double-check).

In all cases, the flue gas outlet (i.e., the stack) should have a temperature between 95°C and 115-120°C. However, the model shows a stack temperature of 225°C, which is incorrect.

Regarding parameter specification, I believe there’s room for a cleaner setup than what I initially provided. I'll write more about this later, along with other pending topics.

Finally, feel free to contact me at pbarral@fi.uba.ar to arrange a virtual meeting.

fwitte Nov 9, 2024
Maintainer

Finally, feel free to contact me at pbarral@fi.uba.ar to arrange a virtual meeting.

I will do so in about a week or two :). Thank you

ibuzzo Jan 4, 2025

Hello Francesco. I am Ignacio, currently working with Pablo in this project in order to get my degree in mechanical engineering. As Pablo explained in the conversation, it seems to be an issue when calculating the gases temperatures through the heat exchangers. The problem seems to begin after HPEV1, which corresponds to connection 45.

The error registered:

Logically, the temperature of the gases upstream this evaporator is also undetermined.

However, the program is able to calculate the gases enthalpy in each point of de gases side, which is expectable as the heat exchanged is already determined in the steam side. Furthermore, the error recorded refers to an "invalid value encoutered in scalar divide". The equation from which Tespy calculates temperatures and KA factors for heat exchangers is the following one:

Taking into consideration:

In our model, we used "in1" and "out1" for de gases flow and "in2" "out2" for de steam flow. ¿ Do you think it is possible that there is a problem with the seed values that the program uses internally to determine the gas side temperatures?

Feel free to contact mi via email (ibuzzo@fi.uba.ar) so that i can send you the last version of the program. If there is there is any possibility of scheduling a virtual meeting, please let us know.

Regards, and happy new year!

fwitte Jan 5, 2025
Maintainer

Hi @ibuzzo, happy new year and thank you for updating.

The issue comes from this specification:

tespy/tutorial/advanced/hrsg.py

Line 144 in 26ed7c5

c16.set_attr(p=2.3, T=55)

It forces a certain steam mass flow in the Rankine cycle, which due to the fixed live steam and condensate return conditions leads to a mass flow, which is much higher than possible, i.e. the flue gas would need to be cooled down much more than physically possible. Remove that specification and fix the live steam mass flow (e.g. to 200 t/h), then the issue is resolved. Nevertheless, it would be nice if you can post your solution here, so we can discuss it further.

Thank you!

Best

Francesco

ibuzzo · 2025-02-01T19:43:50Z

ibuzzo
Feb 1, 2025

Hi Francesco, hope you are doing well.

We resolved the model in EES. We obtained razonable results and we were also able to plot the HRSG T-Q diagram. However, when tryng to resolve the model in Tespy using the same input values used in EES, we are getting Nan results both for steam and gases flow. I tryed defining some initial seed values for temperature and pressure both in steam and gases side (using as reference the results obtained in EES) but it seems like the programm is strugling to converge.

I attach the PDF with the results obtenied in EES. Highlated values are inputs.
Results EES model.pdf

These inputs are:

kA and pr for HPEC1, HPEC2, HPEC3, LPEV1, HPEV1, HPS1, HPS2
Temperature, pressure and mass flow of HP steam at [1]
Temperature and steam title at condeser outlet [7]
Temperature, pressure and mass flow of process steam at [11]
Cond. pump outlet pressure [12]
Condensate return from process Temperature and mass flow [13]
By pass mass flow [20]
Steam tempeature at HP drum inlet (aproach point) [26]
Waste mass flow of HP drum [29]
Steam title at HPEV1 outlet [30]
Steam title at sweet water condenser [35]
Steam title at LPEV1 outlet [40]
Saturated steam to vent [41]
Temperature, pressure and mass flow of gas turbine exahust [42]

Also you will find attached the PFD of the instalation we are modeling.
TPP - PFD.pdf

Finally, the tespy code:

def export(file, results):
import os
path = os.path.dirname(os.path.abspath(file))
text_file = os.path.join(path, 'results.txt')
formatted_text = results.to_string(index=False, justify='left')
with open(text_file, 'w') as file:
file.write(formatted_text)

from tespy.networks import Network
from tespy.components import ( CycleCloser, Turbine,Pump, Valve,Source, Sink, Splitter,Merge, SimpleHeatExchanger, HeatExchanger, Drum, )

from tespy.connections import Bus
my_plant = Network()
my_plant.set_attr(
T_unit='C',
p_unit='bar',
h_unit='kJ / kg',
m_unit='t / h',
s_unit='kJ / kgK',
iterinfo=False
)

powergen = Bus("electrical power output")
my_plant.add_busses(powergen)

pamb = 1.013 # bar(a)
Tamb = 17 # C

cc = CycleCloser('cycle closer HPDRUM to ST')
st_ext = Turbine('extraction st', eta_s=0.9)
st_cond = Turbine('cond st', eta_s=0.9)

att_pump = Pump('att_pump', eta_s=0.7)
cond_pump = Pump('cond_pump', eta_s=0.7)
sg_pump = Pump('steam generator pump', eta_s=0.7)
lp_pump=Pump('low pressure pump', eta_s=0.7)

cond_st_cv = Valve('cond st cv', pr=0.85)
econ_bypass_cv= Valve('econ_bypass_valve', pr=0.85)
hp_attemp_cv = Valve('hp_attemp_valve', pr=0.85)

water_inlet_1 = Source('Process condensate return')
water_inlet_2 = Source('Water makeup')
#water_inlet_3 = Source('Water from boiler to HE')
turbine_exhaust = Source('Hot gases source')

wst = Sink('LPDRUM saturated steam waste')
wst_2 = Sink('HPDRUM saturated liquid waste')
process_steam = Sink('process IP steam')
gases_outlet = Sink('hot gases outlet')

sp_1 = Splitter('st inner splitter')
sp_2 = Splitter('condensate header')
sp_3 = Splitter('HPEC1 splitter')
sp_4 = Splitter('HPDRUM outlet')
bd_1 = Splitter('LPDRUM splitter to waste')
bd_2= Splitter('HPDRUM splitter to waste')

me_1 = Merge('Attemper')
me_2 = Merge('St condensate & process condensate return')
me_3 = Merge('Water from reposition & condensate mixture', num_in=3)
me_4 = Merge('merge at the inlet of sweet water condenser in SG')
me_5 = Merge('attemp HPS2')

A_HE=5000 #m2
HE = HeatExchanger('heat exchanger', pr1=1, pr2=1)

A_LPEV1=5000 #m2
K_LPEV1=35 #[W/m^2-C]
LPEV1 = HeatExchanger('LPEV1', pr1=1, kA=K_LPEV1*A_LPEV1)

LPDRUM = Drum('LP Drum')

A_HPEC1=4700 #[m^2]
K_HPEC1=30 #[W/m^2-C]
HPEC1 = HeatExchanger('HPEC1', pr1=1, kA=K_HPEC1*A_HPEC1)

A_HPEC2=4700 #[m^2]
K_HPEC2= 40 #[W/m^2-C]
HPEC2 = HeatExchanger('HPEC2',pr1=1,pr2=1, kA=K_HPEC2*A_HPEC2)

A_HPEC3=9500 #[m^2]
K_HPEC3=45 #[W/m^2-C]
HPEC3 = HeatExchanger('HPEC3',pr1=1, pr2=1, kA=K_HPEC3*A_HPEC3)

A_HPEV1=12300 #[m^2]
K_HPEV1=85 #[W/m^2-C]
HPEV1 = HeatExchanger('HPEV1', pr1=1,kA=K_HPEV1*A_HPEV1)

A_HPS1=2500 #[m^2]
K_HPS1=110 #[W/m^2-C]
HPS1 = HeatExchanger('HPS1',pr1=1,kA=K_HPS1*A_HPS1)

A_HPS2=175 #[m^2]
K_HPS2=200 #[W/m^2-C]
HPS2 = HeatExchanger('HPS2', pr1=1, pr2=1,kA=K_HPS2*A_HPS2)

HPDRUM = Drum('HP Drum')

condenser = SimpleHeatExchanger('condenser', pr=1)
HE_cond = HeatExchanger('sweet water condenser', pr1=1, pr2=1)

powergen.add_comps(
{"comp": st_ext, "char": 0.97, "base": "component"},
{"comp": st_cond, "char": 0.97, "base": "component"},
{"comp": att_pump, "char": 0.97, "base": "bus"},
{"comp": cond_pump, "char": 0.97, "base": "bus"},
{"comp": sg_pump, "char": 0.97, "base": "bus"},
)

from tespy.connections import (Connection, Ref)

N = 49
c = [None] * N
names = [None] * N

caudal_vapor_sobrecalentado = 2*100 # t/h
c[0] = Connection(HPS2, 'out2', st_ext, 'in1', label='1')
c[0].set_attr(m=caudal_vapor_sobrecalentado, fluid={'water': 1},T=485, p0=91.01)
names[0] = 'hp steam'

c[1] = Connection(st_ext, 'out1', sp_1, 'in1', label='2')
names[1] = 'extraction st outlet'

c[2] = Connection(sp_1, 'out2', me_1, 'in2', label='3')
c[2].set_attr()
names[2] = 'Steam from TV to attemp'

c[3] = Connection(sp_1, 'out1', cond_st_cv, 'in1', label='4')
names[3] = 'cond st cv inlet'

c[4] = Connection(cond_st_cv, 'out1', st_cond, 'in1', label='5')
names[4] = 'cond st inlet'

c[5] = Connection(st_cond, 'out1', condenser, 'in1', label='6')
names[5] = 'condenser inlet'

c[6] = Connection(condenser, 'out1', sp_2, 'in1', label='7')
c[6].set_attr(x=0, T=Tamb + 18)
names[6] = 'condenser outlet'

c[7] = Connection(sp_2, 'out1', cond_pump, 'in1', label='8')
names[7] = 'cond pump inlet'

c[8] = Connection(sp_2, 'out2', att_pump, 'in1', label='9')
names[8] = 'att pump inlet'

c[9] = Connection(att_pump,'out1', me_1,'in1',label='10')
names[9] = 'att pump outlet'

presion_vapor_proceso = 13 # bar(a)
caudal_vapor_proceso = 100 # t/h
grado_sobrecalentamiento = 10 # C
c[10] = Connection(me_1, 'out1',process_steam,'in1',label='11')
c[10].set_attr(Td_bp=grado_sobrecalentamiento, p=presion_vapor_proceso, m=caudal_vapor_proceso )
names[10] = 'process steam'

c[11] = Connection(cond_pump,'out1', me_3, 'in1', label='12')
c[11].set_attr(p=pamb)
names[11] = 'cond pump outlet'

retorno_condensado = 0.5
c[12] = Connection(water_inlet_1, 'out1', me_3, 'in2', label='13')
c[12].set_attr( m=Ref(c[10], retorno_condensado, 0), fluid={'water': 1}, T=70)
names[12] = 'Condensate return from process'

c[13] = Connection(water_inlet_2,'out1',me_3,'in3',label='14')
c[13].set_attr(T=Tamb, fluid={"water": 1})
names[13] = 'Water makeup'

c[14] = Connection(me_3,'out1', lp_pump,'in1', label='15')
names[14] = 'Water mixture feed to low pressure pump'

c[15] = Connection(lp_pump,'out1', HE,'in2', label='16')
c[15].set_attr()
names[15] = 'Water mixture feed to heat exchanger'

c[16] = Connection(HE,'out2', LPDRUM,'in1',label='17')
c[16].set_attr( p0=1.634)
names[16] = 'heated water feed to LPDRUM'

c[17] = Connection(HE,'out1', sg_pump,'in1', label='18')
c[17].set_attr( T0=103.1)
names[17] = 'Cooled water feed to HP pump'

c[18] = Connection(sg_pump, 'out1', sp_3,'in1', label='19')
c[18].set_attr(p0=91.01)
names[18] = 'pressurized water to HPEC1'

c[19] = Connection(sp_3, 'out1', me_4, 'in2', label='20')
c[19].set_attr(m=0)
names[19] = 'pressurized water to sg condenser'

c[20] = Connection(sp_3, 'out2', HPEC1, 'in2', label='21') # in2
c[20].set_attr(T0=104.7)
names[20] = 'pressurized water to HPEC1'

c[21] = Connection(HPEC1, 'out2', HPEC2, 'in2', label='22') # in2
c[21].set_attr( p0=91.01, T0=132.8)
names[21] = 'pressurized water to HPEC2'

c[22] = Connection(HPEC2, 'out2', me_4, 'in1', label='23')
c[22].set_attr( p0=91.01,T0=201.7)
names[22] = 'outlet of HPEC2 to merge with cold flow'

c[23] = Connection(me_4, 'out1', HE_cond, 'in2', label='24')
names[23] = 'outlet of merge to sweet water condenser'

c[24] = Connection(HE_cond, 'out2', HPEC3, 'in2', label='25')
c[24].set_attr(T0=263.9)
names[24] = 'outlet of sweet water condenser to HPEC3'

c[25] = Connection(HPEC3, 'out2', HPDRUM, 'in1', label='26')
c[25].set_attr(Td_bp=-5, p0=91.01)
names[25] = 'outlet of HPEC3 to HP drum'

c[26] = Connection(HPDRUM, 'out1', bd_2, 'in1', label='27')
names[26] = 'saturated liquid outlet of HPDRUM to Splitter'

c[27] = Connection(bd_2, 'out1', HPEV1, 'in2', label='28')
names[27] = 'saturated liquid outlet of HPDRUM to HPEV1'

c[28] = Connection(bd_2, 'out2', wst_2, 'in1', label='29')
names[28] = 'saturated liquid outlet of HPDRUM to waste'
c[28].set_attr(m=2)

c[29] = Connection(HPEV1, 'out2', HPDRUM, 'in2', label='30')
c[29].set_attr(x=0.98)
names[29] = 'saturated steam outlet of HPEV1 to HPDRUM'

c[30] = Connection(HPDRUM, 'out2', sp_4 , 'in1', label='31')
names[30] = 'saturated steam outlet of HPDRUM'

c[31] = Connection(sp_4, 'out1', HPS1, 'in2', label='32') # in2
c[31].set_attr( T0=304.1)
names[31] = 'saturated steam inlet to HPS1'

c[32] = Connection(HPS1, 'out2', me_5, 'in1', label='33')
c[32].set_attr( T0=620.7)
names[32] = 'Steam outlet of HPS1 to attemp'

c[33] = Connection(sp_4, 'out2', HE_cond, 'in1', label='34')
names[33] = 'Steam derivation of HPDRUM to sweet water condenser'

c[34] = Connection(HE_cond, 'out1', me_5, 'in2', label='35')
c[34].set_attr(x=0)
names[34] = 'Sweet water condenser outlet to attemp'

c[35] = Connection(me_5, 'out1', HPS2, 'in2', label='36') # in 2!
c[35].set_attr(T0=304.1)
names[35] = 'Attemp outlet to HPS2'

c[36] = Connection(LPDRUM,'out1', bd_1,'in1', label='37')
names[36] = 'Saturated liquid outlet of LPDRUM to LPEV1'

c[37] = Connection(bd_1, 'out1', HE, 'in1', label='38')
names[37] = 'LPDRUM saturated liquid outlet to HE'

c[38] = Connection(bd_1, 'out2', LPEV1, 'in2', label='39')
names[38] = 'Saturated liquid inlet to LPEV1'

c[39] = Connection(LPEV1, 'out2', LPDRUM, 'in2', label='40')
c[39].set_attr(x=0.95)
names[39] = 'Saturated steam inlet to LPDRUM'

c[40] = Connection(LPDRUM, 'out2', wst, 'in1', label='41')
names[40] = 'Saturated steam outlet to vent'
c[40].set_attr(m=2*0.05)

c[41] = Connection(turbine_exhaust, 'out1', HPS2, 'in1', label='42')
x_gh_CO2 = 0.061 # dim
x_gh_H2O = 0.07768 # dim
x_gh_N2 = 0.7364 # dim
x_gh_O2 = 0.1126 # dim
x_gh_Ar = 1 - x_gh_CO2 - x_gh_H2O - x_gh_N2 - x_gh_O2
T_gh = 712.9 # C
G_gh = 2*481.98 # t/h
p_gh = pamb # bar(a)
c[41].set_attr(
m=G_gh,
T=T_gh,
p=p_gh,
fluid={'O2': x_gh_O2, 'N2': x_gh_N2, 'CO2': x_gh_CO2, 'water': x_gh_H2O, 'Ar': x_gh_Ar}
)
names[41] = 'Hot gases input to HPS2'

c[42] = Connection(HPS2, 'out1', HPS1, 'in1', label='43')
c[42].set_attr(T0=694.9)
names[42] = 'Hot gases input to HPS1'

c[43] = Connection(HPS1, 'out1', HPEV1, 'in1', label='44')
c[43].set_attr(T0=568.5)
names[43] = 'Hot gases input to HPEV1'

c[44] = Connection(HPEV1, 'out1', HPEC3, 'in1', label='45')
names[44] = 'Hot gases input to HPEC3'
c[44].set_attr(T0=313.4)

c[45] = Connection(HPEC3, 'out1', HPEC2, 'in1', label='46')
c[45].set_attr(T0=284.7)
names[45] = 'Hot gases input to HPEC2'

c[46] = Connection(HPEC2, 'out1', LPEV1 , 'in1', label='47')
c[46].set_attr(T0=228.6)
names[46] = 'Hot gases input to LPEV1'

c[47] = Connection(LPEV1, 'out1', HPEC1 , 'in1', label='48')
c[47].set_attr(T0=177.4)
names[47] = 'Hot gases input to HPEC1'

c[48] = Connection(HPEC1, 'out1', gases_outlet , 'in1', label='49')
c[48].set_attr(T0=154.6)
names[48] = 'Hot gases outlet'

for j in range(0,N):
my_plant.add_conns(c[j])
my_plant.solve(mode='design')
my_plant.print_results()

bus_results = my_plant.results['electrical power output']
df_results_for_conns = my_plant.results['Connection']

df_results_for_conns['denomination'] = names

results = df_results_for_conns[['denomination',
'p','p_unit',
'T','T_unit',
'h','h_unit',
's','s_unit',
'x',
'm','m_unit']]

start_index_for_gases = 41

results_gases = results[start_index_for_gases:]
results_gases = results_gases[['denomination',
'p','p_unit',
'T','T_unit',
'h','h_unit',
's','s_unit',
'm','m_unit']]

results = results[0:start_index_for_gases]

results = results.round(3)

export(file, results)

0 replies

PabloMBarral · 2025-02-02T23:43:24Z

PabloMBarral
Feb 2, 2025
Author

Hi, everybody. Finally, we got a working code.

I'll comment about the details in the next post.

    ### GENERAL INFO ###
    
    # ibuzzo@fi.uba.ar
    # pbarral@fi.uba.ar
    # 2025-02-02
    # tespy v0.78.post2

    ### NETWORK ###

from tespy.networks import Network

my_plant = Network()

my_plant.set_attr(
                T_unit = 'C',
                p_unit = 'bar', 
                h_unit = 'kJ / kg', 
                m_unit = 't / h', 
                s_unit = 'kJ / kgK', 
                iterinfo = False
                )

    ### COMPONENTS ###

        ### DEFINITIONS ###

from tespy.components import (
    Turbine, Valve, SimpleHeatExchanger, Pump, Drum, HeatExchanger, Splitter, Merge, Sink, Source
                            )

st_ext = Turbine('extraction st', eta_s = 0.9)
st_cond = Turbine('cond st', eta_s = 0.9)

att_pump = Pump('att_pump', eta_s = 0.7)
cond_pump = Pump('cond_pump', eta_s = 0.7)
sg_pump = Pump('steam generator pump', eta_s = 0.7)
lp_pump = Pump('low pressure pump', eta_s = 0.7)

cond_st_cv = Valve('cond st cv', pr = 0.85)

water_inlet_1 = Source('Process condensate return')
water_inlet_2 = Source('Water makeup')
turbine_exhaust = Source('Hot gases source')

wst = Sink('LPDRUM saturated steam waste')
wst_2 = Sink('HPDRUM saturated liquid waste')
process_steam = Sink('process IP steam')
gases_outlet = Sink('hot gases outlet')

sp_1 = Splitter('st inner splitter')
sp_2 = Splitter('condensate header')
sp_3 = Splitter('HPEC1 splitter')
sp_4 = Splitter('HPDRUM outlet')
bd_1 = Splitter('LPDRUM splitter to waste')
bd_2 = Splitter('HPDRUM splitter to waste')

me_1 = Merge('Attemper')
me_2 = Merge('St condensate & process condensate return')
me_3 = Merge('Water from reposition & condensate mixture', num_in = 3)
me_4 = Merge('merge at the inlet of sweet water condenser in SG')
me_5 = Merge('attemp HPS2')

A_HE = 5000 #[m^2]
HE = HeatExchanger('heat exchanger', pr1 = 1, pr2 = 1)

A_LPEV1 = 5000 #[m^2]
K_LPEV1 = 35 #[W/m^2-C]
#LPEV1 = HeatExchanger('LPEV1', pr1 = 1, kA = K_LPEV1 * A_LPEV1)
LPEV1 = HeatExchanger('LPEV1', pr1 = 1)

LPDRUM = Drum('LP Drum')

A_HPEC1 = 4700 #[m^2]
K_HPEC1 = 30 #[W/m^2-C]
#HPEC1 = HeatExchanger('HPEC1', pr1 = 1, kA = K_HPEC1 * A_HPEC1)
HPEC1 = HeatExchanger('HPEC1', pr1 = 1)

A_HPEC2 = 4700 #[m^2]
K_HPEC2 = 40 #[W/m^2-C]
#HPEC2 = HeatExchanger('HPEC2', pr1 = 1, pr2 = 1, kA = K_HPEC2 * A_HPEC2)
HPEC2 = HeatExchanger('HPEC2', pr1 = 1, pr2 = 1)

A_HPEC3 = 9500 #[m^2]
K_HPEC3 = 45 #[W/m^2-C]
#HPEC3 = HeatExchanger('HPEC3', pr1 = 1, pr2 = 1, kA = K_HPEC3 * A_HPEC3)
HPEC3 = HeatExchanger('HPEC3', pr1 = 1, pr2 = 1)

A_HPEV1 = 12300 #[m^2]
K_HPEV1 = 85 #[W/m^2-C]
#HPEV1 = HeatExchanger('HPEV1', pr1 = 1, kA = K_HPEV1 * A_HPEV1)
HPEV1 = HeatExchanger('HPEV1', pr1 = 1)

A_HPS1 = 2500 #[m^2]
K_HPS1 = 110 #[W/m^2-C]
#HPS1 = HeatExchanger('HPS1', pr1 = 1, kA = K_HPS1 * A_HPS1)
HPS1 = HeatExchanger('HPS1', pr1 = 1)

A_HPS2 = 175 #[m^2]
K_HPS2 = 200 #[W/m^2-C]
#HPS2 = HeatExchanger('HPS2', pr1 = 1, pr2 = 1, kA = K_HPS2 * A_HPS2)
HPS2 = HeatExchanger('HPS2', pr1 = 1, pr2 = 1)

HPDRUM = Drum('HP Drum')

condenser = SimpleHeatExchanger('condenser', pr = 1)
HE_cond = HeatExchanger('sweet water condenser', pr1 = 1, pr2 = 1)

    ### BUSES ###

from tespy.connections import Bus

powergen = Bus("electrical power output")
my_plant.add_busses(powergen)

powergen.add_comps(
                    {"comp": st_ext, "char": 1, "base": "component"},
                    {"comp": st_cond, "char": 1, "base": "component"},
                    {"comp": att_pump, "char": 1, "base": "bus"},
                    {"comp": cond_pump, "char": 1, "base": "bus"},
                    {"comp": sg_pump, "char": 1, "base": "bus"},
                    )

    ### CONNECTIONS ###
            
        ### DEFINITIONS ###

from tespy.connections import (Connection, Ref)

c01 = Connection(HPS2, 'out2', st_ext, 'in1', label = '1 - hp steam')
c02 = Connection(st_ext, 'out1', sp_1, 'in1', label = '2 - extraction st outlet')
c03 = Connection(sp_1, 'out2', me_1, 'in2', label = '3 - Steam from TV to attemp')
c04 = Connection(sp_1, 'out1', cond_st_cv, 'in1', label = '4 - cond st cv inlet')
c05 = Connection(cond_st_cv, 'out1', st_cond, 'in1', label = '5 - cond st inlet')
c06 = Connection(st_cond, 'out1', condenser, 'in1', label = '6 - condenser inlet')
c07 = Connection(condenser, 'out1', sp_2, 'in1', label = '7 - condenser outlet')
c08 = Connection(sp_2, 'out1', cond_pump, 'in1', label = '8 - cond pump inlet')
c09 = Connection(sp_2, 'out2', att_pump, 'in1', label = '9 - att pump inlet')
c10 = Connection(att_pump,'out1', me_1,'in1', label = '10 - att pump outlet')
c11 = Connection(me_1, 'out1',process_steam,'in1', label = '11 - process steam')
c12 = Connection(cond_pump,'out1', me_3, 'in1', label = '12 - cond pump outlet')
c13 = Connection(water_inlet_1, 'out1', me_3, 'in2', label = '13 - Condensate return from process')
c14 = Connection(water_inlet_2,'out1',me_3,'in3', label = '14 - Water makeup')
c15 = Connection(me_3,'out1', lp_pump,'in1', label = '15 - Water mixture feed to low pressure pump')
c16 = Connection(lp_pump,'out1', HE,'in2', label = '16 - Water mixture feed to heat exchanger')
c17 = Connection(HE,'out2', LPDRUM,'in1', label = '17 - heated water feed to LPDRUM')
c18 = Connection(HE,'out1', sg_pump,'in1', label = '18 - Cooled water feed to HP pump')
c19 = Connection(sg_pump, 'out1', sp_3,'in1', label = '19 - pressurized water to HPEC1')
c20 = Connection(sp_3, 'out1', me_4, 'in2', label = '20 - pressurized water to sg condenser')
c21 = Connection(sp_3, 'out2', HPEC1, 'in2', label = '21 - pressurized water to HPEC1')
c22 = Connection(HPEC1, 'out2', HPEC2, 'in2', label = '22 - pressurized water to HPEC2')
c23 = Connection(HPEC2, 'out2', me_4, 'in1', label = '23 - outlet of HPEC2 to merge with cold flow')
c24 = Connection(me_4, 'out1', HE_cond, 'in2', label = '24 - outlet of merge to sweet water condenser')
c25 = Connection(HE_cond, 'out2', HPEC3, 'in2', label = '25 - outlet of sweet water condenser to HPEC3')
c26 = Connection(HPEC3, 'out2', HPDRUM, 'in1', label = '26 - outlet of HPEC3 to HP drum')
c27 = Connection(HPDRUM, 'out1', bd_2, 'in1', label = '27 - saturated liquid outlet of HPDRUM to Splitter')
c28 = Connection(bd_2, 'out1', HPEV1, 'in2', label = '28 - saturated liquid outlet of HPDRUM to HPEV1')
c29 = Connection(bd_2, 'out2', wst_2, 'in1', label = '29 - saturated liquid outlet of HPDRUM to waste')
c30 = Connection(HPEV1, 'out2', HPDRUM, 'in2', label = '30 - saturated steam outlet of HPEV1 to HPDRUM')
c31 = Connection(HPDRUM, 'out2', sp_4 , 'in1', label = '31 - saturated steam outlet of HPDRUM')
c32 = Connection(sp_4, 'out1', HPS1, 'in2', label = '32 - saturated steam inlet to HPS1')
c33 = Connection(HPS1, 'out2', me_5, 'in1', label = '33 - Steam outlet of HPS1 to attemp')
c34 = Connection(sp_4, 'out2', HE_cond, 'in1', label = '34 - Steam derivation of HPDRUM to sweet water condenser')
c35 = Connection(HE_cond, 'out1', me_5, 'in2', label = '35 - Sweet water condenser outlet to attemp')
c36 = Connection(me_5, 'out1', HPS2, 'in2', label = '36 - Attemp outlet to HPS2')
c37 = Connection(LPDRUM,'out1', bd_1,'in1', label = '37 - Saturated liquid outlet of LPDRUM to HE')
c38 = Connection(bd_1, 'out1', HE, 'in1', label = '38 - LPDRUM saturated liquid outlet to HE')
c39 = Connection(bd_1, 'out2', LPEV1, 'in2', label = '39 - Saturated liquid inlet to LPEV1')
c40 = Connection(LPEV1, 'out2', LPDRUM, 'in2', label = '40 - Saturated steam inlet to LPDRUM')
c41 = Connection(LPDRUM, 'out2', wst, 'in1', label = '41 - Saturated steam outlet to vent')
c42 = Connection(turbine_exhaust, 'out1', HPS2, 'in1', label = '42 - Hot gases input to HPS2')
c43 = Connection(HPS2, 'out1', HPS1, 'in1', label = '43 - Hot gases input to HPS1') 
c44 = Connection(HPS1, 'out1', HPEV1, 'in1', label = '44 - Hot gases input to HPEV1')
c45 = Connection(HPEV1, 'out1', HPEC3, 'in1', label = '45 - Hot gases input to HPEC3')
c46 = Connection(HPEC3, 'out1', HPEC2, 'in1', label = '46 - Hot gases input to HPEC2')
c47 = Connection(HPEC2, 'out1', LPEV1 , 'in1', label = '47 - Hot gases input to LPEV1')
c48 = Connection(LPEV1, 'out1', HPEC1 , 'in1', label = '48 - Hot gases input to HPEC1')
c49 = Connection(HPEC1, 'out1', gases_outlet , 'in1', label = '49 - Hot gases outlet')

my_plant.add_conns(c01, c02, c03, c04, c05, c06, c07, c08, c09, c10, 
                   c11, c12, c13, c14, c15, c16, c17, c18, c19, c20,
                   c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, 
                   c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, 
                   c41, c42, c43, c44, c45, c46, c47, c48, c49)

        ### ATTRIBUTRES ###

t_0 = 17 #[C]
p_0 = 1.01325 #[bar(a)] 

x_gh_CO2 = 0.061 #[dim]
x_gh_H2O = 0.07768 #[dim]
x_gh_N2 = 0.7364 #[dim]
x_gh_O2 = 0.1126 #[dim]
x_gh_Ar = 1 - x_gh_CO2 - x_gh_H2O - x_gh_N2 - x_gh_O2
p_gh = p_0
G_dot_gh = 481.98 * 2 #[tonne/h]

p_steam = 90 + p_0 #[bar(a)]
t_steam = 485 #[C]
G_dot_steam = 200 #[tonne/h]
purga = 0.01

p_mix_tank = 0 + p_0 #[bar(a)]

grado_sobrecalentamiento = 10 #[C]
t_cond = t_0 + 18 #[C]

G_dot_process_steam = 100 #[tonne/h]
p_process_steam = 12 + p_0 #[bar(a)]
retorno = 0.5
G_dot_process_cond = G_dot_process_steam * retorno
t_process_cond = 70 #[C]

c01.set_attr(m = G_dot_steam, fluid={'water': 1}, T = t_steam, p = p_steam)

import CoolProp.CoolProp as CP
p_sat = CP.PropsSI('P', 'T', t_cond + 273.15, 'Q', 0, 'Water') / 1e5 #[bar(a)]
c06.set_attr(p = p_sat)

c07.set_attr(x=0)
c11.set_attr(m = G_dot_process_steam, Td_bp = grado_sobrecalentamiento, p = p_process_steam)
c12.set_attr(p = p_mix_tank)
c13.set_attr(T = t_process_cond, m = G_dot_process_cond)
c14.set_attr(T = t_0)
c17.set_attr(T = 50)
c20.set_attr(m = 0)
c29.set_attr(m = Ref(c16, purga, 0))
c30.set_attr(x = 0.98)
c35.set_attr(x = 0)
c40.set_attr(x = 0.98)
c41.set_attr(m = 50 / 1000 * 2)

c42.set_attr(m = G_dot_gh, p = p_gh, fluid={'O2': x_gh_O2, 'N2': x_gh_N2, 'CO2': x_gh_CO2, 'water': x_gh_H2O, 'Ar': x_gh_Ar})

        ### GUESSES ###

c42.set_attr(T = 721.7, T0 = 721.7)
c43.set_attr(T = 694.9, T0 = 694.9)
c44.set_attr(T = 568.5, T0 = 568.5)
c45.set_attr(T = 313.4, T0 = 313.4)
c46.set_attr(T = 284.7, T0 = 284.7)
c47.set_attr(T = 228.6, T0 = 228.6)
c48.set_attr(T = 177.4, T0 = 177.4)
c49.set_attr(T0 = 154.6)

c01.set_attr(p0=91.01, T0=485.0, h0=3348.0, m0=200.01600000000002)
c02.set_attr(p0=13.01, T0=232.1, h0=2890.0, m0=200.01600000000002)
c03.set_attr(p0=13.01, T0=232.1, h0=2890.0, m0=97.236)
c04.set_attr(p0=13.01, T0=232.1, h0=2890.0, m0=102.78)
c05.set_attr(p0=11.06, T0=228.4, h0=2890.0, m0=102.78)
c06.set_attr(p0=0.05629, T0=35.0, h0=2161.0, m0=102.78)
c07.set_attr(p0=0.05629, T0=35.0, h0=146.6, m0=102.78)
c08.set_attr(p0=0.05629, T0=35.0, h0=146.6, m0=100.00800000000001)
c09.set_attr(p0=0.05629, T0=35.0, h0=146.6, m0=2.7702)
c10.set_attr(p0=13.01, T0=35.17, h0=148.5, m0=2.7702)
c11.set_attr(p0=13.01, T0=201.7, h0=2814.0, m0=100.00800000000001)
c12.set_attr(p0=1.013, T0=35.01, h0=146.8, m0=100.00800000000001)
c13.set_attr(p0=1.013, T0=70.0, h0=293.1, m0=50.004000000000005)
c14.set_attr(p0=1.013, T0=17.0, h0=71.45, m0=52.128)
c15.set_attr(p0=1.013, T0=39.03, h0=163.6, m0=202.104)
c16.set_attr(p0=1.634, T0=39.04, h0=163.6, m0=202.104)
c17.set_attr(p0=1.634, T0=50.0, h0=209.5, m0=202.104)
c18.set_attr(p0=1.634, T0=103.1, h0=432.2, m0=202.03199999999998)
c19.set_attr(p0=91.01, T0=104.7, h0=445.6, m0=202.03199999999998)
c20.set_attr(p0=91.01, T0=104.7, h0=445.6, m0=0.0)
c21.set_attr(p0=91.01, T0=104.7, h0=445.6, m0=202.03199999999998)
c22.set_attr(p0=91.01, T0=132.8, h0=564.2, m0=202.03199999999998)
c23.set_attr(p0=91.01, T0=201.7, h0=863.2, m0=202.03199999999998)
c24.set_attr(p0=91.01, T0=201.7, h0=863.2, m0=202.03199999999998)
c25.set_attr(p0=91.01, T0=263.9, h0=1154.0, m0=202.03199999999998)
c26.set_attr(p0=91.01, T0=293.6, h0=1308.0, m0=202.03199999999998)
c27.set_attr(p0=91.01, T0=304.1, h0=1368.0, m0=2090.1600000000003)
c28.set_attr(p0=91.01, T0=304.1, h0=1368.0, m0=2088.0)
c29.set_attr(p0=91.01, T0=304.1, h0=1368.0, m0=2.02104)
c30.set_attr(p0=91.01, T0=304.1, h0=1506.0, m0=2088.0)
c31.set_attr(p0=91.01, T0=304.1, h0=2741.0, m0=200.01600000000002)
c32.set_attr(p0=91.01, T0=304.1, h0=2741.0, m0=157.248)
c33.set_attr(p0=91.01, T0=620.7, h0=3684.0, m0=157.248)
c34.set_attr(p0=91.01, T0=304.1, h0=2741.0, m0=42.768)
c35.set_attr(p0=91.01, T0=304.1, h0=1368.0, m0=42.768)
c36.set_attr(p0=91.01, T0=425.1, h0=3189.0, m0=200.01600000000002)
c37.set_attr(p0=1.634, T0=113.9, h0=478.1, m0=447.84000000000003)
c38.set_attr(p0=1.634, T0=113.9, h0=478.1, m0=202.03199999999998)
c39.set_attr(p0=1.634, T0=113.9, h0=478.1, m0=245.70000000000002)
c40.set_attr(p0=1.634, T0=113.9, h0=700.0, m0=245.70000000000002)
c41.set_attr(p0=1.634, T0=113.9, h0=2697.0, m0=0.100008)

    ### SOLVING AND PRINTING ###

my_plant.solve(mode='design')

results = my_plant.results['Connection']
results = results[[
    'p',
    'T',
    'h',
    's',
    'x',
    'm'
]].copy()

results.columns = ['p [bar(a)]', 't [°C]', 'h [kJ/kg]', 
                   's [kJ/kg-K]', 'x [dim]', 'm [t/h]']

from tabulate import tabulate

columns_to_format = ['p [bar(a)]', 't [°C]', 'h [kJ/kg]', 's [kJ/kg-K]', 'x [dim]', 'm [t/h]']
results[columns_to_format] = results[columns_to_format].apply(
    lambda col: col.apply(lambda x: f"{x:.2f}" if isinstance(x, (int, float)) else x)
)

print(tabulate(results, headers='keys', tablefmt='fancy_grid', numalign='right', stralign='center'))

my_plant.print_results()

0 replies

PabloMBarral · 2025-02-03T00:19:57Z

PabloMBarral
Feb 3, 2025
Author

Firstly, there are a lot of guesses in the code. They were read from an Excel file generated with EES, where we had solved the model (with a simple script, we could read the file and generate a .txt with the equations). This was because we originally worked with EES, and we needed to understand which inputs were required. This wasn't simple at all.

As stated, the original idea was to provide all the kA values. Moreover, we intended to provide both the heat exchanger areas (obtained from the manufacturer's data) and some general k values (which were estimated, though I could find the actual values in a past work of mine). Although we still need to compare the results with the manufacturer's data, the agreement between EES and TESPy is an excellent sign.

The set of inputs is quite reasonable. If kA values are provided, they represent the size of each heat exchanger. The temperature at state 17 corresponds to the plate heat exchanger. These values (kA ones) were not set as inputs due to some convergence issues. We will continue analyzing this. But to summarize, we provided the flue gas temperature at every stage. Considering pinch and approach points, both are ways of defining the flue gas temperature, so this approach is not unusual. It is unclear whether the design process should start with boiler areas. I'd say it starts with steam and gas temperatures.

The steam pressure is controlled by the supplementary firing loop, which is not represented in the model. This steam pressure acts as a setpoint in a control loop and serves as a proxy for steam production. The flue gas inlet temperature is a consequence of this firing.

The steam temperature is a setpoint in the attemperation loop, which is controlled by a valve in that branch (not represented in the model). Obviously, our model would have issues if the pressure ratio in the superheater were not 1. However, we stopped at this level of complexity for simplicity, as our original goal was to understand TESPy to facilitate migration from EES. In this regard, TESPy is extremely useful, as it eliminates the need to repeatedly state the same equations. Moreover, while writing the model in EES, I had to check the TESPy documentation for the drum component to confirm whether a first-law balance was required, which reinforces that solving such models in EES is unnecessary—TESPy makes the process significantly faster.

The main steam flow is a fixed input because we are not providing details about the steam turbine inlet control valve or the turbine size. Therefore, this flow is not actually a setpoint.

The process steam flow is provided as an input since it is controlled by the steam turbine’s extraction control valve (which is not modeled).

The real steam turbine governor can control two parameters, such as power and extraction pressure, frequency and extraction pressure, inlet pressure and extraction pressure, etc.

The process steam and process condensate are inputs that are not directly related to our plant. Rather, they are boundary conditions, just like the flue gas flow.

The process steam temperature is controlled by the attemperation loop.

The boiler has an economizer bypass to reduce performance. However, we are not using it, as off-design data would be required first. Since we already had a lot of work to develop this model, we will stop here for now.

The plate heat exchanger is intended to improve performance, though I am not entirely sure if it actually does. I have conducted some parametric studies, and the results are inconclusive.

To develop this model, we started with a simpler boiler, excluding all its control loops. Then, we used results from this simpler model as initial guesses to aid convergence.

Attached is the EES file with its results.

The T-Q diagram for the boiler is:

The PFD is

EJEMPLO.zip

Here

There are some equations from Ganapathy to account for HRSG partial load. We are not sure whether we will implement them in TESPy, perhaps only in EES.

In conclusion, we are quite satisfied with our progress in learning TESPy, even though we are only using a small portion of its capabilities. We will continue studying it. Personally, I find that it saves a lot of time and, more importantly, helps prevent errors and missing equations.

I would be happy to collaborate in turning this example into a tutorial or similar resource.

Please feel free to contact me (Pablo) if anyone is interested in this work to discuss details. I'll also work in a tespy file of a simple HRSG, solving 1st law and mass balances starting with pinch and approach values. The simpler model for a one-pressure boiler. When it's done, it will be posted in this forum.

Thanks!

PS: Apologies for mixing Spanish and (bad) English in the code. We'll correct these for the final version of this work, which will be presented at our university.

PS 2: Another important benefit of using tespy is that Copilot (which is provided by our university) really helped when coding. Interesting suggestions, and quickly learnt some repetitive patterns in the code, and autocompleted a lot and always pretty accurately.

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Rankine Cycle + HRSG #554

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Rankine Cycle + HRSG #554

PabloMBarral Oct 16, 2024

Issue with NaN Results in TESPy Model

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PabloMBarral Oct 16, 2024 Author

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