def test_turbine(self):
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.properties = iapws95.Iapws95ParameterBlock()
m.fs.unit = PressureChanger(
default={
"property_package": m.fs.properties,
"thermodynamic_assumption": ThermodynamicAssumption.isentropic,
"compressor": False
})
# set inputs
m.fs.unit.inlet.flow_mol[0].fix(1000) # mol/s
Tin = 500 # K
Pin = 1000000 # Pa
Pout = 700000 # Pa
hin = iapws95.htpx(Tin * units.K, Pin * units.Pa)
m.fs.unit.inlet.enth_mol[0].fix(hin)
m.fs.unit.inlet.pressure[0].fix(Pin)
m.fs.unit.deltaP.fix(Pout - Pin)
m.fs.unit.efficiency_isentropic.fix(0.9)
m.fs.unit.initialize()
m.fs.unit.get_costing()
calculate_variable_from_constraint(m.fs.unit.costing.purchase_cost,
m.fs.unit.costing.cp_cost_eq)
assert degrees_of_freedom(m) == 0
assert_units_consistent(m.fs.unit)
solver.solve(m, tee=True)
assert m.fs.unit.costing.purchase_cost.value ==\
pytest.approx(213199, 1e-5)
def test_compressor():
m = pyo.ConcreteModel()
m.fs = idaes.core.FlowsheetBlock(default={"dynamic": False})
m.fs.properties = iapws95.Iapws95ParameterBlock()
m.fs.unit1 = cmodels.Compressor(default={"property_package": m.fs.properties})
m.fs.unit2 = hmodels.HelmIsentropicCompressor(default={"property_package": m.fs.properties})
# set inputs
Fin = 1000 # mol/s
Tin = 500 # K
Pin = 2222782.4 # Pa
Pout = 2.7*Pin # Pa
hin = pyo.value(iapws95.htpx(Tin*pyo.units.K, Pin*pyo.units.Pa)) # J/mol
eff = 0.324
m.fs.unit1.inlet.flow_mol[0].fix(Fin)
m.fs.unit2.inlet.flow_mol[0].fix(Fin)
m.fs.unit1.inlet.enth_mol[0].fix(hin)
m.fs.unit2.inlet.enth_mol[0].fix(hin)
m.fs.unit1.inlet.pressure[0].fix(Pin)
m.fs.unit2.inlet.pressure[0].fix(Pin)
m.fs.unit1.outlet.pressure[0].fix(Pout)
m.fs.unit2.outlet.pressure[0].fix(Pout)
m.fs.unit1.efficiency_isentropic.fix(eff)
m.fs.unit2.efficiency_isentropic.fix(eff)
m.fs.unit1.initialize()
m.fs.unit2.initialize()
assert pyo.value(m.fs.unit1.control_volume.properties_out[0].temperature) == \
pytest.approx(
pyo.value(m.fs.unit2.control_volume.properties_out[0].temperature),
rel=1e-7
)
assert pyo.value(m.fs.unit1.control_volume.work[0]) == pytest.approx(
pyo.value(m.fs.unit2.control_volume.work[0]), rel=1e-7)
def concrete_tube(self):
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.properties = iapws95.Iapws95ParameterBlock(
default={"phase_presentation": iapws95.PhaseType.LG})
m.fs.unit = ConcreteTubeSide(
default={
"property_package": m.fs.properties,
"flow_type": HeatExchangerFlowPattern.cocurrent
})
m.fs.unit.d_tube_outer.fix(0.01167)
m.fs.unit.d_tube_inner.fix(0.01167)
m.fs.unit.tube_length.fix(4.85)
m.fs.unit.tube_heat_transfer_coefficient.fix(500)
m.fs.unit.tube_inlet.flow_mol[0].fix(1) # mol/s
m.fs.unit.tube_inlet.pressure[0].fix(101325) # Pa
m.fs.unit.tube_inlet.enth_mol[0].\
fix(iapws95.htpx(300*pyunits.K, 101325*pyunits.Pa)) # K
m.fs.unit.temperature_wall[0, :].fix(1000)
return m
def test_initialize_unit(build_unit):
m = build_unit
# platen superheater
m.fs.unit.diameter_in.fix(0.035)
m.fs.unit.tube_thickness.fix(0.005)
m.fs.unit.fin_thickness.fix(0.0035)
m.fs.unit.slag_thickness[:].fix(0.001)
m.fs.unit.fin_length.fix(0.00966)
m.fs.unit.tube_length.fix(40.0)
m.fs.unit.number_tubes.fix(200.0)
m.fs.unit.therm_cond_slag.fix(1.3)
m.fs.unit.control_volume.scaling_factor_holdup_energy = 1e-8
m.fs.unit.heat_fireside[:].fix(5.5e7) # initial guess
hpl = iapws95.htpx(798.15 * pyo.units.K, 24790249.01 * pyo.units.Pa)
m.fs.unit.inlet[:].flow_mol.fix(24194.177)
m.fs.unit.inlet[:].enth_mol.fix(hpl)
m.fs.unit.inlet[:].pressure.fix(24790249.01)
state_args = {
'flow_mol': 24194.177,
'pressure': 24790249.01,
'enth_mol': hpl
}
initialization_tester(build_unit, dof=0, state_args=state_args)
def test_initialize_calc_cf(build_turbine):
"""Initialize a turbine model"""
m = build_turbine
hin = iapws95.htpx(T=880, P=2.4233e7)
# set inlet
m.fs.turb.inlet.enth_mol[0].value = hin
m.fs.turb.inlet.flow_mol[0].value = 26000 / 4.0
m.fs.turb.inlet.pressure[0].value = 2.4233e7
m.fs.turb.ratioP[0].value = 0.6
m.fs.turb.initialize(outlvl=1, calculate_cf=True)
eq_cons = activated_equalities_generator(m)
for c in eq_cons:
assert abs(c.body() - c.lower) < 1e-4
m.fs.turb.inlet.enth_mol[0].value = hin
m.fs.turb.inlet.flow_mol[0].value = 26000 / 4.0
m.fs.turb.inlet.pressure[0].value = 2.4233e7
m.fs.turb.inlet.fix()
solver.solve(m)
assert m.fs.turb.ratioP[0].value == pytest.approx(0.6)
assert degrees_of_freedom(m) == 0
def valve_model(self):
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.properties = iapws95.Iapws95ParameterBlock()
m.fs.valve = Valve(
default={
"valve_function_callback": self.type,
"property_package": m.fs.properties
})
fin = 900 # mol/s
pin = 200000 # Pa
pout = 100000 # Pa
tin = 300 # K
hin = iapws95.htpx(T=tin * units.K, P=pin * units.Pa) # J/mol
# Calculate the flow coefficient to give 1000 mol/s flow with given P
if self.type == ValveFunctionType.linear:
cv = 1000 / math.sqrt(pin - pout) / 0.5
elif self.type == ValveFunctionType.quick_opening:
cv = 1000 / math.sqrt(pin - pout) / math.sqrt(0.5)
elif self.type == ValveFunctionType.equal_percentage:
cv = 1000 / math.sqrt(pin - pout) / 100**(0.5 - 1)
# set inlet
m.fs.valve.inlet.enth_mol[0].fix(hin)
m.fs.valve.inlet.flow_mol[0].fix(fin)
m.fs.valve.inlet.flow_mol[0].unfix()
m.fs.valve.inlet.pressure[0].fix(pin)
m.fs.valve.outlet.pressure[0].fix(pout)
m.fs.valve.Cv.fix(cv)
m.fs.valve.valve_opening.fix(0.5)
iscale.calculate_scaling_factors(m)
return m
def test_verify(self, iapws):
# Test the heater model against known test cases
# Test cases from Aspen Plus 10 with iapws-95
cases = {
"F": (1000, 1000, 1000, 1000), # mol/s
"Tin": (300, 300, 300, 800), # K
"Pin": (1000, 1000, 1000, 1000), # kPa
"xin": (0, 0, 0, 1), # vapor fraction
"Tout": (400, 400, 453.028, 300), # K
"Pout": (1000, 100, 1000, 1000), # kPa
"xout": (0, 1, 0.228898, 0), # vapor fraction
"duty": (7566.19, 47145, 20000, -61684.4), # kW
}
for i in [0, 1, 2, 3]:
F = cases["F"][i]
Tin = cases["Tin"][i]
Pin = cases["Pin"][i]*1000
xin = cases["xin"][i]
hin = iapws95.htpx(T=Tin, P=Pin)
Tout = cases["Tout"][i]
Pout = cases["Pout"][i]*1000
xout = cases["xout"][i]
duty = cases["duty"][i]*1000
if xout != 0 and xout != 1:
hout = iapws95.htpx(T=Tout, x=xout)
else:
hout = iapws95.htpx(T=Tout, P=Pout)
prop_in = iapws.fs.unit.control_volume.properties_in[0]
prop_out = iapws.fs.unit.control_volume.properties_out[0]
prop_in.flow_mol = F
prop_in.enth_mol = hin
prop_in.pressure = Pin
iapws.fs.unit.deltaP[0] = Pout - Pin
iapws.fs.unit.heat_duty[0] = duty
results = solver.solve(iapws)
# Check for optimal solution
assert results.solver.termination_condition == \
TerminationCondition.optimal
assert results.solver.status == SolverStatus.ok
assert Tin == pytest.approx(value(prop_in.temperature), rel=1e-3)
assert Tout == pytest.approx(value(prop_out.temperature), rel=1e-3)
assert Pout == pytest.approx(value(prop_out.pressure), rel=1e-3)
assert xout == pytest.approx(value(prop_out.vapor_frac), rel=1e-3)
def test_verify(self, iapws_turb):
iapws = iapws_turb
# Verify the turbine results against 3 known test cases
# Case Data (90% isentropic efficency)
# Run with Aspen Plus v10 using iapws-95
cases = {
"F": (1000, 1000, 1000), # mol/s
"Tin": (500, 800, 400), # K
"Pin": (1000, 10000, 200), # kPa
"W": (-1224.64, -1911.55, -1010.64), # kW
"Tout": (463.435, 742.992, 382.442), # K
"Pout": (700, 7000, 140), # kPa
"xout": (1.0, 1.0, 0.9886), # vapor fraction
"Tisen": (460.149, 738.224, 382.442),
}
for i in [0, 1, 2]:
F = cases["F"][i]
Tin = cases["Tin"][i]
Tout = cases["Tout"][i]
Pin = cases["Pin"][i] * 1000
Pout = cases["Pout"][i] * 1000
hin = iapws95.htpx(T=Tin * units.K, P=Pin * units.Pa)
W = cases["W"][i] * 1000
Tis = cases["Tisen"][i]
xout = cases["xout"][i]
iapws.fs.unit.inlet.flow_mol[0].fix(F)
iapws.fs.unit.inlet.enth_mol[0].fix(hin)
iapws.fs.unit.inlet.pressure[0].fix(Pin)
iapws.fs.unit.deltaP.fix(Pout - Pin)
iapws.fs.unit.efficiency_isentropic.fix(0.9)
iapws.fs.unit.initialize(optarg={'tol': 1e-6})
results = solver.solve(iapws)
# Check for optimal solution
assert results.solver.termination_condition == \
TerminationCondition.optimal
assert results.solver.status == SolverStatus.ok
Tout = pytest.approx(cases["Tout"][i], rel=1e-2)
Pout = pytest.approx(cases["Pout"][i] * 1000, rel=1e-2)
Pout = pytest.approx(cases["Pout"][i] * 1000, rel=1e-2)
W = pytest.approx(cases["W"][i] * 1000, rel=1e-2)
xout = pytest.approx(xout, rel=1e-2)
prop_out = iapws.fs.unit.control_volume.properties_out[0]
prop_in = iapws.fs.unit.control_volume.properties_in[0]
prop_is = iapws.fs.unit.properties_isentropic[0]
assert value(prop_in.temperature) == pytest.approx(Tin, rel=1e-3)
assert value(prop_is.temperature) == pytest.approx(Tis, rel=1e-3)
assert value(iapws.fs.unit.control_volume.work[0]) == W
assert value(prop_out.pressure) == Pout
assert value(prop_out.temperature) == Tout
assert value(prop_out.vapor_frac) == xout
def test_discharge():
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.steam_prop = Iapws95ParameterBlock()
m.fs.therminol66_prop = ThermalOilParameterBlock()
m.fs.discharge_hx = HeatExchanger(
default={
"hot_side_name": "tube",
"cold_side_name": "shell",
"tube": {
"property_package": m.fs.therminol66_prop
},
"shell": {
"property_package": m.fs.steam_prop
},
"flow_pattern": HeatExchangerFlowPattern.countercurrent
})
# Set inputs
# Steam
m.fs.discharge_hx.inlet_2.flow_mol[0].fix(4163)
m.fs.discharge_hx.inlet_2.pressure[0].fix(1.379e+6)
m.fs.discharge_hx.inlet_2.enth_mol[0].fix(
htpx(T=300.15 * units.K, P=1.379e+6 * units.Pa))
# Thermal Oil
m.fs.discharge_hx.inlet_1.flow_mass[0].fix(833.3)
m.fs.discharge_hx.inlet_1.temperature[0].fix(256 + 273.15)
m.fs.discharge_hx.inlet_1.pressure[0].fix(101325)
# Designate the Area
m.fs.discharge_hx.area.fix(12180)
m.fs.discharge_hx.overall_heat_transfer_coefficient.fix(432.677)
# Designate the U Value.
m.fs.discharge_hx.initialize()
m.fs.discharge_hx.heat_duty.fix(1.066e+08)
m.fs.discharge_hx.area.unfix()
solver = get_solver()
results = solver.solve(m, tee=False)
# Check for optimal solution
assert results.solver.termination_condition == \
TerminationCondition.optimal
assert results.solver.status == SolverStatus.ok
# Tests to make sure the discharge cycle is functioning properly.
assert value(m.fs.discharge_hx.outlet_1.temperature[0]) == \
pytest.approx(473.5, rel=1e-1)
assert value(m.fs.discharge_hx.outlet_2.enth_mol[0]) == \
pytest.approx(27668.5, rel=1e-1)
def test_charge():
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.steam_prop = Iapws95ParameterBlock()
m.fs.therminol66_prop = ThermalOilParameterBlock()
m.fs.charge_hx = HeatExchanger(
default={
"shell": {
"property_package": m.fs.steam_prop
},
"tube": {
"property_package": m.fs.therminol66_prop
},
"flow_pattern": HeatExchangerFlowPattern.countercurrent
})
# Set inputs
# Steam
m.fs.charge_hx.inlet_1.flow_mol[0].fix(4163)
m.fs.charge_hx.inlet_1.enth_mol[0].fix(
htpx(T=573.15 * units.K, P=5.0e+6 * units.Pa))
m.fs.charge_hx.inlet_1.pressure[0].fix(5.0e+6)
# Thermal Oil
m.fs.charge_hx.inlet_2.flow_mass[0].fix(833.3)
m.fs.charge_hx.inlet_2.temperature[0].fix(200 + 273.15)
m.fs.charge_hx.inlet_2.pressure[0].fix(101325)
m.fs.charge_hx.area.fix(12180)
m.fs.charge_hx.overall_heat_transfer_coefficient.fix(432.677)
m.fs.charge_hx.initialize()
m.fs.charge_hx.heat_duty.fix(1.066e+08)
# Needed to make the system solve.
m.fs.charge_hx.overall_heat_transfer_coefficient.unfix()
solver = get_solver()
results = solver.solve(m)
# Check for optimal solution
assert results.solver.termination_condition == \
TerminationCondition.optimal
assert results.solver.status == SolverStatus.ok
# Testing the exit values of the heat exchanger.
assert value(m.fs.charge_hx.outlet_2.temperature[0]) == \
pytest.approx(528.83, rel=1e-1)
assert value(m.fs.charge_hx.outlet_1.enth_mol[0]) == \
pytest.approx(27100.28, rel=1e-1)
def test_initialize_dyn(build_turbine_dyn):
"""Initialize a turbine model"""
m = build_turbine_dyn
hin = iapws95.htpx(T=880, P=2.4233e7)
discretizer = TransformationFactory('dae.finite_difference')
discretizer.apply_to(m, nfe=4, wrt=m.fs.time, scheme='BACKWARD')
# fix inlet
m.fs.turb.inlet.enth_mol.fix(hin)
m.fs.turb.inlet.flow_mol.fix(26000 / 4.0)
m.fs.turb.inlet.pressure.fix(2.4233e7)
m.fs.turb.initialize()
def test_initialize(build_turbine):
"""Initialize a turbine model"""
m = build_turbine
hin = value(iapws95.htpx(T=880*pyunits.K, P=2.4233e7*pyunits.Pa))
# set inlet
m.fs.turb.inlet.enth_mol[0].value = hin
m.fs.turb.inlet.flow_mol[0].value = 26000/4.0
m.fs.turb.inlet.pressure[0].value = 2.4233e7
m.fs.turb.initialize(outlvl=1)
eq_cons = activated_equalities_generator(m)
for c in eq_cons:
assert abs(c.body() - c.lower) < 1e-4
assert degrees_of_freedom(m)==3 #inlet was't fixed and still shouldn't be
def create_isentropic_compressor(f=1000, T_in=500, p_in=1e6, ratioP=1.5):
m = pyo.ConcreteModel()
m.fs = idaes_core.FlowsheetBlock(default={"dynamic": False})
m.fs.properties = iapws95.Iapws95ParameterBlock()
m.fs.unit = HelmIsentropicCompressor(default={"property_package": m.fs.properties})
hin = iapws95.htpx(T_in, p_in) # J/mol
m.fs.unit.inlet.flow_mol[0].fix(f)
m.fs.unit.inlet.enth_mol[0].fix(hin)
m.fs.unit.inlet.pressure[0].fix(p_in)
m.fs.unit.ratioP[0].fix(ratioP)
m.fs.unit.efficiency_isentropic.fix(0.9)
m.fs.unit.initialize()
return m
def test_turbine_performance_way1(self):
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.properties = iapws95.Iapws95ParameterBlock()
def perf_callback(b):
unit_hd = units.J / units.kg
unit_vflw = units.m**3 / units.s
@b.Constraint(m.fs.config.time)
def pc_isen_eff_eqn(b, t):
prnt = b.parent_block()
vflw = prnt.control_volume.properties_in[t].flow_vol
return prnt.efficiency_isentropic[
t] == 0.9 / 3.975 * vflw / unit_vflw
@b.Constraint(m.fs.config.time)
def pc_isen_head_eqn(b, t):
prnt = b.parent_block()
vflw = prnt.control_volume.properties_in[t].flow_vol
return b.head_isentropic[t]/1000 == \
-75530.8/3.975/1000*vflw/unit_vflw*unit_hd
m.fs.unit = Turbine(
default={
"property_package": m.fs.properties,
"support_isentropic_performance_curves": True,
"isentropic_performance_curves": {
"build_callback": perf_callback
}
})
# set inputs
m.fs.unit.inlet.flow_mol[0].fix(1000) # mol/s
Tin = 500 # K
Pin = 1000000 # Pa
Pout = 700000 # Pa
hin = iapws95.htpx(Tin * units.K, Pin * units.Pa)
m.fs.unit.inlet.enth_mol[0].fix(hin)
m.fs.unit.inlet.pressure[0].fix(Pin)
m.fs.unit.initialize()
assert degrees_of_freedom(m) == 0
assert_units_consistent(m.fs.unit)
solver.solve(m, tee=True)
assert value(m.fs.unit.efficiency_isentropic[0]) \
== pytest.approx(0.9, rel=1e-3)
assert value(m.fs.unit.deltaP[0]) == pytest.approx(-3e5, rel=1e-3)
def test_initialize(build_turbine):
"""Initialize a turbine model"""
hin = value(iapws95.htpx(T=880*pyunits.K, P=2.4233e7*pyunits.Pa))
# set inlet
build_turbine.fs.turb.inlet.enth_mol[0].value = hin
build_turbine.fs.turb.inlet.flow_mol[0].value = 26000/4.0
build_turbine.fs.turb.inlet.pressure[0].value = 2.4233e7
build_turbine.fs.turb.initialize(outlvl=1)
eq_cons = activated_equalities_generator(build_turbine)
for c in eq_cons:
assert(abs(c.body() - c.lower) < 1e-4)
assert degrees_of_freedom(build_turbine) == 3
def test_vapor_steady_state_initialize(build_valve_vapor):
"""Initialize a turbine model"""
m = build_valve_vapor
# set inlet
hin = iapws95.htpx(T=880, P=2.4233e7)
# set inlet
m.fs.valve.inlet.enth_mol[0].value = hin
m.fs.valve.inlet.flow_mol[0].value = 26000/4.0
m.fs.valve.inlet.pressure[0].value = 2.5e7
m.fs.valve.Cv.fix(0.01)
m.fs.valve.initialize(outlvl=1)
eq_cons = activated_equalities_generator(m)
for c in eq_cons:
assert(abs(c.body() - c.lower) < 1e-4)
assert(degrees_of_freedom(m)==3) #inlet was't fixed and still shouldn't be
def test_vapor_steady_state_initialize(build_valve_vapor):
"""Initialize a turbine model"""
# set inlet
hin = value(iapws95.htpx(T=880 * pyunits.K, P=2.4233e7 * pyunits.Pa))
# set inlet
build_valve_vapor.fs.valve.inlet.enth_mol[0].value = hin
build_valve_vapor.fs.valve.inlet.flow_mol[0].value = 26000 / 4.0
build_valve_vapor.fs.valve.inlet.pressure[0].value = 2.5e7
build_valve_vapor.fs.valve.Cv.fix(0.01)
build_valve_vapor.fs.valve.initialize(outlvl=1)
eq_cons = activated_equalities_generator(build_valve_vapor)
for c in eq_cons:
assert (abs(c.body() - c.lower) < 1e-4)
# inlet was't fixed and still shouldn't be
assert degrees_of_freedom(build_valve_vapor) == 3
def test_initialize_dyn(build_turbine_dyn):
"""Initialize a turbine model"""
m = build_turbine_dyn
hin = value(iapws95.htpx(T=880*pyunits.K, P=2.4233e7*pyunits.Pa))
discretizer = TransformationFactory('dae.finite_difference')
discretizer.apply_to(m, nfe=4, wrt=m.fs.time, scheme='BACKWARD')
# fix inlet
m.fs.turb.inlet.enth_mol.fix(hin)
m.fs.turb.inlet.flow_mol.fix(26000/4.0)
m.fs.turb.inlet.pressure.fix(2.4233e7)
m.fs.turb.flow_coeff[:].fix()
m.fs.turb.initialize()
eq_cons = activated_equalities_generator(m)
for c in eq_cons:
assert(abs(c.body() - c.lower) < 1e-4)
assert(degrees_of_freedom(m)==0)
def test_initialize_dyn2(build_turbine_dyn):
"""Initialize a turbine model"""
m = build_turbine_dyn
hin = iapws95.htpx(T=880, P=2.4233e7)
discretizer = TransformationFactory('dae.finite_difference')
discretizer.apply_to(m, nfe=4, wrt=m.fs.time, scheme='BACKWARD')
# fix inlet
m.fs.turb.inlet.enth_mol.fix(hin)
m.fs.turb.inlet.flow_mol.fix(26000/4.0)
m.fs.turb.inlet.pressure.fix(2.4233e7)
m.fs.turb.flow_coeff[:].fix()
m.fs.turb.ratioP[0].value = 0.6 # used for flow coeff calc
m.fs.turb.initialize(calculate_cf=True)
eq_cons = activated_equalities_generator(m)
for c in eq_cons:
assert(abs(c.body() - c.lower) < 1e-4)
assert m.fs.turb.ratioP[0].value == pytest.approx(0.6)
assert(degrees_of_freedom(m)==0)
def test_initialize_unit(build_unit):
m = build_unit
# Set inputs
h = pyo.value(iapws95.htpx(773.15 * pyunits.K, 2.5449e7 * pyunits.Pa))
print(h)
m.fs.unit.tube_inlet.flow_mol[0].fix(24678.26) # mol/s
m.fs.unit.tube_inlet.enth_mol[0].fix(h) # J/mol
m.fs.unit.tube_inlet.pressure[0].fix(2.5449e7) # Pascals
# FLUE GAS Inlet relative to a primary superheater
FGrate = 5109.76 # mol/s equivalent of ~1930.08 klb/hr
# Use FG molar composition to set component flow rates (baseline report)
m.fs.unit.shell_inlet.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.unit.shell_inlet.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.unit.shell_inlet.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.unit.shell_inlet.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.unit.shell_inlet.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.unit.shell_inlet.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.unit.shell_inlet.temperature[0].fix(1102.335)
m.fs.unit.shell_inlet.pressure[0].fix(100145)
initialization_tester(build_unit, dof=0)
def test_verify(self, iapws):
# Test the heater model against known test cases
cases = {
"F": (1000, 1000, 1000, 1000), # mol/s
"Tin": (300, 300, 300, 800), # K
"Pin": (1000, 1000, 1000, 1000), # kPa
"xin": (0, 0, 0, 1), # vapor fraction
"Tout": (400, 400, 453.028, 300), # K
"Pout": (1000, 100, 1000, 1000), # kPa
"xout": (0, 1, 0.228898, 0), # vapor fraction
"duty": (7566.19, 47145, 20000, -61684.4), # kW
}
for i in [0, 1, 2, 3]:
F = cases["F"][i]
Tin = cases["Tin"][i]
Pin = cases["Pin"][i] * 1000
hin = iapws95.htpx(T=Tin * pyunits.K, P=Pin * pyunits.Pa)
Tout = cases["Tout"][i]
Pout = cases["Pout"][i] * 1000
xout = cases["xout"][i]
duty = cases["duty"][i] * 1000
prop_in = iapws.fs.unit.control_volume.properties_in[0]
prop_out = iapws.fs.unit.control_volume.properties_out[0]
prop_in.flow_mol = F
prop_in.enth_mol = hin
prop_in.pressure = Pin
iapws.fs.unit.deltaP[0] = Pout - Pin
iapws.fs.unit.heat_duty[0] = duty
results = solver.solve(iapws)
# Check for optimal solution
assert check_optimal_termination(results)
assert Tin == pytest.approx(value(prop_in.temperature), rel=1e-3)
assert Tout == pytest.approx(value(prop_out.temperature), rel=1e-3)
assert Pout == pytest.approx(value(prop_out.pressure), rel=1e-3)
assert xout == pytest.approx(value(prop_out.vapor_frac), rel=1e-3)
def initialize(m, fileinput=None, outlvl=idaeslog.NOTSET):
""" Initialize a mode from create_model(), set model inputs before
initializing.
Args:
m (ConcreteModel): A Pyomo model from create_model()
fileinput (str|None): File to load initialized model state from. If a
file is supplied skip initialization routine. If None, initialize.
Returns:
solver: A Pyomo solver object, that can be used to solve the model.
"""
init_log = idaeslog.getInitLogger(m.name, outlvl, tag="flowsheet")
solve_log = idaeslog.getSolveLogger(m.name, outlvl, tag="flowsheet")
iscale.calculate_scaling_factors(m)
solver = pyo.SolverFactory("ipopt")
solver.options = {
"tol": 1e-7,
"linear_solver": "ma27",
"max_iter": 40,
}
if fileinput is not None:
init_log.info("Loading initial values from file: {}".format(fileinput))
ms.from_json(m, fname=fileinput)
return solver
init_log.info("Starting initialization")
############################################################################
# Initialize turbine #
############################################################################
# Extraction rates are calculated from the feedwater heater models, so to
# initialize the turbine fix some initial guesses. They get unfixed after
# solving the turbine
m.fs.turb.outlet_stage.control_volume.properties_out[:].pressure.fix(3500)
m.fs.turb.lp_split[11].split_fraction[:, "outlet_2"].fix(0.04403)
m.fs.turb.lp_split[10].split_fraction[:, "outlet_2"].fix(0.04025)
m.fs.turb.lp_split[8].split_fraction[:, "outlet_2"].fix(0.04362)
m.fs.turb.lp_split[4].split_fraction[:, "outlet_2"].fix(0.08025)
m.fs.turb.ip_split[10].split_fraction[:, "outlet_2"].fix(0.045)
m.fs.turb.ip_split[10].split_fraction[:, "outlet_3"].fix(0.04)
m.fs.turb.ip_split[5].split_fraction[:, "outlet_2"].fix(0.05557)
m.fs.turb.hp_split[7].split_fraction[:, "outlet_2"].fix(0.09741)
m.fs.turb.hp_split[4].split_fraction[:, "outlet_2"].fix(0.0740)
# Put in a rough initial guess for the IP section inlet, since it is
# disconnected from the HP section for the reheater.
ip1_pin = 5.35e6
ip1_hin = pyo.value(
iapws95.htpx(T=866 * pyo.units.K, P=ip1_pin * pyo.units.Pa))
ip1_fin = pyo.value(m.fs.turb.inlet_split.inlet.flow_mol[0])
m.fs.turb.ip_stages[1].inlet.enth_mol[:].value = ip1_hin
m.fs.turb.ip_stages[1].inlet.flow_mol[:].value = ip1_fin
m.fs.turb.ip_stages[1].inlet.pressure[:].value = ip1_pin
# initialize turbine
assert degrees_of_freedom(m.fs.turb) == 0
m.fs.turb.initialize(outlvl=outlvl, optarg=solver.options)
with idaeslog.solver_log(solve_log, idaeslog.DEBUG) as slc:
res = solver.solve(m.fs.turb, tee=slc.tee)
init_log.info("Full turbine solve complete: {}".format(
idaeslog.condition(res)))
# The turbine outlet pressure is determined by the condenser once hooked up
m.fs.turb.outlet_stage.control_volume.properties_out[:].pressure.unfix()
# Extraction rates are calculated once the feedwater heater models are
# added so unfix the splits.
m.fs.turb.lp_split[11].split_fraction[:, "outlet_2"].unfix()
m.fs.turb.lp_split[10].split_fraction[:, "outlet_2"].unfix()
m.fs.turb.lp_split[8].split_fraction[:, "outlet_2"].unfix()
m.fs.turb.lp_split[4].split_fraction[:, "outlet_2"].unfix()
m.fs.turb.ip_split[10].split_fraction[:, "outlet_3"].unfix()
m.fs.turb.ip_split[5].split_fraction[:, "outlet_2"].unfix()
m.fs.turb.hp_split[7].split_fraction[:, "outlet_2"].unfix()
m.fs.turb.hp_split[4].split_fraction[:, "outlet_2"].unfix()
# Initialize the boiler feed pump turbine.
_set_port(m.fs.bfpt.inlet, m.fs.turb.ip_split[10].outlet_3)
m.fs.bfpt.control_volume.properties_out[:].pressure.fix(10000)
m.fs.bfpt.efficiency_isentropic.fix()
m.fs.bfpt.initialize(outlvl=idaeslog.DEBUG, optarg=solver.options)
m.fs.bfpt.control_volume.properties_out[:].pressure.unfix()
m.fs.bfpt.efficiency_isentropic.unfix()
############################################################################
# Condenser section #
############################################################################
# initialize condenser mixer
_set_port(m.fs.condenser_mix.main, m.fs.turb.outlet_stage.outlet)
_set_port(m.fs.condenser_mix.bfpt, m.fs.bfpt.outlet)
m.fs.condenser_mix.initialize(outlvl=outlvl, optarg=solver.options)
# initialize condenser hx
_set_port(m.fs.condenser.inlet_1, m.fs.condenser_mix.outlet_tpx)
_set_port(m.fs.condenser.outlet_2, m.fs.condenser.inlet_2)
# This still has the outlet vapor fraction fixed at 0, so if that isn't
# true for the initial pressure guess this could fail to initialize
m.fs.condenser.inlet_1.fix()
m.fs.condenser.inlet_1.pressure.unfix()
with idaeslog.solver_log(solve_log, idaeslog.DEBUG) as slc:
res = solver.solve(m.fs.condenser, tee=slc.tee)
init_log.info("Condenser initialized: {}".format(idaeslog.condition(res)))
init_log.info_high("Init condenser pressure: {}".format(
m.fs.condenser.shell.properties_in[0].pressure.value))
m.fs.condenser.inlet_1.unfix()
# initialize hotwell
_set_port(m.fs.hotwell.condensate, m.fs.condenser.outlet_1_ph)
m.fs.hotwell.initialize(outlvl=outlvl, optarg=solver.options)
m.fs.hotwell.condensate.unfix()
# initialize condensate pump
_set_port(m.fs.cond_pump.inlet, m.fs.hotwell.outlet)
m.fs.cond_pump.initialize(outlvl=outlvl, optarg=solver.options)
############################################################################
# Low-pressure FWH section #
############################################################################
# fwh1
m.fs.fwh1.drain_mix.drain.flow_mol[:] = 1000
m.fs.fwh1.drain_mix.drain.pressure[:] = 1e5
m.fs.fwh1.drain_mix.drain.enth_mol[:] = 6117
_set_port(m.fs.fwh1.condense.inlet_2, m.fs.cond_pump.outlet)
_set_port(m.fs.fwh1.drain_mix.steam, m.fs.turb.lp_split[11].outlet_2)
m.fs.fwh1.initialize(outlvl=outlvl, optarg=solver.options)
# initialize fwh1 drain pump
_set_port(m.fs.fwh1_pump.inlet, m.fs.fwh1.condense.outlet_1)
m.fs.fwh1_pump.initialize(outlvl=5, optarg=solver.options)
# initialize mixer to add fwh1 drain to feedwater
_set_port(m.fs.fwh1_return.feedwater, m.fs.fwh1.condense.outlet_2)
_set_port(m.fs.fwh1_return.fwh1_drain, m.fs.fwh1.condense.outlet_1)
m.fs.fwh1_return.initialize(outlvl=outlvl, optarg=solver.options)
m.fs.fwh1_return.feedwater.unfix()
m.fs.fwh1_return.fwh1_drain.unfix()
# fwh2
m.fs.fwh2.drain_mix.drain.flow_mol[:] = 100
m.fs.fwh2.drain_mix.drain.pressure[:] = 1.5e5
m.fs.fwh2.drain_mix.drain.enth_mol[:] = 7000
_set_port(m.fs.fwh2.cooling.inlet_2, m.fs.fwh1_return.outlet)
_set_port(m.fs.fwh2.desuperheat.inlet_1, m.fs.turb.lp_split[10].outlet_2)
m.fs.fwh2.initialize(outlvl=outlvl, optarg=solver.options)
# fwh3
m.fs.fwh3.drain_mix.drain.flow_mol[:] = 100
m.fs.fwh3.drain_mix.drain.pressure[:] = 2.5e5
m.fs.fwh3.drain_mix.drain.enth_mol[:] = 8000
_set_port(m.fs.fwh3.cooling.inlet_2, m.fs.fwh2.desuperheat.outlet_2)
_set_port(m.fs.fwh3.desuperheat.inlet_1, m.fs.turb.lp_split[8].outlet_2)
m.fs.fwh3.initialize(outlvl=outlvl, optarg=solver.options)
# fwh4
_set_port(m.fs.fwh4.cooling.inlet_2, m.fs.fwh3.desuperheat.outlet_2)
_set_port(m.fs.fwh4.desuperheat.inlet_1, m.fs.turb.lp_split[4].outlet_2)
m.fs.fwh4.initialize(outlvl=outlvl, optarg=solver.options)
############################################################################
# boiler feed pump and deaerator #
############################################################################
_set_port(m.fs.fwh5_da.feedwater, m.fs.fwh4.desuperheat.outlet_2)
_set_port(m.fs.fwh5_da.steam, m.fs.turb.ip_split[10].outlet_2)
m.fs.fwh5_da.drain.flow_mol[:] = 2000
m.fs.fwh5_da.drain.pressure[:] = 3e6
m.fs.fwh5_da.drain.enth_mol[:] = 9000
m.fs.fwh5_da.initialize(outlvl=outlvl, optarg=solver.options)
_set_port(m.fs.bfp.inlet, m.fs.fwh5_da.outlet)
m.fs.bfp.control_volume.properties_out[:].pressure.fix()
m.fs.bfp.initialize(outlvl=outlvl, optarg=solver.options)
m.fs.bfp.control_volume.properties_out[:].pressure.unfix()
############################################################################
# High-pressure feedwater heaters #
############################################################################
# fwh6
m.fs.fwh6.drain_mix.drain.flow_mol[:] = 1000
m.fs.fwh6.drain_mix.drain.pressure[:] = 1e7
m.fs.fwh6.drain_mix.drain.enth_mol[:] = 9500
_set_port(m.fs.fwh6.cooling.inlet_2, m.fs.bfp.outlet)
_set_port(m.fs.fwh6.desuperheat.inlet_1, m.fs.turb.ip_split[5].outlet_2)
m.fs.fwh6.initialize(outlvl=outlvl, optarg=solver.options)
# fwh7
m.fs.fwh7.drain_mix.drain.flow_mol[:] = 2000
m.fs.fwh7.drain_mix.drain.pressure[:] = 1e7
m.fs.fwh7.drain_mix.drain.enth_mol[:] = 9500
_set_port(m.fs.fwh7.cooling.inlet_2, m.fs.fwh6.desuperheat.outlet_2)
_set_port(m.fs.fwh7.desuperheat.inlet_1, m.fs.turb.hp_split[7].outlet_2)
m.fs.fwh7.initialize(outlvl=outlvl, optarg=solver.options)
# fwh8
_set_port(m.fs.fwh8.cooling.inlet_2, m.fs.fwh7.desuperheat.outlet_2)
_set_port(m.fs.fwh8.desuperheat.inlet_1, m.fs.turb.hp_split[4].outlet_2)
m.fs.fwh8.initialize(outlvl=outlvl, optarg=solver.options)
with idaeslog.solver_log(solve_log, idaeslog.DEBUG) as slc:
res = solver.solve(m, tee=slc.tee)
init_log.info("Initialization Complete: {}".format(
idaeslog.condition(res)))
return solver
def initialize(m):
# ------------- ECONOMIZER -----------------------------------------------
# BFW Boiler Feed Water inlet temeperature = 555 F = 563.706 K
m.fs.ECON.side_1_inlet.flow_mol[0].fix(24194.177) # mol/s
m.fs.ECON.side_1_inlet.enth_mol[0].fix(14990.97)
m.fs.ECON.side_1_inlet.pressure[0].fix(26922222.222) # Pa
# FLUE GAS Inlet from Primary Superheater
FGrate = 21290.6999 # mol/s
# Use FG molar composition to set component flow rates (baseline report)
m.fs.ECON.side_2_inlet.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.ECON.side_2_inlet.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.ECON.side_2_inlet.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.ECON.side_2_inlet.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.ECON.side_2_inlet.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.ECON.side_2_inlet.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.ECON.side_2_inlet.temperature[0].fix(682.335) # K
m.fs.ECON.side_2_inlet.pressure[0].fix(100145) # Pa
# economizer design variables and parameters
ITM = 0.0254 # inch to meter conversion
# Based on NETL Baseline Report Rev3
m.fs.ECON.tube_di.fix((2 - 2 * 0.188) * ITM) # calc inner diameter
# (2 = outer diameter, thickness = 0.188)
m.fs.ECON.tube_thickness.fix(0.188 * ITM) # tube thickness
m.fs.ECON.pitch_x.fix(3.5 * ITM)
# pitch_y = (54.5) gas path transverse width /columns
m.fs.ECON.pitch_y.fix(5.03 * ITM)
m.fs.ECON.tube_length.fix(53.41 * 12 * ITM) # use tube length (53.41 ft)
m.fs.ECON.tube_nrow.fix(36 * 2.5) # use to match baseline performance
m.fs.ECON.tube_ncol.fix(130) # 130 from NETL
m.fs.ECON.nrow_inlet.fix(2)
m.fs.ECON.delta_elevation.fix(50)
# parameters
# heat transfer resistance due to tube side fouling (water scales)
m.fs.ECON.tube_r_fouling = 0.000176
# heat transfer resistance due to tube shell fouling (ash deposition)
m.fs.ECON.shell_r_fouling = 0.00088
if m.fs.ECON.config.has_radiation is True:
m.fs.ECON.emissivity_wall.fix(0.7) # wall emissivity
# correction factor for overall heat transfer coefficient
m.fs.ECON.fcorrection_htc.fix(1.5)
# correction factor for pressure drop calc tube side
m.fs.ECON.fcorrection_dp_tube.fix(1.0)
# correction factor for pressure drop calc shell side
m.fs.ECON.fcorrection_dp_shell.fix(1.0)
# --------- Primary Superheater ------------
# Steam from water wall
hprsh = value(iapws95.htpx(773.15 * pyunits.K, 24865516.722 * pyunits.Pa))
print(hprsh)
m.fs.PrSH.side_1_inlet.flow_mol[0].fix(24190.26) # mol/s
m.fs.PrSH.side_1_inlet.enth_mol[0].fix(hprsh) # J/mol
m.fs.PrSH.side_1_inlet.pressure[0].fix(2.5449e7) # Pascals
# FLUE GAS Inlet from Primary Superheater
FGrate = 21290.6999 * 0.18 # mol/s
# Use FG molar composition to set component flow rates (baseline report)
m.fs.PrSH.side_2_inlet.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.PrSH.side_2_inlet.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.PrSH.side_2_inlet.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.PrSH.side_2_inlet.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.PrSH.side_2_inlet.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.PrSH.side_2_inlet.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.PrSH.side_2_inlet.temperature[0].fix(1180.335)
m.fs.PrSH.side_2_inlet.pressure[0].fix(100145)
# Primary Superheater
ITM = 0.0254 # inch to meter conversion
m.fs.PrSH.tube_di.fix((2.5 - 2 * 0.165) * ITM)
m.fs.PrSH.tube_thickness.fix(0.165 * ITM)
m.fs.PrSH.pitch_x.fix(3 * ITM)
# gas path transverse width 54.78 ft / number of columns
m.fs.PrSH.pitch_y.fix(54.78 / 108 * 12 * ITM)
m.fs.PrSH.tube_length.fix(53.13 * 12 * ITM)
m.fs.PrSH.tube_nrow.fix(20 * 2)
m.fs.PrSH.tube_ncol.fix(108)
m.fs.PrSH.nrow_inlet.fix(4)
m.fs.PrSH.delta_elevation.fix(50)
m.fs.PrSH.tube_r_fouling = 0.000176 # (0.001 h-ft^2-F/BTU)
m.fs.PrSH.shell_r_fouling = 0.003131 # (0.03131 - 0.1779 h-ft^2-F/BTU)
if m.fs.PrSH.config.has_radiation is True:
m.fs.PrSH.emissivity_wall.fix(0.7) # wall emissivity
# correction factor for overall heat transfer coefficient
m.fs.PrSH.fcorrection_htc.fix(1.5)
# correction factor for pressure drop calc tube side
m.fs.PrSH.fcorrection_dp_tube.fix(1.0)
# correction factor for pressure drop calc shell side
m.fs.PrSH.fcorrection_dp_shell.fix(1.0)
# ----- Finishing Superheater ----------------------
# Steam from Platen Supeheater
hfsh = value(iapws95.htpx(823.15 * pyunits.K, 24790249.01 * pyunits.Pa))
m.fs.FSH.side_1_inlet.flow_mol[0].fix(24194.177) # mol/s
m.fs.FSH.side_1_inlet.enth_mol[0].fix(hfsh) # J/mol
m.fs.FSH.side_1_inlet.pressure[0].fix(24790249.01) # Pascals
# FLUE GAS Inlet from Primary Superheater
FGrate = 21290.6999 # mol/s
# Use FG molar composition to set component flow rates (baseline report)
m.fs.FSH.side_2_inlet.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.FSH.side_2_inlet.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.FSH.side_2_inlet.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.FSH.side_2_inlet.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.FSH.side_2_inlet.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.FSH.side_2_inlet.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.FSH.side_2_inlet.temperature[0].fix(1300.335)
m.fs.FSH.side_2_inlet.pressure[0].fix(100145)
# Finishing Superheater
ITM = 0.0254 # inch to meter conversion
m.fs.FSH.tube_di.fix((2.5 - 2 * 0.165) * ITM)
m.fs.FSH.tube_thickness.fix(0.165 * ITM)
m.fs.FSH.pitch_x.fix(3 * ITM)
# gas path transverse width 54.78 ft / number of columns
m.fs.FSH.pitch_y.fix(54.78 / 108 * 12 * ITM)
m.fs.FSH.tube_length.fix(53.13 * 12 * ITM)
m.fs.FSH.tube_nrow.fix(8 * 2)
m.fs.FSH.tube_ncol.fix(85)
m.fs.FSH.nrow_inlet.fix(2)
m.fs.FSH.delta_elevation.fix(50)
m.fs.FSH.tube_r_fouling = 0.000176 # (0.001 h-ft^2-F/BTU)
m.fs.FSH.shell_r_fouling = 0.003131 # (0.03131 - 0.1779 h-ft^2-F/BTU)
if m.fs.FSH.config.has_radiation is True:
m.fs.FSH.emissivity_wall.fix(0.7) # wall emissivity
# correction factor for overall heat transfer coefficient
m.fs.FSH.fcorrection_htc.fix(1.0)
# correction factor for pressure drop calc tube side
m.fs.FSH.fcorrection_dp_tube.fix(1.0)
# correction factor for pressure drop calc shell side
m.fs.FSH.fcorrection_dp_shell.fix(1.0)
# ----- Reheater Superheater ----------------------
# Steam from HP Turbine outlet
m.fs.RH.side_1_inlet.flow_mol[0].fix(21235.27) # mol/s
m.fs.RH.side_1_inlet.enth_mol[0].fix(53942.7569) # J/mol
m.fs.RH.side_1_inlet.pressure[0].fix(3677172.33638) # Pascals
# FLUE GAS Inlet from Finishing Superheater
FGrate = 21290.6999 * 0.85 # mol/s
# Use FG molar composition to set component flow rates (baseline report)
m.fs.RH.side_2_inlet.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.RH.side_2_inlet.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.RH.side_2_inlet.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.RH.side_2_inlet.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.RH.side_2_inlet.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.RH.side_2_inlet.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.RH.side_2_inlet.temperature[0].fix(1180.335)
m.fs.RH.side_2_inlet.pressure[0].fix(100145)
# Reheater Superheater
ITM = 0.0254 # inch to meter conversion
m.fs.RH.tube_di.fix((2.5 - 2 * 0.165) * ITM)
m.fs.RH.tube_thickness.fix(0.11 * ITM)
m.fs.RH.pitch_x.fix(3 * ITM)
# gas path transverse width 54.08 ft / number of columns
m.fs.RH.pitch_y.fix(54.08 / 108 * 12 * ITM)
m.fs.RH.tube_length.fix(53.82 * 12 * ITM)
m.fs.RH.tube_nrow.fix(18 * 2)
m.fs.RH.tube_ncol.fix(82 + 70)
m.fs.RH.nrow_inlet.fix(2)
m.fs.RH.delta_elevation.fix(30)
m.fs.RH.tube_r_fouling = 0.000176 # (0.001 h-ft^2-F/BTU)
m.fs.RH.shell_r_fouling = 0.00088 # (0.03131 - 0.1779 h-ft^2-F/BTU)
if m.fs.RH.config.has_radiation is True:
m.fs.RH.emissivity_wall.fix(0.7) # wall emissivity
# correction factor for overall heat transfer coefficient
m.fs.RH.fcorrection_htc.fix(1.8)
# correction factor for pressure drop calc tube side
m.fs.RH.fcorrection_dp_tube.fix(1.0)
# correction factor for pressure drop calc shell side
m.fs.RH.fcorrection_dp_shell.fix(1.0)
# Platen Superheater ------------------------------------------
hpl = value(iapws95.htpx(798.15 * pyunits.K, 24790249.01 * pyunits.Pa))
m.fs.PlSH.inlet[:].flow_mol.fix(24194.177)
m.fs.PlSH.inlet[:].enth_mol.fix(hpl)
m.fs.PlSH.inlet[:].pressure.fix(24790249.01)
m.fs.PlSH.heat_duty[:].fix(5.5e7)
# Water wall Superheater ------------------------------------------
hww = value(iapws95.htpx(588.15 * pyunits.K, 2.5449e7 * pyunits.Pa))
m.fs.Water_wall.inlet[:].flow_mol.fix(24194.177)
m.fs.Water_wall.inlet[:].enth_mol.fix(hww)
m.fs.Water_wall.inlet[:].pressure.fix(24865516.722)
m.fs.Water_wall.heat_duty[:].fix(7.51e8) # 8.76e8
# splitter flue gas from Finishing SH to Reheater and Primary SH
m.fs.Spl1.split_fraction[0, 'outlet_1'].fix(0.75) # 0.85)
# FLUE GAS Inlet from Primary Superheater
FGrate = 21290.6999 # mol/s
# Use FG molar composition to set component flow rates (baseline report)
m.fs.Spl1.inlet.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.Spl1.inlet.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.Spl1.inlet.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.Spl1.inlet.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.Spl1.inlet.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.Spl1.inlet.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.Spl1.inlet.temperature[0].fix(1180.335)
m.fs.Spl1.inlet.pressure[0].fix(100145)
# mixer (econ inlet) fluegas outlet from reheater and primary superheater
# Mixer inlets ['Reheat_out', 'PrSH_out']
m.fs.mix1.Reheat_out.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.mix1.Reheat_out.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.mix1.Reheat_out.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.mix1.Reheat_out.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.mix1.Reheat_out.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.mix1.Reheat_out.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.mix1.Reheat_out.pressure.fix(100145)
m.fs.mix1.Reheat_out.temperature.fix(731.5)
# Fixed SprayWater as small flow and arbitrary conditions
# (will be connected from FW pump splitter)
m.fs.mix1.PrSH_out.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.mix1.PrSH_out.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.mix1.PrSH_out.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.mix1.PrSH_out.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.mix1.PrSH_out.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.mix1.PrSH_out.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.mix1.PrSH_out.pressure.fix(100145)
m.fs.mix1.PrSH_out.temperature.fix(731.15)
# Attemperator inputs
hatt = value(iapws95.htpx(875.15 * pyunits.K, 24865516.722 * pyunits.Pa))
m.fs.ATMP1.Steam.flow_mol.fix(24194.177)
m.fs.ATMP1.Steam.enth_mol.fix(hatt)
m.fs.ATMP1.Steam.pressure.fix(24865516.722)
# Fixed SprayWater from FW pump splitter (splitter is needded)
hatt2 = value(iapws95.htpx(563.15 * pyunits.K, 2.5449e7 * pyunits.Pa))
m.fs.ATMP1.SprayWater_state[:].flow_mol.fix(0.001)
m.fs.ATMP1.SprayWater_state[:].pressure.fix(1.22e8)
m.fs.ATMP1.SprayWater_state[:].enth_mol.fix(hatt2)
# --------- Initialization ------------------------------------------
# Initialize Units
m.fs.ECON.initialize(outlvl=logging.INFO)
m.fs.PrSH.initialize(outlvl=logging.INFO)
m.fs.FSH.initialize(outlvl=logging.INFO)
m.fs.RH.initialize(outlvl=logging.INFO)
m.fs.PlSH.initialize(outlvl=logging.INFO)
m.fs.Water_wall.initialize(outlvl=logging.INFO)
m.fs.Spl1.initialize(outlvl=logging.INFO)
m.fs.mix1.initialize(outlvl=logging.INFO)
m.fs.ATMP1.initialize(outlvl=logging.INFO)
print('initialization done')
def test_initialize_dyn(build_turbine_dyn):
"""Initialize a turbine model"""
m = build_turbine_dyn
hin = iapws95.htpx(T=880, P=2.4233e7)
"""
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.steam_prop = Iapws95ParameterBlock()
m.fs.therminol66_prop = ThermalOilParameterBlock()
m.fs.discharge_hx = HeatExchanger(
default={"hot_side_name": "tube", "cold_side_name": "shell",
"tube": {"property_package": m.fs.therminol66_prop},
"shell": {"property_package": m.fs.steam_prop},
"flow_pattern": HeatExchangerFlowPattern.countercurrent})
# Set inputs
#Steam
m.fs.discharge_hx.inlet_2.flow_mol[0].fix(4163)
m.fs.discharge_hx.inlet_2.pressure[0].fix(1.379e+6)
m.fs.discharge_hx.inlet_2.enth_mol[0].fix(htpx(T=300.15*units.K,
P=1.379e+6*units.Pa))
#Thermal Oil
m.fs.discharge_hx.inlet_1.flow_mass[0].fix(833.3)
m.fs.discharge_hx.inlet_1.temperature[0].fix(256 + 273.15)
m.fs.discharge_hx.inlet_1.pressure[0].fix(101325)
#Designate the Area
m.fs.discharge_hx.area.fix(12180)
m.fs.discharge_hx.overall_heat_transfer_coefficient.fix(432.677)
#Designate the U Value.
print("Degrees of Freedom =", degrees_of_freedom(m))
def test_boiler_hx():
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.properties = PhysicalParameterTestBlock()
m.fs.prop_steam = iapws95.Iapws95ParameterBlock()
m.fs.prop_fluegas = FlueGasParameterBlock()
m.fs.unit = BoilerHeatExchanger(
default={
"side_1_property_package": m.fs.prop_steam,
"side_2_property_package": m.fs.prop_fluegas,
"has_pressure_change": True,
"has_holdup": False,
"delta_T_method": DeltaTMethod.counterCurrent,
"tube_arrangement": TubeArrangement.inLine,
"side_1_water_phase": "Liq",
"has_radiation": True
})
# Set inputs
h = iapws95.htpx(773.15, 2.5449e7)
print(h)
m.fs.unit.side_1_inlet.flow_mol[0].fix(24678.26) # mol/s
m.fs.unit.side_1_inlet.enth_mol[0].fix(h) # J/mol
m.fs.unit.side_1_inlet.pressure[0].fix(2.5449e7) # Pascals
# FLUE GAS Inlet from Primary Superheater
FGrate = 28.3876e3 * 0.18 # mol/s equivalent of ~1930.08 klb/hr
# Use FG molar composition to set component flow rates (baseline report)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.unit.side_2_inlet.temperature[0].fix(1102.335)
m.fs.unit.side_2_inlet.pressure[0].fix(100145)
# Primary Superheater
ITM = 0.0254 # inch to meter conversion
m.fs.unit.tube_di.fix((2.5 - 2 * 0.165) * ITM)
m.fs.unit.tube_thickness.fix(0.165 * ITM)
m.fs.unit.pitch_x.fix(3 * ITM)
# gas path transverse width 54.78 ft / number of columns
m.fs.unit.pitch_y.fix(54.78 / 108 * 12 * ITM)
m.fs.unit.tube_length.fix(53.13 * 12 * ITM)
m.fs.unit.tube_nrow.fix(20 * 2)
m.fs.unit.tube_ncol.fix(108)
m.fs.unit.nrow_inlet.fix(4)
m.fs.unit.delta_elevation.fix(50)
m.fs.unit.tube_r_fouling = 0.000176 # (0.001 h-ft^2-F/BTU)
m.fs.unit.tube_r_fouling = 0.003131 # (0.03131 - 0.1779 h-ft^2-F/BTU)
if m.fs.unit.config.has_radiation is True:
m.fs.unit.emissivity_wall.fix(0.7) # wall emissivity
# correction factor for overall heat transfer coefficient
m.fs.unit.fcorrection_htc.fix(1.5)
# correction factor for pressure drop calc tube side
m.fs.unit.fcorrection_dp_tube.fix(1.0)
# correction factor for pressure drop calc shell side
m.fs.unit.fcorrection_dp_shell.fix(1.0)
assert degrees_of_freedom(m) == 0
m.fs.unit.initialize()
# Create a solver
solver = SolverFactory('ipopt')
results = solver.solve(m)
# Check for optimal solution
assert results.solver.termination_condition == \
TerminationCondition.optimal
assert results.solver.status == SolverStatus.ok
assert value(m.fs.unit.side_1.properties_out[0].temperature) == \
pytest.approx(588.07, 1)
assert value(m.fs.unit.side_2.properties_out[0].temperature) == \
pytest.approx(573.07, 1)
def test_initialize():
"""Make a turbine model and make sure it doesn't throw exception"""
m = build_turbine_for_run_test()
turb = m.fs.turb
# Set the inlet of the turbine
p = 2.4233e7
hin = pyo.value(iapws95.htpx(T=880 * pyo.units.K, P=p * pyo.units.Pa))
m.fs.turb.inlet_split.inlet.enth_mol[0].fix(hin)
m.fs.turb.inlet_split.inlet.flow_mol[0].fix(26000)
m.fs.turb.inlet_split.inlet.pressure[0].fix(p)
# Set the inlet of the ip section, which is disconnected
# here to insert reheater
p = 7.802e+06
hin = pyo.value(iapws95.htpx(T=880 * pyo.units.K, P=p * pyo.units.Pa))
m.fs.turb.ip_stages[1].inlet.enth_mol[0].value = hin
m.fs.turb.ip_stages[1].inlet.flow_mol[0].value = 25220.0
m.fs.turb.ip_stages[1].inlet.pressure[0].value = p
for i, s in turb.hp_stages.items():
s.ratioP[:] = 0.88
s.efficiency_isentropic[:] = 0.9
for i, s in turb.ip_stages.items():
s.ratioP[:] = 0.85
s.efficiency_isentropic[:] = 0.9
for i, s in turb.lp_stages.items():
s.ratioP[:] = 0.82
s.efficiency_isentropic[:] = 0.9
turb.hp_split[4].split_fraction[0, "outlet_2"].fix(0.03)
turb.hp_split[7].split_fraction[0, "outlet_2"].fix(0.03)
turb.ip_split[5].split_fraction[0, "outlet_2"].fix(0.04)
turb.ip_split[14].split_fraction[0, "outlet_2"].fix(0.04)
turb.ip_split[14].split_fraction[0, "outlet_3"].fix(0.15)
turb.lp_split[4].split_fraction[0, "outlet_2"].fix(0.04)
turb.lp_split[7].split_fraction[0, "outlet_2"].fix(0.04)
turb.lp_split[9].split_fraction[0, "outlet_2"].fix(0.04)
turb.lp_split[11].split_fraction[0, "outlet_2"].fix(0.04)
# Congiure with reheater for a full test
turb.ip_stages[1].inlet.fix()
for i in turb.throttle_valve:
turb.throttle_valve[i].Cv.fix()
turb.throttle_valve[i].valve_opening.fix()
turb.inlet_split.inlet.flow_mol.unfix()
turb.inlet_mix.use_equal_pressure_constraint()
iscale.calculate_scaling_factors(m)
turb.initialize(outlvl=1)
turb.ip_stages[1].inlet.unfix()
for t in m.fs.time:
m.fs.reheat.inlet.flow_mol[t].value = \
pyo.value(turb.hp_split[7].outlet_1_state[t].flow_mol)
m.fs.reheat.inlet.enth_mol[t].value = \
pyo.value(turb.hp_split[7].outlet_1_state[t].enth_mol)
m.fs.reheat.inlet.pressure[t].value = \
pyo.value(turb.hp_split[7].outlet_1_state[t].pressure)
m.fs.reheat.initialize(outlvl=4)
def reheat_T_rule(b, t):
return m.fs.reheat.control_volume.properties_out[t].temperature == 880
m.fs.reheat.temperature_out_equation = pyo.Constraint(
m.fs.reheat.flowsheet().config.time, rule=reheat_T_rule)
pyo.TransformationFactory("network.expand_arcs").apply_to(m)
m.fs.turb.outlet_stage.control_volume.properties_out[0].pressure.fix()
assert degrees_of_freedom(m) == 0
solver.solve(m, tee=True)
eq_cons = activated_equalities_generator(m)
for c in eq_cons:
assert abs(c.body() - c.lower) < 1e-4
return m
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.steam_prop = Iapws95ParameterBlock()
m.fs.therminol66_prop = ThermalOilParameterBlock()
m.fs.charge_hx = HeatExchanger(
default={"shell": {"property_package": m.fs.steam_prop},
"tube": {"property_package": m.fs.therminol66_prop},
"flow_pattern": HeatExchangerFlowPattern.countercurrent})
# Set inputs
#Steam
m.fs.charge_hx.inlet_1.flow_mol[0].fix(4163)
m.fs.charge_hx.inlet_1.enth_mol[0].fix(htpx(T=573.15*units.K,
P=5.0e+6*units.Pa))
m.fs.charge_hx.inlet_1.pressure[0].fix(5.0e+6)
#Thermal Oil
m.fs.charge_hx.inlet_2.flow_mass[0].fix(833.3)
m.fs.charge_hx.inlet_2.temperature[0].fix(200 + 273.15)
m.fs.charge_hx.inlet_2.pressure[0].fix(101325)
m.fs.charge_hx.area.fix(12180)
m.fs.charge_hx.overall_heat_transfer_coefficient.fix(432.677)
print("Degrees of Freedom =", degrees_of_freedom(m))
m.fs.charge_hx.initialize()
def th(
delta_temperature_callback=delta_temperature_underwood_tune_callback,
tout_1=809.55,
tout_2=788.53,
):
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.properties = PhysicalParameterTestBlock()
m.fs.prop_steam = iapws95.Iapws95ParameterBlock()
m.fs.prop_fluegas = FlueGasParameterBlock()
m.fs.unit = BoilerHeatExchanger(
default={
"delta_temperature_callback": delta_temperature_callback,
"tube": {
"property_package": m.fs.prop_steam
},
"shell": {
"property_package": m.fs.prop_fluegas
},
"has_pressure_change": True,
"has_holdup": False,
"flow_pattern": HeatExchangerFlowPattern.countercurrent,
"tube_arrangement": TubeArrangement.inLine,
"side_1_water_phase": "Liq",
"has_radiation": True,
})
# Set inputs
h = value(iapws95.htpx(773.15 * pyunits.K, 2.5449e7 * pyunits.Pa))
m.fs.unit.side_1_inlet.flow_mol[0].fix(24678.26) # mol/s
m.fs.unit.side_1_inlet.enth_mol[0].fix(h) # J/mol
m.fs.unit.side_1_inlet.pressure[0].fix(2.5449e7) # Pascals
# FLUE GAS Inlet from Primary Superheater
FGrate = 28.3876e3 * 0.18 # mol/s equivalent of ~1930.08 klb/hr
# Use FG molar composition to set component flow rates (baseline report)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "H2O"].fix(FGrate * 8.69 / 100)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "CO2"].fix(FGrate * 14.49 / 100)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "N2"].fix(FGrate * 74.34 / 100)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "O2"].fix(FGrate * 2.47 / 100)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "NO"].fix(FGrate * 0.0006)
m.fs.unit.side_2_inlet.flow_mol_comp[0, "SO2"].fix(FGrate * 0.002)
m.fs.unit.side_2_inlet.temperature[0].fix(1102.335)
m.fs.unit.side_2_inlet.pressure[0].fix(100145)
# Primary Superheater
ITM = 0.0254 # inch to meter conversion
m.fs.unit.tube_di.fix((2.5 - 2 * 0.165) * ITM)
m.fs.unit.tube_thickness.fix(0.165 * ITM)
m.fs.unit.pitch_x.fix(3 * ITM)
# gas path transverse width 54.78 ft / number of columns
m.fs.unit.pitch_y.fix(54.78 / 108 * 12 * ITM)
m.fs.unit.tube_length.fix(53.13 * 12 * ITM)
m.fs.unit.tube_nrow.fix(20 * 2)
m.fs.unit.tube_ncol.fix(108)
m.fs.unit.nrow_inlet.fix(4)
m.fs.unit.delta_elevation.fix(50)
m.fs.unit.tube_r_fouling = 0.000176 # (0.001 h-ft^2-F/BTU)
m.fs.unit.tube_r_fouling = 0.003131 # (0.03131 - 0.1779 h-ft^2-F/BTU)
if m.fs.unit.config.has_radiation is True:
m.fs.unit.emissivity_wall.fix(0.7) # wall emissivity
# correction factor for overall heat transfer coefficient
m.fs.unit.fcorrection_htc.fix(1.5)
# correction factor for pressure drop calc tube side
m.fs.unit.fcorrection_dp_tube.fix(1.0)
# correction factor for pressure drop calc shell side
m.fs.unit.fcorrection_dp_shell.fix(1.0)
assert degrees_of_freedom(m) == 0
iscale.calculate_scaling_factors(m)
m.fs.unit.initialize()
results = solver.solve(m)
# Check for optimal solution
assert check_optimal_termination(results)
assert value(
m.fs.unit.side_1.properties_out[0].temperature) == pytest.approx(
tout_1, abs=0.5)
assert value(
m.fs.unit.side_2.properties_out[0].temperature) == pytest.approx(
tout_2, abs=0.5)
