Supercritical Steam Cycle Example#

Maintainer: Andrew Lee
Author: Andrew Lee

This example uses Jupyter Lab or Jupyter notebook, and demonstrates a supercritical pulverized coal (SCPC) steam cycle model. See the supercritical_steam_cycle.py to see more information on how to assemble a power plant model flowsheet. Code comments in that file will guide you through the process.

Model Description#

The example model doesn’t represent any particular power plant, but should be a reasonable approximation of a typical plant. The gross power output is about 620 MW. The process flow diagram (PFD) can be shown using the code below. The initial PFD contains spaces for model results, to be filled in later.

To get a more detailed look at the model structure, you may find it useful to review supercritical_steam_cycle.py first. Although there is no detailed boiler model, there are constraints in the model to complete the steam loop through the boiler and calculate boiler heat input to the steam cycle. The efficiency calculation for the steam cycle doesn’t account for heat loss in the boiler, which would be a result of a more detailed boiler model.

# pkg_resources is used here to get the svg information from the
# installed IDAES package

import pkg_resources
from IPython.display import SVG, display

# Get the contents of the PFD (which is an svg file)
init_pfd = pkg_resources.resource_string(
    "idaes.models_extra.power_generation.flowsheets.supercritical_steam_cycle",
    "supercritical_steam_cycle.svg",
)

# Make the svg contents into an SVG object and display it.
display(SVG(init_pfd))

/tmp/ipykernel_1377/1084714406.py:4: DeprecationWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html
  import pkg_resources
../../../_images/ffa7ad7b99d4bb609ab7442bf5a3c75113cb024844500ca0d004c0296404e941.svg

Initialize the steam cycle flowsheet#

This example is part of the idaes package, which you should have installed. To run the example, the example flowsheet is imported from the idaes package. When you write your own model, you can import and run it in whatever way is appropriate for you. The Pyomo environment is also imported as pyo, providing easy access to Pyomo functions and classes.

The supercritical flowsheet example main function returns a Pyomo concrete mode (m) and a solver object (solver). The model is also initialized by the main() function.

import pyomo.environ as pyo
from idaes.models_extra.power_generation.flowsheets.supercritical_steam_cycle import (
    main,
    pfd_result,
)
from idaes.core.util.tables import create_stream_table_dataframe

m, solver = main()

2024-05-09 18:34:39 [ERROR] idaes.core.base.process_block: Failure in build: fs.prop_water
Traceback (most recent call last):
  File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/core/base/process_block.py", line 41, in _rule_default
    b.build()
  File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/general_helmholtz/helmholtz_functions.py", line 1441, in build
    raise RuntimeError("Helmholtz EoS external functions not available")
RuntimeError: Helmholtz EoS external functions not available

ERROR: Constructing component 'fs.prop_water' from data=None failed:
        RuntimeError: Helmholtz EoS external functions not available

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
Cell In[2], line 8
      2 from idaes.models_extra.power_generation.flowsheets.supercritical_steam_cycle import (
      3     main,
      4     pfd_result,
      5 )
      6 from idaes.core.util.tables import create_stream_table_dataframe
----> 8 m, solver = main()

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models_extra/power_generation/flowsheets/supercritical_steam_cycle/supercritical_steam_cycle.py:980, in main(initialize_from_file, store_initialization)
    971 def main(initialize_from_file=None, store_initialization=None):
    972     """Create and initialize a model and solver
    973 
    974     Args:
   (...)
    978         A tuple of a model and solver
    979     """
--> 980     m = create_model()
    981     _stream_dict(m)
    982     set_model_input(m)

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models_extra/power_generation/flowsheets/supercritical_steam_cycle/supercritical_steam_cycle.py:88, in create_model()
     83 m.fs = FlowsheetBlock(dynamic=False)  # Add steady state flowsheet
     85 # A physical property parameter block for IAPWS-95 with pressure and enthalpy
     86 # (PH) state variables.  Usually pressure and enthalpy state variables are
     87 # more robust especially when the phases are unknown.
---> 88 m.fs.prop_water = iapws95.Iapws95ParameterBlock(
     89     phase_presentation=iapws95.PhaseType.MIX
     90 )
     92 # A physical property parameter block with temperature, pressure and vapor
     93 # fraction (TPx) state variables. There are a few instances where the vapor
     94 # fraction is known and the temperature and pressure state variables are
     95 # preferable.
     96 m.fs.prop_water_tpx = iapws95.Iapws95ParameterBlock(
     97     phase_presentation=iapws95.PhaseType.LG, state_vars=iapws95.StateVars.TPX
     98 )

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:571, in BlockData.__setattr__(self, name, val)
    566 if name not in self.__dict__:
    567     if isinstance(val, Component):
    568         #
    569         # Pyomo components are added with the add_component method.
    570         #
--> 571         self.add_component(name, val)
    572     else:
    573         #
    574         # Other Python objects are added with the standard __setattr__
    575         # method.
    576         #
    577         super(BlockData, self).__setattr__(name, val)

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:1129, in BlockData.add_component(self, name, val)
   1121     logger.debug(
   1122         "Constructing %s '%s' on %s from data=%s",
   1123         val.__class__.__name__,
   (...)
   1126         str(data),
   1127     )
   1128 try:
-> 1129     val.construct(data)
   1130 except:
   1131     err = sys.exc_info()[1]

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:2186, in Block.construct(self, data)
   2184                     obj.construct(data.get(name, None))
   2185         # Trigger the (normal) initialization of the block
-> 2186         self._getitem_when_not_present(_idx)
   2187 finally:
   2188     # We must allow that id(self) may no longer be in
   2189     # _BlockConstruction.data, as _getitem_when_not_present will
   2190     # have already removed the entry for scalar blocks (as the
   2191     # BlockData and the Block component are the same object)
   2192     if data is not None:

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:2101, in Block._getitem_when_not_present(self, idx)
   2098     data = None
   2100 try:
-> 2101     obj = self._rule(_block, idx)
   2102     # If the user returns a block, transfer over everything
   2103     # they defined into the empty one we created.  We do
   2104     # this inside the try block so that any abstract
   2105     # components declared by the rule have the opportunity
   2106     # to be initialized with data from
   2107     # _BlockConstruction.data as they are transferred over.
   2108     if obj is not _block and isinstance(obj, BlockData):

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/initializer.py:316, in IndexedCallInitializer.__call__(self, parent, idx)
    314     return self._fcn(parent, *idx)
    315 else:
--> 316     return self._fcn(parent, idx)

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/core/base/process_block.py:41, in _rule_default(b, *args)
     35 """
     36 Default rule for ProcessBlock, which calls build(). A different rule can
     37 be specified to add additional build steps, or to not call build at all
     38 using the normal rule argument to ProcessBlock init.
     39 """
     40 try:
---> 41     b.build()
     42 except Exception:
     43     logging.getLogger(__name__).exception(f"Failure in build: {b}")

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/general_helmholtz/helmholtz_functions.py:1441, in HelmholtzParameterBlockData.build(self)
   1439 """Populate the parameter block"""
   1440 if not self.available():
-> 1441     raise RuntimeError("Helmholtz EoS external functions not available")
   1442 super().build()
   1443 # Check if the specified component is supported

RuntimeError: Helmholtz EoS external functions not available

Inside the model, there is a subblock fs. This is an IDAES flowsheet model, which contains the supercritical steam cycle model. In the flowsheet, the model called turb is a multistage turbine model. The turbine model contains an expression for total power, power. In this case the model is steady-state, but all IDAES models allow for dynamic simulation, and contain time indexes. Power is indexed by time, and only the “0” time point exists. By convention, in the IDAES framework, power going into a model is positive, so power produced by the turbine is negative.

The property package used for this model uses SI (mks) units of measure, so the power is in Watts. Here a function is defined which can be used to report power output in MW.

# Define a function to report gross power output in MW
def gross_power_mw(model):
    # pyo.value(m.fs.turb.power[0]) is the power consumed in Watts
    return -pyo.value(model.fs.turb.power[0]) / 1e6


# Show the gross power
gross_power_mw(m)

622.3884026414165

Change the model inputs#

The turbine in this example simulates partial arc admission with four arcs, so there are four throttle valves. For this example, we will close one of the valves to 25% open, and observe the result.

m.fs.turb.throttle_valve[1].valve_opening[:].value = 0.25

Next, we re-solve the model using the solver created by the supercritical_steam_cycle.py script.

solver.solve(m, tee=True)

WARNING: model contains export suffix
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Skipping.

WARNING: model contains export suffix
'fs.fwh2.desuperheat.hot_side.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.fwh2.desuperheat.hot_side.properties_in[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh2.drain_mix.mixed_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh2.drain_mix.drain_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh2.drain_mix.steam_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh2.condense.cold_side.properties_out[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh2.condense.cold_side.properties_in[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh2.condense.hot_side.properties_out[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh2.condense.hot_side.properties_in[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1_return.mixed_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1_return.fwh1_drain_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1_return.feedwater_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1_pump.control_volume.properties_out[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1_pump.control_volume.properties_in[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1_pump.control_volume.scaling_factor' that contains 1 component keys
that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1.drain_mix.mixed_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1.drain_mix.drain_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1.drain_mix.steam_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1.condense.cold_side.properties_out[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1.condense.cold_side.properties_in[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1.condense.hot_side.properties_out[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.fwh1.condense.hot_side.properties_in[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.cond_pump.control_volume.properties_out[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.cond_pump.control_volume.properties_in[0.0].scaling_factor' that contains
60 component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.cond_pump.control_volume.scaling_factor' that contains 1 component keys
that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.hotwell.mixed_state[0.0].scaling_factor' that contains 60 component keys
that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.hotwell.makeup_state[0.0].scaling_factor' that contains 62 component keys
that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.hotwell.condensate_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.condenser.cold_side.properties_out[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.condenser.cold_side.properties_in[0.0].scaling_factor' that contains 63
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.condenser.hot_side.properties_out[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.condenser.hot_side.properties_in[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix 'fs.condenser.scaling_factor' that
contains 2 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.condenser_mix.mixed_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.condenser_mix.bfpt_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.condenser_mix.main_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[11].outlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[11].outlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[11].mixed_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[10].outlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[10].outlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[10].mixed_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[8].outlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[8].outlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[8].mixed_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[4].outlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[4].outlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.lp_split[4].mixed_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.ip_split[10].outlet_3_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.ip_split[10].outlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.ip_split[10].outlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.ip_split[10].mixed_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.ip_split[5].outlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.ip_split[5].outlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.ip_split[5].mixed_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.hp_split[7].outlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.hp_split[7].outlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.hp_split[7].mixed_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.hp_split[4].outlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.hp_split[4].outlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.hp_split[4].mixed_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.outlet_stage.control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.outlet_stage.control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[11].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[11].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[10].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[10].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[9].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[9].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[8].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[8].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[7].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[7].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[6].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[6].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[5].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[5].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[4].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[4].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[3].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[3].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[2].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[2].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[1].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.lp_stages[1].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[10].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[10].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[9].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[9].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[8].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[8].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[7].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[7].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[6].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[6].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[5].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[5].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[4].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[4].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[3].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[3].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[2].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[2].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[1].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.ip_stages[1].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[7].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[7].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[6].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[6].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[5].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[5].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[4].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[4].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[3].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[3].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[2].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[2].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[1].control_volume.properties_out[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.hp_stages[1].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_mix.mixed_state[0.0].scaling_factor' that contains 60 component
keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_mix.inlet_4_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_mix.inlet_3_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_mix.inlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_mix.inlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_stage[4].control_volume.properties_out[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_stage[4].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_stage[3].control_volume.properties_out[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_stage[3].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_stage[2].control_volume.properties_out[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_stage[2].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_stage[1].control_volume.properties_out[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_stage[1].control_volume.properties_in[0.0].scaling_factor' that
contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.throttle_valve[4].control_volume.properties_out[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.throttle_valve[4].control_volume.properties_in[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.throttle_valve[3].control_volume.properties_out[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.throttle_valve[3].control_volume.properties_in[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.throttle_valve[2].control_volume.properties_out[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.throttle_valve[2].control_volume.properties_in[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.throttle_valve[1].control_volume.properties_out[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.throttle_valve[1].control_volume.properties_in[0.0].scaling_factor'
that contains 60 component keys that are not exported as part of the NL file.
Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_split.outlet_4_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_split.outlet_3_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_split.outlet_2_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_split.outlet_1_state[0.0].scaling_factor' that contains 60
component keys that are not exported as part of the NL file.  Skipping.

WARNING: model contains export suffix
'fs.turb.inlet_split.mixed_state[0.0].scaling_factor' that contains 62
component keys that are not exported as part of the NL file.  Skipping.

Ipopt 3.13.2: nlp_scaling_method=gradient-based
tol=1e-06
max_iter=200

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit http://projects.coin-or.org/Ipopt

This version of Ipopt was compiled from source code available at
    https://github.com/IDAES/Ipopt as part of the Institute for the Design of
    Advanced Energy Systems Process Systems Engineering Framework (IDAES PSE
    Framework) Copyright (c) 2018-2019. See https://github.com/IDAES/idaes-pse.

This version of Ipopt was compiled using HSL, a collection of Fortran codes
    for large-scale scientific computation.  All technical papers, sales and
    publicity material resulting from use of the HSL codes within IPOPT must
    contain the following acknowledgement:
        HSL, a collection of Fortran codes for large-scale scientific
        computation. See http://www.hsl.rl.ac.uk.
******************************************************************************

This is Ipopt version 3.13.2, running with linear solver ma27.

Number of nonzeros in equality constraint Jacobian...:     2341
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:     1021

Total number of variables............................:      858
                     variables with only lower bounds:        0
                variables with lower and upper bounds:      444
                     variables with only upper bounds:        0
Total number of equality constraints.................:      858
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  0.0000000e+00 3.51e-01 0.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0

   1  0.0000000e+00 3.46e-01 8.48e+01  -1.0 2.63e+07    -  9.82e-01 1.56e-02h  7

   2  0.0000000e+00 3.41e-01 8.75e+01  -1.0 2.61e+07    -  9.83e-01 1.56e-02h  7

   3  0.0000000e+00 3.35e-01 8.51e+01  -1.0 2.59e+07    -  9.88e-01 1.56e-02h  7

   4  0.0000000e+00 3.30e-01 8.25e+01  -1.0 2.56e+07    -  9.88e-01 1.56e-02h  7

   5  0.0000000e+00 3.25e-01 7.99e+01  -1.0 2.54e+07    -  9.92e-01 1.56e-02h  7

   6  0.0000000e+00 3.20e-01 7.74e+01  -1.0 2.52e+07    -  1.00e+00 1.56e-02h  7

   7  0.0000000e+00 3.15e-01 7.50e+01  -1.0 2.50e+07    -  1.00e+00 1.56e-02h  7

   8  0.0000000e+00 3.10e-01 7.26e+01  -1.0 2.48e+07    -  1.00e+00 1.56e-02h  7

   9  0.0000000e+00 3.05e-01 7.03e+01  -1.7 2.46e+07    -  1.00e+00 1.56e-02h  7

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10  0.0000000e+00 3.00e-01 6.80e+01  -1.7 2.44e+07    -  1.00e+00 1.56e-02h  7

  11  0.0000000e+00 2.96e-01 6.58e+01  -1.7 2.42e+07    -  1.00e+00 1.56e-02h  7

  12  0.0000000e+00 2.91e-01 6.37e+01  -1.7 2.40e+07    -  1.00e+00 1.56e-02h  7

  13  0.0000000e+00 2.87e-01 6.17e+01  -1.7 2.37e+07    -  1.00e+00 1.56e-02h  7

  14  0.0000000e+00 2.82e-01 5.96e+01  -1.7 2.35e+07    -  1.00e+00 1.56e-02h  7

  15  0.0000000e+00 2.78e-01 5.77e+01  -1.7 2.33e+07    -  1.00e+00 1.56e-02h  7

  16  0.0000000e+00 2.73e-01 5.58e+01  -1.7 2.31e+07    -  1.00e+00 1.56e-02h  7

  17  0.0000000e+00 2.69e-01 5.39e+01  -1.7 2.29e+07    -  1.00e+00 1.56e-02h  7

  18  0.0000000e+00 2.65e-01 5.22e+01  -1.7 2.27e+07    -  1.00e+00 1.56e-02h  7

  19  0.0000000e+00 5.87e+01 3.75e+03  -1.7 2.25e+07    -  1.00e+00 1.00e+00w  1

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  20  0.0000000e+00 2.58e+01 8.24e+01  -1.7 7.28e+06    -  1.00e+00 1.00e+00w  1
  21  0.0000000e+00 1.46e-01 5.49e-01  -1.7 5.67e+05    -  1.00e+00 1.00e+00h  1

  22  0.0000000e+00 4.29e-06 4.85e-05  -1.7 3.35e+03    -  1.00e+00 1.00e+00h  1

Number of Iterations....: 22

                                   (scaled)                 (unscaled)
Objective...............:   0.0000000000000000e+00    0.0000000000000000e+00
Dual infeasibility......:   0.0000000000000000e+00    0.0000000000000000e+00
Constraint violation....:   3.6219717003405094e-08    4.2896717786788940e-06
Complementarity.........:   0.0000000000000000e+00    0.0000000000000000e+00
Overall NLP error.......:   3.6219717003405094e-08    4.2896717786788940e-06


Number of objective function evaluations             = 203
Number of objective gradient evaluations             = 23
Number of equality constraint evaluations            = 203
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 23
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 22
Total CPU secs in IPOPT (w/o function evaluations)   =      0.413
Total CPU secs in NLP function evaluations           =     58.164

EXIT: Optimal Solution Found.

{'Problem': [{'Lower bound': -inf, 'Upper bound': inf, 'Number of objectives': 1, 'Number of constraints': 858, 'Number of variables': 858, 'Sense': 'unknown'}], 'Solver': [{'Status': 'ok', 'Message': 'Ipopt 3.13.2\\x3a Optimal Solution Found', 'Termination condition': 'optimal', 'Id': 0, 'Error rc': 0, 'Time': 58.77723503112793}], 'Solution': [OrderedDict([('number of solutions', 0), ('number of solutions displayed', 0)])]}

Now we can check the gross power output again.

gross_power_mw(m)

594.6634894062614

Creating a PFD with results and a stream table#

A more detailed look at the model results can be obtained by creating a stream table and putting key results on the PFD. Of course, any unit model or stream result can be obtained from the model.

# Create a Pandas dataframe with stream results
df = create_stream_table_dataframe(streams=m._streams, orient="index")

# Create a new PFD with simulation results
res_pfd = pfd_result(m, df, svg=init_pfd)

# Display PFD with results.
display(SVG(res_pfd))
../../../_images/7b8c8dc6db8cad75534bf1b1b25cebc482d61fa2123f41b4e281d6a2b8056bb4.svg
# Display the stream table.
df
Molar Flow Mass Flow T P Vapor Fraction Molar Enthalpy
Units mole / second kilogram / second kelvin pascal dimensionless joule / mole
COND_01 17752.680698 319.819301 301.687808 3903.244367 0.0 2155.010494
COND_02 17752.680698 319.819301 301.687808 3903.244367 0.0 2155.010494
COND_03 17752.680698 319.819301 301.768944 1003903.244367 0.0 2177.614149
CW01 2500000 45038.17 295.536861 500000 0.0 1700
CW02 2500000.0 45038.17 299.504714 500000.0 0.0 1998.82683
EXHST_BFPT 1868.202969 33.656177 301.687808 3903.244367 0.995438 45791.271303
EXHST_MAIN 15884.47773 286.163123 301.687808 3903.244367 0.95581 44054.13332
EXTR_BFPT_A 1868.202969 33.656177 523.019743 341629.073316 1.0 53436.755973
EXTR_HP4 1785.002753 32.157303 689.81885 8004585.263907 1.0 57382.396471
EXTR_HP7 1256.160836 22.630074 597.344823 4098347.65512 1.0 54488.822683
EXTR_IP10 882.779889 15.903516 523.019743 341629.073316 1.0 53436.755973
EXTR_IP5 872.73243 15.722509 676.748649 1183264.430102 1.0 58896.697245
EXTR_LP10 149.150914 2.686994 335.245948 21962.953684 0.958364 45299.885617
EXTR_LP11 413.26152 7.445017 329.351251 16691.8448 0.9478 44653.506513
EXTR_LP4 275.725374 4.967267 413.655212 113974.892707 1.0 49660.709547
EXTR_LP8 143.732463 2.589379 347.794222 38024.504301 0.980791 46648.886248
FW01A 17752.680698 319.819301 314.196315 1003903.244367 0.0 3112.798156
FW01B 18734.550969 337.507957 314.999488 1003903.244367 0.0 3173.242224
FW02 18734.550969 337.507957 319.589523 1003903.244367 0.0 3518.711421
FW03 18734.550969 337.507957 324.035742 1003903.244367 0.0 3853.440557
FW04 18734.550969 337.507957 332.610921 1003903.244367 0.0 4499.343989
FW05A 23531.226877 423.921359 376.645137 1003903.244367 0.0 7829.048167
FW05B 23531.226877 423.921359 380.085034 26922222.222222 0.0 8436.042321
FW06 23531.226877 423.921359 411.316976 26922222.222222 0.0 10790.741011
FW07 23531.226877 423.921359 439.458355 26922222.222222 0.0 12937.958691
FW08 23531.226877 423.921359 474.205958 26922222.222222 0.0 15639.852538
FWH1_DRN1 981.870271 17.688656 329.351251 16691.8448 0.0 4238.674177
FWH1_DRN2 981.870271 17.688656 329.471936 1216691.8448 0.0 4266.099683
FWH2_DRN 568.60875 10.243639 327.019485 21962.953684 0.0 4063.031468
FWH3_DRN 419.457837 7.556645 337.189254 38024.504301 0.0 4829.96387
FWH4_DRN 275.725374 4.967267 349.678211 113974.892707 0.0 5773.886242
FWH6_DRN 3913.89602 70.509886 449.769309 1183264.430102 0.0 13480.436276
FWH7_DRN 3041.163589 54.787377 512.845012 4098347.65512 0.0 18666.841026
FWH8_DRN 1785.002753 32.157303 547.774255 8004585.263907 0.0 21764.032855
MAKEUP_01 0.0 0.0 306.248085 101325 0.0 2500
RHT_COLD 20490.063288 369.133981 597.344823 4098347.65512 1.0 54488.822683
RHT_HOT 20490.063288 369.133981 866.0 4098347.65512 1.0 65893.572327
STEAM_LP 16866.348 303.851779 523.019743 341629.073316 1.0 53436.755973
STEAM_MAIN 23531.226877 423.921359 866.4817 24230000.0 0.0 62710
THRTL1 3025.648119 54.507862 852.999851 20155950.787034 1.0 62710.0
THRTL2 6835.19292 123.137832 861.573043 22713089.898646 0.0 62710.0
THRTL3 6835.19292 123.137832 861.573043 22713089.898646 0.0 62710.0
THRTL4 6835.19292 123.137832 861.573043 22713089.898646 0.0 62710.0
condenser_mix_to_condenser 17752.680698 319.819301 301.687808 3903.244367 0.95998 44236.940998