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###############################################################################
# The Institute for the Design of Advanced Energy Systems Integrated Platform
# Framework (IDAES IP) was produced under the DOE Institute for the
# Design of Advanced Energy Systems (IDAES).
#
# Copyright (c) 2018-2023 by the software owners: The Regents of the
# University of California, through Lawrence Berkeley National Laboratory,
# National Technology & Engineering Solutions of Sandia, LLC, Carnegie Mellon
# University, West Virginia University Research Corporation, et al.
# All rights reserved. Please see the files COPYRIGHT.md and LICENSE.md
# for full copyright and license information.
###############################################################################
Using Parameter Estimation with Modular Property Packages#
Author: Alejandro Garciadego
Maintainer: Andrew Lee
Updated: 2023-06-01
1. Introduction#
This Jupyter Notebook estimates binary interaction parameters for a CO\(_2\)-Ionic liquid property package. A property package has been created for CO\(_2\)-[bmim][PF6]. We will utilize Pyomo’s parmest
tool in conjunction with IDAES models for parameter estimation. We demonstrate these tools by estimating the parameters associated with the Peng-Robinson property model for a benzene-toluene mixture. The Peng-Robinson EOS the binary interaction parameter (kappa_ij). When estimating parameters associated with the property package, IDAES provides the flexibility of doing the parameter estimation by just using the state block or by using a unit model with a specified property package. This module will demonstrate parameter estimation by using the flash unit model with a Modular Property Package.
1.1 Tutorial objectives#
Utilize the Modular Property Package framework, which provides a flexible platform for users to build property packages by calling upon libraries of modular sub-models to build up complex property calculations with the least effort possible.
Set up a method to return an initialized model
Set up the parameter estimation problem using
parmest
2. Problem Statement#
2.1 Importing Pyomo and IDAES model and flowsheet components.#
In the next cell, we will be importing the necessary components from Pyomo and IDAES.
# Import objects from pyomo package
from pyomo.environ import ConcreteModel, SolverFactory, units as pyunits
# Import the main FlowsheetBlock from IDAES. The flowsheet block will contain the unit model
from idaes.core import FlowsheetBlock
# Import idaes logger to set output levels
import idaes.logger as idaeslog
# Import Flash unit model from idaes.models.unit_models
from idaes.models.unit_models import Flash
2.2 Import parmest#
import pyomo.contrib.parmest.parmest as parmest
2.3 Import the Modular Property framework#
from idaes.models.properties.modular_properties.examples.CO2_bmimPF6_PR import (
configuration,
)
from idaes.models.properties.modular_properties import GenericParameterBlock
2.4 Import data#
In the next cell, we will be importing pandas
and the .csv
file with preassure and composition data. For this example, we load data from the csv file CO2_IL_298.csv. The dataset consists of ninteen data points which provide the mole fraction of [bmim][PF6] and carbon dioxide and the pressure at three different temperatures.
import pandas as pd
# Load data from csv
data = pd.read_csv("CO2_IL_298.csv")
3.0 Setting up an initialized model#
We need to provide a method that returns an initialized model to the parmest
tool in Pyomo.
How we build the model will depend on the data we provided in the data dataframe from pir .csv file.
In this case we have data on the liquid mixture, the temperature and the pressure. We will fix the temperature, mole franction in the liquid phase, and the mole fraction of the inlet.
def PR_model(data):
m = ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False)
m.fs.properties = GenericParameterBlock(**configuration)
m.fs.state_block = m.fs.properties.build_state_block([1], defined_state=True)
m.fs.state_block[1].flow_mol.fix(1)
x = float(data["x_carbon_dioxide"]) + 0.5
m.fs.state_block[1].temperature.fix(float(data["temperature"]))
m.fs.state_block[1].pressure.fix(float(data["pressure"]))
m.fs.state_block[1].mole_frac_comp["bmimPF6"].fix(1 - x)
m.fs.state_block[1].mole_frac_comp["carbon_dioxide"].fix(x)
# parameter - kappa_ij (set at 0.3, 0 if i=j)
m.fs.properties.PR_kappa["bmimPF6", "bmimPF6"].fix(0)
m.fs.properties.PR_kappa["bmimPF6", "carbon_dioxide"].fix(-0.047)
m.fs.properties.PR_kappa["carbon_dioxide", "carbon_dioxide"].fix(0)
m.fs.properties.PR_kappa["carbon_dioxide", "bmimPF6"].fix(0.002)
# Initialize the flash unit
m.fs.state_block.initialize(outlvl=idaeslog.INFO)
# Fix the state variables on the state block
m.fs.state_block[1].pressure.unfix()
m.fs.state_block[1].temperature.fix(float(data["temperature"]))
m.fs.state_block[1].mole_frac_phase_comp["Liq", "bmimPF6"].fix(
float(data["x_bmimPF6"])
)
m.fs.state_block[1].mole_frac_phase_comp["Liq", "carbon_dioxide"].fix(
float(data["x_carbon_dioxide"])
)
m.fs.state_block[1].mole_frac_comp["bmimPF6"].fix(float(data["x_bmimPF6"]))
m.fs.state_block[1].mole_frac_comp["carbon_dioxide"].unfix()
# Set bounds on variables to be estimated
m.fs.properties.PR_kappa["bmimPF6", "carbon_dioxide"].setlb(-5)
m.fs.properties.PR_kappa["bmimPF6", "carbon_dioxide"].setub(5)
m.fs.properties.PR_kappa["carbon_dioxide", "bmimPF6"].setlb(-5)
m.fs.properties.PR_kappa["carbon_dioxide", "bmimPF6"].setub(5)
# Return initialized flash model
return m
3.1 Solving square problem#
from idaes.core.util.model_statistics import degrees_of_freedom
import pytest
test_data = {
"temperature": 298,
"pressure": 812323,
"x_bmimPF6": 0.86,
"x_carbon_dioxide": 0.14,
}
m = PR_model(test_data)
# Check that degrees of freedom is 0
assert degrees_of_freedom(m) == 0
ERROR: Rule failed when generating expression for Constraint
fs.state_block[1].eq_temperature_bubble with index ('Vap', 'Liq',
'carbon_dioxide'): RuntimeError: Cubic root external functions are not
available.
ERROR: Constructing component 'fs.state_block[1].eq_temperature_bubble' from
data=None failed:
RuntimeError: Cubic root external functions are not available.
ERROR: Rule failed when generating expression for Constraint
fs.state_block[1]._t1_constraint_Vap_Liq with index None: RuntimeError: Cubic
root external functions are not available.
ERROR: Constructing component 'fs.state_block[1]._t1_constraint_Vap_Liq' from
data=None failed:
RuntimeError: Cubic root external functions are not available.
2024-05-09 18:34:58 [ERROR] idaes.core.base.process_block: Failure in build: fs.state_block[1]
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/property_base.py", line 792, in __getattr__
return super().__getattr__(attr)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py", line 550, in __getattr__
raise AttributeError(
AttributeError: 'GenericStateBlockData' object has no attribute 'temperature_bubble'
During handling of the above exception, another exception occurred:
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/modular_properties/base/generic_property.py", line 2446, in build
pe_form_config[pp].phase_equil(self, pp)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/phase_equil/smooth_VLE.py", line 94, in phase_equil
b.add_component("_t1_constraint" + suffix, Constraint(rule=rule_t1))
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py", line 1129, in add_component
val.construct(data)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/disable_methods.py", line 124, in construct
return base.construct(self, data)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/constraint.py", line 720, in construct
self._setitem_when_not_present(index, rule(block, index))
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/initializer.py", line 438, in __call__
return self._fcn(parent)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/phase_equil/smooth_VLE.py", line 91, in rule_t1
b.temperature, b.temperature_bubble[phase_pair], eps_1
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/core/base/property_base.py", line 794, in __getattr__
return build_on_demand(self, attr)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/core/base/util.py", line 220, in build_on_demand
f()
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/base/generic_property.py", line 3036, in _temperature_bubble
_temperature_pressure_bubble_dew(b, "temperature_bubble")
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/base/generic_property.py", line 5069, in _temperature_pressure_bubble_dew
tmp(b)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/phase_equil/bubble_dew.py", line 527, in temperature_bubble
b.eq_temperature_bubble = Constraint(
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py", line 571, in __setattr__
self.add_component(name, val)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py", line 1129, in add_component
val.construct(data)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/constraint.py", line 720, in construct
self._setitem_when_not_present(index, rule(block, index))
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/initializer.py", line 314, in __call__
return self._fcn(parent, *idx)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/phase_equil/bubble_dew.py", line 521, in rule_bubble_temp
return l_eos.log_fug_phase_comp_Tbub(
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/eos/ceos.py", line 819, in log_fug_phase_comp_Tbub
return _bubble_dew_log_fug_coeff_method(blk, p, j, pp, blk.temperature_bubble)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/eos/ceos.py", line 1343, in _bubble_dew_log_fug_coeff_method
expr_write = CubicThermoExpressions(blk)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/eos/ceos_common.py", line 106, in __init__
raise RuntimeError("Cubic root external functions are not available.")
RuntimeError: Cubic root external functions are not available.
ERROR: Constructing component 'fs.state_block' from data=None failed:
RuntimeError: Cubic root external functions are not available.
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/core/base/property_base.py:792, in StateBlockData.__getattr__(self, attr)
788 try:
789 # try the Pyomo Block's __getattr__ method first which will return
790 # decorators for creating components on the block (e.g. Expression,
791 # Constraint, ...).
--> 792 return super().__getattr__(attr)
793 except AttributeError:
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:550, in BlockData.__getattr__(self, val)
548 # Since the base classes don't support getattr, we can just
549 # throw the "normal" AttributeError
--> 550 raise AttributeError(
551 "'%s' object has no attribute '%s'" % (self.__class__.__name__, val)
552 )
AttributeError: 'GenericStateBlockData' object has no attribute 'temperature_bubble'
During handling of the above exception, another exception occurred:
RuntimeError Traceback (most recent call last)
Cell In[7], line 11
2 import pytest
4 test_data = {
5 "temperature": 298,
6 "pressure": 812323,
7 "x_bmimPF6": 0.86,
8 "x_carbon_dioxide": 0.14,
9 }
---> 11 m = PR_model(test_data)
13 # Check that degrees of freedom is 0
14 assert degrees_of_freedom(m) == 0
Cell In[6], line 9, in PR_model(data)
5 m.fs = FlowsheetBlock(dynamic=False)
7 m.fs.properties = GenericParameterBlock(**configuration)
----> 9 m.fs.state_block = m.fs.properties.build_state_block([1], defined_state=True)
11 m.fs.state_block[1].flow_mol.fix(1)
12 x = float(data["x_carbon_dioxide"]) + 0.5
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:2162, in Block.construct(self, data)
2157 if self.index_set().isfinite() and (
2158 self._dense or self._rule is not None
2159 ):
2160 for _idx in self.index_set():
2161 # Trigger population & call the rule
-> 2162 self._getitem_when_not_present(_idx)
2163 else:
2164 # We must check that any pre-existing components are
2165 # constructed. This catches the case where someone is
2166 # building a Concrete model by building (potentially
2167 # pseudo-abstract) sub-blocks and then adding them to a
2168 # Concrete model block.
2169 _idx = next(iter(UnindexedComponent_set))
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/modular_properties/base/generic_property.py:2446, in GenericStateBlockData.build(self)
2444 pe_form_config = self.params.config.phase_equilibrium_state
2445 for pp in self.params._pe_pairs:
-> 2446 pe_form_config[pp].phase_equil(self, pp)
2448 def rule_equilibrium(b, phase1, phase2, j):
2449 if (phase1, j) not in b.phase_component_set or (
2450 phase2,
2451 j,
2452 ) not in b.phase_component_set:
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/phase_equil/smooth_VLE.py:94, in SmoothVLE.phase_equil(b, phase_pair)
89 def rule_t1(b):
90 return _t1 == smooth_max(
91 b.temperature, b.temperature_bubble[phase_pair], eps_1
92 )
---> 94 b.add_component("_t1_constraint" + suffix, Constraint(rule=rule_t1))
95 else:
96 _t1 = b.temperature
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/disable_methods.py:124, in disable_methods.<locals>.class_decorator.<locals>.construct(self, data)
122 self._name = base.__name__
123 self.__class__ = base
--> 124 return base.construct(self, data)
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/constraint.py:720, in Constraint.construct(self, data)
717 else:
718 # Bypass the index validation and create the member directly
719 for index in self.index_set():
--> 720 self._setitem_when_not_present(index, rule(block, index))
721 except Exception:
722 err = sys.exc_info()[1]
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/initializer.py:438, in ScalarCallInitializer.__call__(self, parent, idx)
437 def __call__(self, parent, idx):
--> 438 return self._fcn(parent)
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/phase_equil/smooth_VLE.py:91, in SmoothVLE.phase_equil.<locals>.rule_t1(b)
89 def rule_t1(b):
90 return _t1 == smooth_max(
---> 91 b.temperature, b.temperature_bubble[phase_pair], eps_1
92 )
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/core/base/property_base.py:794, in StateBlockData.__getattr__(self, attr)
792 return super().__getattr__(attr)
793 except AttributeError:
--> 794 return build_on_demand(self, attr)
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/core/base/util.py:220, in build_on_demand(self, attr)
218 if callable(f):
219 try:
--> 220 f()
221 except Exception:
222 # Clear call list and reraise error
223 clear_call_list(self, attr)
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/base/generic_property.py:3036, in GenericStateBlockData._temperature_bubble(b)
3035 def _temperature_bubble(b):
-> 3036 _temperature_pressure_bubble_dew(b, "temperature_bubble")
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/base/generic_property.py:5069, in _temperature_pressure_bubble_dew(b, name)
5055 setattr(
5056 b,
5057 "_mole_frac_" + abbrv,
(...)
5065 ),
5066 )
5068 tmp = getattr(b.params.config.bubble_dew_method, name)
-> 5069 tmp(b)
5071 except AttributeError:
5072 if hasattr(b, name):
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/phase_equil/bubble_dew.py:527, in LogBubbleDew.temperature_bubble(b)
524 else:
525 return b._mole_frac_tbub[p1, p2, j] == 0
--> 527 b.eq_temperature_bubble = Constraint(
528 b.params._pe_pairs, b.component_list, rule=rule_bubble_temp
529 )
530 except AttributeError:
531 b.del_component(b.eq_temperature_bubble)
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/constraint.py:720, in Constraint.construct(self, data)
717 else:
718 # Bypass the index validation and create the member directly
719 for index in self.index_set():
--> 720 self._setitem_when_not_present(index, rule(block, index))
721 except Exception:
722 err = sys.exc_info()[1]
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/initializer.py:314, in IndexedCallInitializer.__call__(self, parent, idx)
308 def __call__(self, parent, idx):
309 # Note: this is called by a component using data from a Set (so
310 # any tuple-like type should have already been checked and
311 # converted to a tuple; or flattening is turned off and it is
312 # the user's responsibility to sort things out.
313 if idx.__class__ is tuple:
--> 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/models/properties/modular_properties/phase_equil/bubble_dew.py:521, in LogBubbleDew.temperature_bubble.<locals>.rule_bubble_temp(b, p1, p2, j)
518 v_eos = b.params.get_phase(v_phase).config.equation_of_state
520 if j in vl_comps or j in henry_comps:
--> 521 return l_eos.log_fug_phase_comp_Tbub(
522 b, l_phase, j, (p1, p2)
523 ) == v_eos.log_fug_phase_comp_Tbub(b, v_phase, j, (p1, p2))
524 else:
525 return b._mole_frac_tbub[p1, p2, j] == 0
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/eos/ceos.py:819, in Cubic.log_fug_phase_comp_Tbub(blk, p, j, pp)
817 @staticmethod
818 def log_fug_phase_comp_Tbub(blk, p, j, pp):
--> 819 return _bubble_dew_log_fug_coeff_method(blk, p, j, pp, blk.temperature_bubble)
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/eos/ceos.py:1343, in _bubble_dew_log_fug_coeff_method(blk, p, j, pp, pt_var)
1334 B = bm * P / (R * T)
1336 delta = (
1337 2
1338 * sqrt(a(j))
1339 / am
1340 * sum(x[xidx, i] * sqrt(a(i)) * (1 - kappa[j, i]) for i in blk.component_list)
1341 )
-> 1343 expr_write = CubicThermoExpressions(blk)
1344 if pobj.is_vapor_phase():
1345 Z = expr_write.z_vap(eos=pobj._cubic_type, A=A, B=B)
File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/eos/ceos_common.py:106, in CubicThermoExpressions.__init__(self, blk)
104 def __init__(self, blk):
105 if not cubic_roots_available():
--> 106 raise RuntimeError("Cubic root external functions are not available.")
107 self.blk = blk
RuntimeError: Cubic root external functions are not available.
4.0 Parameter estimation using parmest#
4.1 List of variable names to be estimated#
Create a list of vars to estimate
variable_name = [
"fs.properties.PR_kappa['bmimPF6', 'carbon_dioxide']",
"fs.properties.PR_kappa['carbon_dioxide', 'bmimPF6']",
]
4.2 Create method to return an expression that computes the sum of squared error#
We need to provide a method to return an expression to compute the sum of squared errors that will be used as the objective in solving the parameter estimation problem. For this problem, the error will be computed for the pressure.
def SSE(m, data):
expr = (float(data["pressure"]) - m.fs.state_block[1].pressure) ** 2
return expr * 1e-7
4.3 Run the parameter estimation#
We are now ready to set up the parameter estimation problem. We will create a parameter estimation object called pest. As shown below, we pass the method that returns an initialized model, data, variable_name, and the SSE expression to the Estimator method. tee=True will print the solver output after solving the parameter estimation problem.
pest = parmest.Estimator(PR_model, data, variable_name, SSE, tee=True)
obj_value, parameters = pest.theta_est()
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `4.301303339264284e-06` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
C:\Users\dkgun\AppData\Local\Temp\ipykernel_28652\3856510393.py:12: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
x = float(data["x_carbon_dioxide"]) + 0.5
C:\Users\dkgun\AppData\Local\Temp\ipykernel_28652\3856510393.py:13: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
m.fs.state_block[1].temperature.fix(float(data["temperature"]))
C:\Users\dkgun\AppData\Local\Temp\ipykernel_28652\3856510393.py:14: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
m.fs.state_block[1].pressure.fix(float(data["pressure"]))
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `4.814447495739171e-09` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
C:\Users\dkgun\AppData\Local\Temp\ipykernel_28652\3856510393.py:29: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
m.fs.state_block[1].temperature.fix(float(data["temperature"]))
C:\Users\dkgun\AppData\Local\Temp\ipykernel_28652\3856510393.py:31: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
float(data["x_bmimPF6"])
C:\Users\dkgun\AppData\Local\Temp\ipykernel_28652\3856510393.py:34: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
float(data["x_carbon_dioxide"])
C:\Users\dkgun\AppData\Local\Temp\ipykernel_28652\3856510393.py:36: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
m.fs.state_block[1].mole_frac_comp["bmimPF6"].fix(float(data["x_bmimPF6"]))
C:\Users\dkgun\AppData\Local\Temp\ipykernel_28652\1809745473.py:2: FutureWarning: Calling float on a single element Series is deprecated and will raise a TypeError in the future. Use float(ser.iloc[0]) instead
expr = (float(data["pressure"]) - m.fs.state_block[1].pressure) ** 2
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `6.357548229111755e-06` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:00 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `6.169320987299437e-07` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `7.629131479751715e-08` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `1.3059472085065408e-08` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:01 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `4.761445527533956e-06` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `7.219204097329158e-09` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `1.03769179356835e-05` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:02 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `1.269889598521249e-06` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `2.021447098567687e-07` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `4.096574706592338e-08` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `6.21086636630859e-06` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:03 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `1.1919675619879674e-08` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `1.0197309662820167e-10` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:04 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `2.385494860297472e-06` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `4.578395178499122e-07` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Starting initialization
WARNING (W1002): Setting Var
'fs.state_block[1].log_mole_frac_tbub[Vap,Liq,carbon_dioxide]' to a numeric
value `1.0835202436687703e-07` outside the bounds (None, 0).
See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: State variable initialization completed.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Phase equilibrium initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Property initialization: optimal - Optimal Solution Found.
2023-11-02 10:30:05 [INFO] idaes.init.fs.state_block: Property package initialization: optimal - Optimal Solution Found.
Ipopt 3.13.2:
******************************************************************************
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...: 842
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 720
Total number of variables............................: 360
variables with only lower bounds: 72
variables with lower and upper bounds: 234
variables with only upper bounds: 18
Total number of equality constraints.................: 358
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 5.00e-01 6.99e-14 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 1.1422488e+01 2.60e-01 2.37e+03 -1.0 3.35e+04 - 3.39e-01 6.89e-01h 1
2 2.8748813e+01 1.27e-01 1.10e+03 -1.0 1.36e+04 - 8.22e-02 9.88e-01h 1
3 2.9813930e+01 1.87e-01 5.94e+02 -1.0 5.01e+02 - 8.73e-01 9.90e-01h 1
4 2.9709737e+01 4.27e-02 1.57e+03 -1.0 5.49e+02 - 9.85e-01 9.90e-01h 1
5 2.9285216e+01 8.02e-03 9.53e+04 -1.0 2.77e+03 - 9.87e-01 1.00e+00h 1
6 2.9283589e+01 1.44e-04 9.56e+04 -1.0 3.48e+02 - 9.90e-01 1.00e+00h 1
7 2.9283603e+01 7.59e-08 9.12e+02 -1.0 5.97e-01 - 9.90e-01 1.00e+00h 1
8 2.9282891e+01 3.35e-07 1.47e+04 -2.5 1.24e+02 - 9.98e-01 1.00e+00f 1
9 2.9282892e+01 2.21e-12 4.97e-08 -2.5 2.39e-01 - 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 2.9282891e+01 2.85e-10 3.05e+00 -8.6 3.61e+00 - 1.00e+00 1.00e+00h 1
11 2.9282891e+01 2.72e-12 3.60e-12 -8.6 2.03e-04 - 1.00e+00 1.00e+00h 1
Number of Iterations....: 11
(scaled) (unscaled)
Objective...............: 2.9282891309640156e+01 2.9282891309640156e+01
Dual infeasibility......: 3.6021722623181066e-12 3.6021722623181066e-12
Constraint violation....: 2.7191470654339899e-12 2.7191470654339899e-12
Complementarity.........: 2.5059037693947522e-09 2.5059037693947522e-09
Overall NLP error.......: 2.5059037693947522e-09 2.5059037693947522e-09
Number of objective function evaluations = 12
Number of objective gradient evaluations = 12
Number of equality constraint evaluations = 12
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 12
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 11
Total CPU secs in IPOPT (w/o function evaluations) = 0.000
Total CPU secs in NLP function evaluations = 0.048
EXIT: Optimal Solution Found.
5.0 Display results#
Let us display the results by running the next cell.
print("The SSE at the optimal solution is %0.6f" % obj_value)
print()
print("The values for the parameters are as follows:")
for k, v in parameters.items():
print(k, "=", v)
The SSE at the optimal solution is 29.282891
The values for the parameters are as follows:
fs.properties.PR_kappa[bmimPF6,carbon_dioxide] = -0.4071428400296551
fs.properties.PR_kappa[carbon_dioxide,bmimPF6] = 0.020593684002515204
Now we can use this parameters and include them in the configuration dictionary. We can also use m.fs.properties = GenericParameterBlock(**configuration)
to solve unit models.