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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.
###############################################################################


# Flowsheet Equilibrium Reactor Simulation and Optimization of Steam Methane Reforming#

Maintainer: Brandon Paul
Author: Brandon Paul
Updated: 2023-06-01

## Learning Outcomes#

• Call and implement the IDAES EquilibriumReactor unit model

• Construct a steady-state flowsheet using the IDAES unit model library

• Connecting unit models in a flowsheet using Arcs

• Fomulate and solve an optimization problem

• Defining an objective function

• Setting variable bounds

## Problem Statement#

This example is adapted from S.Z. Abbas, V. Dupont, T. Mahmud, Kinetics study and modelling of steam methane reforming process over a NiO/Al2O3 catalyst in an adiabatic packed bed reactor. Int. J. Hydrogen Energy, 42 (2017), pp. 2889-2903

Steam methane reforming (SMR) is one of the most common pathways for hydrogen production, taking advantage of chemical equilibria in natural gas systems. The process is typically done in two steps: methane reformation at a high temperature to partially oxidize methane, and water gas shift at a low temperature to complete the oxidation reaction:

CH4 + H2O → CO + 3H2
CO + H2O → CO2 + H2

This reaction is often carried out in two separate reactors to allow for different reaction temperatures and pressures; in this example, we will minimize operating cost for a single reactor.

The flowsheet that we will be using for this module is shown below with the stream conditions. We will be processing natural gas and steam feeds of fixed composition to produce hydrogen. As shown in the flowsheet, the process consists of a mixer M101 for the two inlet streams, a compressor to compress the feed to the reaction pressure, a heater H101 to heat the feed to the reaction temperature, and a EquilibriumReactor unit R101. We will use thermodynamic properties from the Peng-Robinson equation of state for this flowsheet.

The state variables chosen for the property package are total molar flows of each stream, temperature of each stream and pressure of each stream, and mole fractions of each component in each stream. The components considered are: CH4, H2O, CO, CO2, and H2 and the process occurs in vapor phase only. Therefore, every stream has 1 flow variable, 5 mole fraction variables, 1 temperature and 1 pressure variable.

## Importing Required Pyomo and IDAES Components#

To construct a flowsheet, we will need several components from the Pyomo and IDAES packages. Let us first import the following components from Pyomo:

• Constraint (to write constraints)

• Var (to declare variables)

• ConcreteModel (to create the concrete model object)

• Expression (to evaluate values as a function of variables defined in the model)

• Objective (to define an objective function for optimization)

• TransformationFactory (to apply certain transformations)

• Arc (to connect two unit models)

For further details on these components, please refer to the pyomo documentation: https://pyomo.readthedocs.io/en/stable/

From IDAES, we will be needing the FlowsheetBlock and the following unit models:

• Feed

• Mixer

• Compressor

• Heater

• EquilibriumReactor

• Product

We will also be needing some utility tools to put together the flowsheet and calculate the degrees of freedom, tools for model expressions and calling variable values, and built-in functions to define property packages, add unit containers to objects and define our initialization scheme.

from pyomo.environ import (
Constraint,
Var,
ConcreteModel,
Expression,
Objective,
TransformationFactory,
value,
units as pyunits,
)
from pyomo.network import Arc

from idaes.core import FlowsheetBlock
from idaes.models.properties.modular_properties.base.generic_property import (
GenericParameterBlock,
)
from idaes.models.properties.modular_properties.base.generic_reaction import (
GenericReactionParameterBlock,
)
from idaes.models.unit_models import (
Feed,
Mixer,
Compressor,
Heater,
EquilibriumReactor,
Product,
)

from idaes.core.solvers import get_solver
from idaes.core.util.model_statistics import degrees_of_freedom
from idaes.core.util.initialization import propagate_state


## Importing Required Thermophysical and Reaction Packages#

The final step is to import the thermophysical and reaction packages. We will import natural gas properties from an existing IDAES module, and reaction properties from a custom module to describe equilibrium behavior. These configuration dictionaries provide parameter data that we will pass to the Modular Property Framework.

The reaction package here assumes all reactions reach chemical equilibrium at the given conditions.

$${K_{eq}^{MSR}} = \exp\left(\frac {-26830} {T} + 30.114\right)$$, $${K_{eq}^{WGS}} = \exp\left(\frac {4400} {T} - 4.036\right)$$ with the reactor temperature $$T$$ in K.
The total reaction equilibrium constant is given by $$K_{eq} = {K_{eq}^{MSR}}{K_{eq}^{WGS}}$$.

The correlations are taken from the following literature:

Int. J. Hydrogen Energy, 42 (2017), pp. 2889-2903

### Determining $$k_{eq}^{ref}$$#

As part of the parameter dictionary, users may define equilibrium reactions using a constant coefficient or built-in correlations for van’t Hoff and Gibbs formulations. Using the literature correlations above for $$k_{eq}$$, we can easily calculate the necessary parameters to use the van’t Hoff equilibrium constant form:

For an empirical correlation $$ln(k_{eq}) = f(T)$$ for a catalyst (reaction) temperature $$T$$, we obtain $$k_{eq}^{ref} = \exp\left({f(T_{eq}^{ref})}\right)$$. From the paper, we obtain a reference catalyst temperature of 973.15 K and reaction energies for the two reaction steps; these values exist in the reaction property parameter module in this same directory.

These calculations are contained within the property, reaction and unit model packages, and do not need to be entered into the flowsheet. More information on property estimation may be found in the IDAES documentation on Parameter Estimation.

Let us import the following modules:

• natural_gas_PR as get_prop (method to get configuration dictionary)

• msr_reaction as reaction_props (contains configuration dictionary)

from idaes.models_extra.power_generation.properties.natural_gas_PR import get_prop
import msr_reaction as reaction_props


## Constructing the Flowsheet#

We have now imported all the components, unit models, and property modules we need to construct a flowsheet. Let us create a ConcreteModel and add the flowsheet block.

m = ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False)


We now need to add the property packages to the flowsheet. Unlike the basic Flash unit model example, where we only had a thermophysical property package, for this flowsheet we will also need to add a reaction property package. We will use the Modular Property Framework and Modular Reaction Framework. The get_prop method for the natural gas property module automatically returns the correct dictionary using a component list argument. The GenericParameterBlock and GenericReactionParameterBlock methods build states blocks from passed parameter data; the reaction block unpacks using **reaction_props.config_dict to allow for optional or empty keyword arguments:

thermo_props_config_dict = get_prop(components=["CH4", "H2O", "H2", "CO", "CO2"])
m.fs.thermo_params = GenericParameterBlock(**thermo_props_config_dict)
m.fs.reaction_params = GenericReactionParameterBlock(
property_package=m.fs.thermo_params, **reaction_props.config_dict
)


Let us start adding the unit models we have imported to the flowsheet. Here, we are adding a Mixer, a Compressor, a Heater and an EquilibriumReactor. Note that all unit models should be explicitly defined with a given property package. In addition to that, there are several arguments depending on the unit model, please refer to the documentation for more details on IDAES Unit Models. For example, the Mixer is given a list consisting of names to the two inlets. Note that the Compressor is a PressureChanger assuming compression operation and with a fixed isentropic compressor efficiency as the default thermodynamic behavior.

m.fs.CH4 = Feed(property_package=m.fs.thermo_params)
m.fs.H2O = Feed(property_package=m.fs.thermo_params)
m.fs.PROD = Product(property_package=m.fs.thermo_params)
m.fs.M101 = Mixer(
property_package=m.fs.thermo_params, inlet_list=["methane_feed", "steam_feed"]
)
m.fs.H101 = Heater(
property_package=m.fs.thermo_params,
has_pressure_change=False,
has_phase_equilibrium=False,
)
m.fs.C101 = Compressor(property_package=m.fs.thermo_params)

ERROR: Rule failed for Expression
'fs.M101.methane_feed_state[0.0].compress_fact_phase' with index Vap:
RuntimeError: Cubic root external functions are not available.

ERROR: Constructing component
'fs.M101.methane_feed_state[0.0].compress_fact_phase' from data=None failed:
RuntimeError: Cubic root external functions are not available.

ERROR: Rule failed for Expression
'fs.M101.methane_feed_state[0.0].enth_mol_phase' with index Vap: RuntimeError:
Cubic root external functions are not available.

ERROR: Constructing component 'fs.M101.methane_feed_state[0.0].enth_mol_phase'
from data=None failed:
RuntimeError: Cubic root external functions are not available.

ERROR: Rule failed for Expression
'fs.M101.methane_feed_state[0.0]._enthalpy_flow_term' with index Vap:
RuntimeError: Cubic root external functions are not available.

ERROR: Constructing component
'fs.M101.methane_feed_state[0.0]._enthalpy_flow_term' from data=None failed:
RuntimeError: Cubic root external functions are not available.

ERROR: Rule failed when generating expression for Constraint
fs.M101.enthalpy_mixing_equations with index 0.0: RuntimeError: Cubic root
external functions are not available.

ERROR: Constructing component 'fs.M101.enthalpy_mixing_equations' from
data=None failed:
RuntimeError: Cubic root external functions are not available.

2024-03-18 23:19:05 [ERROR] idaes.core.base.process_block: Failure in build: fs.M101
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 547, in __getattr__
raise AttributeError(
AttributeError: 'GenericStateBlockData' object has no attribute '_enthalpy_flow_term'

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/models/properties/modular_properties/state_definitions/FTPx.py", line 279, in get_enthalpy_flow_terms_FTPx
eflow = b._enthalpy_flow_term
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 85, in build_on_demand
raise PropertyPackageError(
idaes.core.util.exceptions.PropertyPackageError: fs.M101.methane_feed_state[0.0] _enthalpy_flow_term does not exist, but is a protected attribute. Check the naming of your components to avoid any reserved names

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/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 547, in __getattr__
raise AttributeError(
AttributeError: 'GenericStateBlockData' object has no attribute 'enth_mol_phase'

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/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 547, in __getattr__
raise AttributeError(
AttributeError: 'GenericStateBlockData' object has no attribute 'compress_fact_phase'

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/unit_models/mixer.py", line 450, in build
def enthalpy_mixing_equations(b, t):
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py", line 74, in __call__
setattr(
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py", line 568, in __setattr__
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 800, 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 316, 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/unit_models/mixer.py", line 799, in enthalpy_mixing_equations
sum(
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/unit_models/mixer.py", line 800, in <genexpr>
sum(
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/unit_models/mixer.py", line 801, in <genexpr>
inlet_blocks[i][t].get_enthalpy_flow_terms(p)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/idaes/models/properties/modular_properties/state_definitions/FTPx.py", line 285, in get_enthalpy_flow_terms_FTPx
eflow = b._enthalpy_flow_term = Expression(b.phase_list, rule=rule_eflow)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py", line 568, in __setattr__
val.construct(data)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/expression.py", line 400, in construct
self._construct_from_rule_using_setitem()
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/indexed_component.py", line 784, in _construct_from_rule_using_setitem
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 316, 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/state_definitions/FTPx.py", line 283, in rule_eflow
return b.flow_mol_phase[p] * b.enth_mol_phase[p]
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 3537, in _enth_mol_phase
self.enth_mol_phase = Expression(self.phase_list, rule=rule_enth_mol_phase)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py", line 568, in __setattr__
val.construct(data)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/expression.py", line 400, in construct
self._construct_from_rule_using_setitem()
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/indexed_component.py", line 784, in _construct_from_rule_using_setitem
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 316, 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/base/generic_property.py", line 3535, in rule_enth_mol_phase
return p_config.equation_of_state.enth_mol_phase(b, p)
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 690, in enth_mol_phase
Z = blk.compress_fact_phase[p]
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 3164, in _compress_fact_phase
self.compress_fact_phase = Expression(
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py", line 568, in __setattr__
val.construct(data)
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/expression.py", line 400, in construct
self._construct_from_rule_using_setitem()
File "/home/docs/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/indexed_component.py", line 784, in _construct_from_rule_using_setitem
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 316, 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/base/generic_property.py", line 3162, in rule_Z_phase
return p_config.equation_of_state.compress_fact_phase(b, p)
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 551, in compress_fact_phase
expr_write = CubicThermoExpressions(b)
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.M101' from data=None failed:
RuntimeError: Cubic root external functions are not available.

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
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:

545 # Since the base classes don't support getattr, we can just
546 # throw the "normal" AttributeError
--> 547 raise AttributeError(
548     "'%s' object has no attribute '%s'" % (self.__class__.__name__, val)
549 )

AttributeError: 'GenericStateBlockData' object has no attribute '_enthalpy_flow_term'

During handling of the above exception, another exception occurred:

PropertyPackageError                      Traceback (most recent call last)
278 try:
--> 279     eflow = b._enthalpy_flow_term
280 except AttributeError:

793 except AttributeError:
--> 794     return build_on_demand(self, attr)

82 if attr == "domain" or attr.startswith("_"):
83     # Don't interfere with anything by getting attributes that are
84     # none of my business
---> 85     raise PropertyPackageError(
86         "{} {} does not exist, but is a protected "
87         "attribute. Check the naming of your "
88         "components to avoid any reserved names".format(self.name, attr)
89     )
91 if attr == "config":

PropertyPackageError: fs.M101.methane_feed_state[0.0] _enthalpy_flow_term does not exist, but is a protected attribute. Check the naming of your components to avoid any reserved names

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
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:

545 # Since the base classes don't support getattr, we can just
546 # throw the "normal" AttributeError
--> 547 raise AttributeError(
548     "'%s' object has no attribute '%s'" % (self.__class__.__name__, val)
549 )

AttributeError: 'GenericStateBlockData' object has no attribute 'enth_mol_phase'

During handling of the above exception, another exception occurred:

AttributeError                            Traceback (most recent call last)
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:

545 # Since the base classes don't support getattr, we can just
546 # throw the "normal" AttributeError
--> 547 raise AttributeError(
548     "'%s' object has no attribute '%s'" % (self.__class__.__name__, val)
549 )

AttributeError: 'GenericStateBlockData' object has no attribute 'compress_fact_phase'

During handling of the above exception, another exception occurred:

RuntimeError                              Traceback (most recent call last)
Cell In[6], line 4
2 m.fs.H2O = Feed(property_package=m.fs.thermo_params)
3 m.fs.PROD = Product(property_package=m.fs.thermo_params)
----> 4 m.fs.M101 = Mixer(
5     property_package=m.fs.thermo_params, inlet_list=["methane_feed", "steam_feed"]
6 )
7 m.fs.H101 = Heater(
8     property_package=m.fs.thermo_params,
9     has_pressure_change=False,
10     has_phase_equilibrium=False,
11 )
12 m.fs.C101 = Compressor(property_package=m.fs.thermo_params)

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:568, in _BlockData.__setattr__(self, name, val)
563 if name not in self.__dict__:
564     if isinstance(val, Component):
565         #
567         #
569     else:
570         #
571         # Other Python objects are added with the standard __setattr__
572         # method.
573         #
574         super(_BlockData, self).__setattr__(name, val)

1118     logger.debug(
1119         "Constructing %s '%s' on %s from data=%s",
1120         val.__class__.__name__,
(...)
1123         str(data),
1124     )
1125 try:
-> 1126     val.construct(data)
1127 except:
1128     err = sys.exc_info()[1]

2165                     obj.construct(data.get(name, None))
2166         # Trigger the (normal) initialization of the block
-> 2167         self._getitem_when_not_present(_idx)
2168 finally:
2169     # We must allow that id(self) may no longer be in
2170     # _BlockConstruction.data, as _getitem_when_not_present will
2171     # have already removed the entry for scalar blocks (as the
2172     # BlockData and the Block component are the same object)
2173     if data is not None:

2079     data = None
2081 try:
-> 2082     obj = self._rule(_block, idx)
2083     # If the user returns a block, transfer over everything
2084     # they defined into the empty one we created.  We do
2085     # this inside the try block so that any abstract
2086     # components declared by the rule have the opportunity
2087     # to be initialized with data from
2088     # _BlockConstruction.data as they are transferred over.
2089     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)

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}")

442     raise BurntToast(
443         "{} received unrecognised value for "
444         "material_mixing_type argument. This "
446         "the IDAES developers with this bug.".format(self.name)
447     )
449 if self.config.energy_mixing_type == MixingType.extensive:
451         inlet_blocks=inlet_blocks, mixed_block=mixed_block
452     )
453 elif self.config.energy_mixing_type == MixingType.none:
454     pass

792     """
793     Add energy mixing equations (total enthalpy balance).
794     """
796     @self.Constraint(self.flowsheet().time, doc="Energy balances")
--> 797     def enthalpy_mixing_equations(b, t):
798         return 0 == (
799             sum(
800                 sum(
(...)
809             )
810         )

73 def __call__(self, rule):
---> 74     setattr(
75         self._block,
76         rule.__name__,
77         self._component(*self._args, rule=rule, **(self._kwds)),
78     )
79     return rule

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:568, in _BlockData.__setattr__(self, name, val)
563 if name not in self.__dict__:
564     if isinstance(val, Component):
565         #
567         #
569     else:
570         #
571         # Other Python objects are added with the standard __setattr__
572         # method.
573         #
574         super(_BlockData, self).__setattr__(name, val)

1118     logger.debug(
1119         "Constructing %s '%s' on %s from data=%s",
1120         val.__class__.__name__,
(...)
1123         str(data),
1124     )
1125 try:
-> 1126     val.construct(data)
1127 except:
1128     err = sys.exc_info()[1]

797     else:
798         # Bypass the index validation and create the member directly
799         for index in self.index_set():
--> 800             self._setitem_when_not_present(index, rule(block, index))
801 except Exception:
802     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:316, in IndexedCallInitializer.__call__(self, parent, idx)
314     return self._fcn(parent, *idx)
315 else:
--> 316     return self._fcn(parent, idx)

796 @self.Constraint(self.flowsheet().time, doc="Energy balances")
797 def enthalpy_mixing_equations(b, t):
798     return 0 == (
--> 799         sum(
800             sum(
801                 inlet_blocks[i][t].get_enthalpy_flow_terms(p)
802                 for p in mixed_block.phase_list
803             )
804             for i in range(len(inlet_blocks))
805         )
806         - sum(
807             mixed_block[t].get_enthalpy_flow_terms(p)
808             for p in mixed_block.phase_list
809         )
810     )

796 @self.Constraint(self.flowsheet().time, doc="Energy balances")
797 def enthalpy_mixing_equations(b, t):
798     return 0 == (
799         sum(
--> 800             sum(
801                 inlet_blocks[i][t].get_enthalpy_flow_terms(p)
802                 for p in mixed_block.phase_list
803             )
804             for i in range(len(inlet_blocks))
805         )
806         - sum(
807             mixed_block[t].get_enthalpy_flow_terms(p)
808             for p in mixed_block.phase_list
809         )
810     )

796 @self.Constraint(self.flowsheet().time, doc="Energy balances")
797 def enthalpy_mixing_equations(b, t):
798     return 0 == (
799         sum(
800             sum(
--> 801                 inlet_blocks[i][t].get_enthalpy_flow_terms(p)
802                 for p in mixed_block.phase_list
803             )
804             for i in range(len(inlet_blocks))
805         )
806         - sum(
807             mixed_block[t].get_enthalpy_flow_terms(p)
808             for p in mixed_block.phase_list
809         )
810     )

282     def rule_eflow(b, p):
283         return b.flow_mol_phase[p] * b.enth_mol_phase[p]
--> 285     eflow = b._enthalpy_flow_term = Expression(b.phase_list, rule=rule_eflow)
286 return eflow[p]

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:568, in _BlockData.__setattr__(self, name, val)
563 if name not in self.__dict__:
564     if isinstance(val, Component):
565         #
567         #
569     else:
570         #
571         # Other Python objects are added with the standard __setattr__
572         # method.
573         #
574         super(_BlockData, self).__setattr__(name, val)

1118     logger.debug(
1119         "Constructing %s '%s' on %s from data=%s",
1120         val.__class__.__name__,
(...)
1123         str(data),
1124     )
1125 try:
-> 1126     val.construct(data)
1127 except:
1128     err = sys.exc_info()[1]

397 try:
398     # We do not (currently) accept data for constructing Constraints
399     assert data is None
--> 400     self._construct_from_rule_using_setitem()
401 finally:
402     timer.report()

782     else:
783         for index in self.index_set():
--> 784             self._setitem_when_not_present(index, rule(block, index))
785 except:
786     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:316, in IndexedCallInitializer.__call__(self, parent, idx)
314     return self._fcn(parent, *idx)
315 else:
--> 316     return self._fcn(parent, idx)

282 def rule_eflow(b, p):
--> 283     return b.flow_mol_phase[p] * b.enth_mol_phase[p]

792     return super().__getattr__(attr)
793 except AttributeError:
--> 794     return 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)

3534         p_config = b.params.get_phase(p).config
3535         return p_config.equation_of_state.enth_mol_phase(b, p)
-> 3537     self.enth_mol_phase = Expression(self.phase_list, rule=rule_enth_mol_phase)
3538 except AttributeError:
3539     self.del_component(self.enth_mol_phase)

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:568, in _BlockData.__setattr__(self, name, val)
563 if name not in self.__dict__:
564     if isinstance(val, Component):
565         #
567         #
569     else:
570         #
571         # Other Python objects are added with the standard __setattr__
572         # method.
573         #
574         super(_BlockData, self).__setattr__(name, val)

1118     logger.debug(
1119         "Constructing %s '%s' on %s from data=%s",
1120         val.__class__.__name__,
(...)
1123         str(data),
1124     )
1125 try:
-> 1126     val.construct(data)
1127 except:
1128     err = sys.exc_info()[1]

397 try:
398     # We do not (currently) accept data for constructing Constraints
399     assert data is None
--> 400     self._construct_from_rule_using_setitem()
401 finally:
402     timer.report()

782     else:
783         for index in self.index_set():
--> 784             self._setitem_when_not_present(index, rule(block, index))
785 except:
786     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:316, in IndexedCallInitializer.__call__(self, parent, idx)
314     return self._fcn(parent, *idx)
315 else:
--> 316     return self._fcn(parent, idx)

3533 def rule_enth_mol_phase(b, p):
3534     p_config = b.params.get_phase(p).config
-> 3535     return p_config.equation_of_state.enth_mol_phase(b, p)

688 B = getattr(blk, cname + "_B")[p]
689 dam_dT = getattr(blk, cname + "_dam_dT")[p]
--> 690 Z = blk.compress_fact_phase[p]
691 R = Cubic.gas_constant(blk)
692 T = blk.temperature

792     return super().__getattr__(attr)
793 except AttributeError:
--> 794     return 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)

3161         p_config = b.params.get_phase(p).config
3162         return p_config.equation_of_state.compress_fact_phase(b, p)
-> 3164     self.compress_fact_phase = Expression(
3165         self.phase_list, doc="Compressibility of each phase", rule=rule_Z_phase
3166     )
3167 except AttributeError:
3168     self.del_component(self.compress_fact_phase)

File ~/checkouts/readthedocs.org/user_builds/idaes-examples/envs/latest/lib/python3.8/site-packages/pyomo/core/base/block.py:568, in _BlockData.__setattr__(self, name, val)
563 if name not in self.__dict__:
564     if isinstance(val, Component):
565         #
567         #
569     else:
570         #
571         # Other Python objects are added with the standard __setattr__
572         # method.
573         #
574         super(_BlockData, self).__setattr__(name, val)

1118     logger.debug(
1119         "Constructing %s '%s' on %s from data=%s",
1120         val.__class__.__name__,
(...)
1123         str(data),
1124     )
1125 try:
-> 1126     val.construct(data)
1127 except:
1128     err = sys.exc_info()[1]

397 try:
398     # We do not (currently) accept data for constructing Constraints
399     assert data is None
--> 400     self._construct_from_rule_using_setitem()
401 finally:
402     timer.report()

782     else:
783         for index in self.index_set():
--> 784             self._setitem_when_not_present(index, rule(block, index))
785 except:
786     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:316, in IndexedCallInitializer.__call__(self, parent, idx)
314     return self._fcn(parent, *idx)
315 else:
--> 316     return self._fcn(parent, idx)

3160 def rule_Z_phase(b, p):
3161     p_config = b.params.get_phase(p).config
-> 3162     return p_config.equation_of_state.compress_fact_phase(b, p)

548 A = getattr(b, cname + "_A")
549 B = getattr(b, cname + "_B")
--> 551 expr_write = CubicThermoExpressions(b)
552 if pobj.is_vapor_phase():
553     return expr_write.z_vap(eos=pobj._cubic_type, A=A[p], B=B[p])

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.

m.fs.R101 = EquilibriumReactor(
property_package=m.fs.thermo_params,
reaction_package=m.fs.reaction_params,
has_equilibrium_reactions=True,
has_rate_reactions=False,
has_heat_of_reaction=True,
has_heat_transfer=True,
has_pressure_change=False,
)


## Connecting Unit Models Using Arcs#

We have now added all the unit models we need to the flowsheet. However, we have not yet specifed how the units are to be connected. To do this, we will be using the Arc which is a Pyomo component that takes in two arguments: source and destination. Let us connect the outlet of the Mixer to the inlet of the Compressor, the outlet of the compressor Compressor to the inlet of the Heater, and the outlet of the Heater to the inlet of the EquilibriumReactor. Additionally, we will connect the Feed and Product blocks to the flowsheet:

m.fs.s01 = Arc(source=m.fs.CH4.outlet, destination=m.fs.M101.methane_feed)
m.fs.s02 = Arc(source=m.fs.H2O.outlet, destination=m.fs.M101.steam_feed)
m.fs.s03 = Arc(source=m.fs.M101.outlet, destination=m.fs.C101.inlet)
m.fs.s04 = Arc(source=m.fs.C101.outlet, destination=m.fs.H101.inlet)
m.fs.s05 = Arc(source=m.fs.H101.outlet, destination=m.fs.R101.inlet)
m.fs.s06 = Arc(source=m.fs.R101.outlet, destination=m.fs.PROD.inlet)


We have now connected the unit model block using the arcs. However, we also need to link the state variables on connected ports. Pyomo provides a convenient method TransformationFactory to write these equality constraints for us between two ports:

TransformationFactory("network.expand_arcs").apply_to(m)


## Adding Expressions to Compute Operating Costs#

In this section, we will add a few Expressions that allow us to evaluate the performance. Expressions provide a convenient way of calculating certain values that are a function of the variables defined in the model. For more details on Expressions, please refer to the Pyomo Expression documentation.

For this flowsheet, we are interested in computing hydrogen production in millions of pounds per year, as well as the total costs due to pressurizing, cooling, and heating utilities.

Let us first add an Expression to convert the product flow from mol/s to MM lb/year of hydrogen. We see that the molecular weight exists in the thermophysical property package, so we may use that value for our calculations.

m.fs.hyd_prod = Expression(
expr=pyunits.convert(
m.fs.PROD.inlet.flow_mol[0]
* m.fs.PROD.inlet.mole_frac_comp[0, "H2"]
* m.fs.thermo_params.H2.mw,  # MW defined in properties as kg/mol
to_units=pyunits.Mlb / pyunits.yr,
)
)  # converting kg/s to MM lb/year



operating cost = $45.933 million per year  For this operating cost, what conversion did we achieve of methane to hydrogen? m.fs.R101.report() print() print(f"Conversion achieved = {value(m.fs.R101.conversion):.1%}")  ==================================================================================== Unit : fs.R101 Time: 0.0 ------------------------------------------------------------------------------------ Unit Performance Variables: Key : Value : Units : Fixed : Bounds Heat Duty : 2.7605e+07 : watt : False : (None, None) ------------------------------------------------------------------------------------ Stream Table Units Inlet Outlet Total Molar Flowrate mole / second 309.01 429.02 Total Mole Fraction CH4 dimensionless 0.24272 0.034965 Total Mole Fraction H2O dimensionless 0.75725 0.31487 Total Mole Fraction H2 dimensionless 9.9996e-06 0.51029 Total Mole Fraction CO dimensionless 9.9996e-06 0.049157 Total Mole Fraction CO2 dimensionless 9.9996e-06 0.090717 Temperature kelvin 500.00 868.56 Pressure pascal 2.0000e+05 2.0000e+05 ==================================================================================== Conversion achieved = 80.0%  ## Optimizing Hydrogen Production# Now that the flowsheet has been squared and solved, we can run a small optimization problem to determine optimal conditions for producing hydrogen. Suppose we wish to find ideal conditions for the competing reactions. As mentioned earlier, the two reactions have competing equilibria - steam methane reformation occurs more readily at higher temperatures (500-700 C) while water gas shift occurs more readily at lower temperatures (300-400 C). We will allow for variable reactor temperature and pressure by freeing our heater and compressor specifications, and minimize cost to achieve 90% methane conversion. Since we assume an isentopic compressor, allowing compression will heat our feed stream and reduce or eliminate the required heater duty. Let us declare our objective function for this problem. m.fs.objective = Objective(expr=m.fs.operating_cost)  Now, we need to add the design constraints and unfix the decision variables as we had solved a square problem until now, as well as set bounds for the design variables (reactor outlet temperature is set by state variable bounds in property package): m.fs.R101.conversion.fix(0.90) m.fs.C101.outlet.pressure.unfix() m.fs.C101.outlet.pressure[0].setlb( pyunits.convert(2 * pyunits.bar, to_units=pyunits.Pa) ) # pressurize to at least 2 bar m.fs.C101.outlet.pressure[0].setub( pyunits.convert(10 * pyunits.bar, to_units=pyunits.Pa) ) # at most, pressurize to 10 bar m.fs.H101.outlet.temperature.unfix() m.fs.H101.heat_duty[0].setlb( 0 * pyunits.J / pyunits.s ) # outlet temperature is equal to or greater than inlet temperature m.fs.H101.outlet.temperature[0].setub(1000 * pyunits.K) # at most, heat to 1000 K  We have now defined the optimization problem and we are now ready to solve this problem. results = solver.solve(m, tee=True)  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...: 569 Number of nonzeros in inequality constraint Jacobian.: 0 Number of nonzeros in Lagrangian Hessian.............: 493 Total number of variables............................: 206 variables with only lower bounds: 14 variables with lower and upper bounds: 176 variables with only upper bounds: 0 Total number of equality constraints.................: 204 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 4.5933014e+07 1.49e+06 3.46e+01 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0 1 4.5420427e+07 1.49e+06 1.33e+03 -1.0 1.08e+07 - 4.58e-01 5.96e-03f 1 2 4.2830345e+07 8.68e+05 6.47e+06 -1.0 5.32e+06 - 8.03e-01 4.18e-01f 1 3 4.3111576e+07 1.26e+05 1.06e+07 -1.0 2.54e+06 - 9.54e-01 8.85e-01h 1 4 4.3307552e+07 2.24e+03 3.12e+05 -1.0 3.51e+05 - 9.89e-01 9.86e-01h 1 5 4.3309118e+07 2.20e+01 3.08e+03 -1.0 2.69e+03 - 9.90e-01 9.90e-01h 1 6 4.3309131e+07 5.79e-06 3.84e+01 -1.0 2.31e+01 - 9.92e-01 1.00e+00h 1 7 4.3309131e+07 7.77e-09 1.30e-06 -2.5 1.97e-02 - 1.00e+00 1.00e+00f 1 8 4.3309131e+07 2.20e-08 1.95e-06 -3.8 5.56e-04 - 1.00e+00 1.00e+00f 1 9 4.3309131e+07 1.79e-08 1.27e-06 -5.7 3.08e-05 - 1.00e+00 1.00e+00f 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls 10 4.3309131e+07 5.88e-09 1.09e-06 -7.0 3.56e-07 - 1.00e+00 1.00e+00f 1 Number of Iterations....: 10 (scaled) (unscaled) Objective...............: 4.3309130854568668e+07 4.3309130854568668e+07 Dual infeasibility......: 1.0873799957492332e-06 1.0873799957492332e-06 Constraint violation....: 1.4551915228366852e-11 5.8780968648563987e-09 Complementarity.........: 9.0909090913936446e-08 9.0909090913936446e-08 Overall NLP error.......: 9.0909090913936446e-08 1.0873799957492332e-06 Number of objective function evaluations = 11 Number of objective gradient evaluations = 11 Number of equality constraint evaluations = 11 Number of inequality constraint evaluations = 0 Number of equality constraint Jacobian evaluations = 11 Number of inequality constraint Jacobian evaluations = 0 Number of Lagrangian Hessian evaluations = 10 Total CPU secs in IPOPT (w/o function evaluations) = 0.000 Total CPU secs in NLP function evaluations = 0.007 EXIT: Optimal Solution Found.  print(f"operating cost =${value(m.fs.operating_cost)/1e6:0.3f} million per year")

print()
print("Compressor results")

m.fs.C101.report()

print()
print("Heater results")

m.fs.H101.report()

print()
print("Equilibrium reactor results")

m.fs.R101.report()

operating cost = \$43.309 million per year

Compressor results

====================================================================================
Unit : fs.C101                                                             Time: 0.0
------------------------------------------------------------------------------------
Unit Performance

Variables:

Key                   : Value      : Units         : Fixed : Bounds
Isentropic Efficiency :    0.90000 : dimensionless :  True : (None, None)
Mechanical Work : 7.5471e+05 :          watt : False : (None, None)
Pressure Change : 1.0000e+05 :        pascal : False : (None, None)
Pressure Ratio :     2.0000 : dimensionless : False : (None, None)

------------------------------------------------------------------------------------
Stream Table
Units         Inlet     Outlet
Total Molar Flowrate     mole / second     309.01     309.01
Total Mole Fraction CH4  dimensionless    0.24272    0.24272
Total Mole Fraction H2O  dimensionless    0.75725    0.75725
Total Mole Fraction H2   dimensionless 9.9996e-06 9.9996e-06
Total Mole Fraction CO   dimensionless 9.9996e-06 9.9996e-06
Total Mole Fraction CO2  dimensionless 9.9996e-06 9.9996e-06
Temperature                     kelvin     353.80     423.34
Pressure                        pascal 1.0000e+05 2.0000e+05
====================================================================================

Heater results

====================================================================================
Unit : fs.H101                                                             Time: 0.0
------------------------------------------------------------------------------------
Unit Performance

Variables:

Key       : Value      : Units : Fixed : Bounds
Heat Duty : 5.8781e-09 :  watt : False : (0.0, None)

------------------------------------------------------------------------------------
Stream Table
Units         Inlet     Outlet
Total Molar Flowrate     mole / second     309.01     309.01
Total Mole Fraction CH4  dimensionless    0.24272    0.24272
Total Mole Fraction H2O  dimensionless    0.75725    0.75725
Total Mole Fraction H2   dimensionless 9.9996e-06 9.9996e-06
Total Mole Fraction CO   dimensionless 9.9996e-06 9.9996e-06
Total Mole Fraction CO2  dimensionless 9.9996e-06 9.9996e-06
Temperature                     kelvin     423.34     423.34
Pressure                        pascal 2.0000e+05 2.0000e+05
====================================================================================

Equilibrium reactor results

====================================================================================
Unit : fs.R101                                                             Time: 0.0
------------------------------------------------------------------------------------
Unit Performance

Variables:

Key       : Value      : Units : Fixed : Bounds
Heat Duty : 3.2486e+07 :  watt : False : (None, None)

------------------------------------------------------------------------------------
Stream Table
Units         Inlet     Outlet
Total Molar Flowrate     mole / second     309.01     444.02
Total Mole Fraction CH4  dimensionless    0.24272   0.016892
Total Mole Fraction H2O  dimensionless    0.75725    0.29075
Total Mole Fraction H2   dimensionless 9.9996e-06    0.54032
Total Mole Fraction CO   dimensionless 9.9996e-06   0.067801
Total Mole Fraction CO2  dimensionless 9.9996e-06   0.084239
Temperature                     kelvin     423.34     910.04
Pressure                        pascal 2.0000e+05 2.0000e+05
====================================================================================


Display optimal values for the decision variables and design variables:

print("Optimal Values")
print()

print(f"C101 outlet pressure = {value(m.fs.C101.outlet.pressure[0])/1E6:0.3f} MPa")
print()

print(f"C101 outlet temperature = {value(m.fs.C101.outlet.temperature[0]):0.3f} K")
print()

print(f"H101 outlet temperature = {value(m.fs.H101.outlet.temperature[0]):0.3f} K")

print()
print(f"R101 outlet temperature = {value(m.fs.R101.outlet.temperature[0]):0.3f} K")

print()
print(f"Hydrogen produced = {value(m.fs.hyd_prod):0.3f} MM lb/year")

print()
print(f"Conversion achieved = {value(m.fs.R101.conversion):.1%}")

Optimal Values

C101 outlet pressure = 0.200 MPa

C101 outlet temperature = 423.345 K

H101 outlet temperature = 423.345 K

R101 outlet temperature = 910.044 K

Hydrogen produced = 33.648 MM lb/year

Conversion achieved = 90.0%