Separator¶
Tutorial: Separator Unit Model with Modular Property Package¶
Learning Outcomes¶
- Demonstrate use of the separator unit model in IDAES
- Demonstrate different separation options available
Problem Statement¶
In this example, we will be separating a feed stream of liquid H2O and CO2 vapor. The inlet conditions are as follows:
Inlet:
Flow Rate = 100 mol/s
Mole Fraction (H2O) = 0.9
Mole Fraction (CO2) = 0.1
Temperature = 298 K
Pressure = 101325 Pa
We will look at three cases in this tutorial:
Case 1: Separate on a total flow split basis
Case 2: Separate on a phase flow split basis
Case 3: Separate on a component flow split basis
For more details, please refer to the IDAES documentation: https://idaes-pse.readthedocs.io/en/stable
Importing necessary tools¶
In the following cell, we will be importing the necessary components from Pyomo and IDAES.
# Import objects from pyomo package
from pyomo.environ import ConcreteModel, value
# Import the solver
from idaes.core.solvers import get_solver
# Import the main FlowsheetBlock from IDAES. The flowsheet block will contain the unit model
from idaes.core import FlowsheetBlock
# Import the option to set the type of material balance
from idaes.core import MaterialBalanceType
# Import the separator unit model
from idaes.models.unit_models import Separator
# Import the option to set the basis for splitting
from idaes.models.unit_models.separator import SplittingType
# Import idaes logger to set output levels
import idaes.logger as idaeslog
# Import the modular property package to create a property block for the flowsheet
from idaes.models.properties.modular_properties.base.generic_property import GenericParameterBlock
# Import the BT_Ideal property package to create a configuration file for the GenericParameterBlock
from idaes.models.properties.modular_properties.examples.CO2_H2O_Ideal_VLE import configuration
# Import the degrees_of_freedom function from the idaes.core.util.model_statistics package
# DOF = Number of Model Variables - Number of Model Constraints
from idaes.core.util.model_statistics import degrees_of_freedom
Setting up the flowsheet¶
In the following cell, we will create the ConcreteModel foundation, attach the steady state flowsheet, and declare the property parameter block that will used.
More information on this general workflow can be found here: https://idaes-pse.readthedocs.io/en/stable/how_to_guides/workflow/general.html
m = ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False) # dynamic or ss flowsheet needs to be specified here
m.fs.properties = GenericParameterBlock(**configuration)
Case 1:¶
In the following cell, we will be creating the separator unit model that splits on a total flow basis and determining the initial degrees of freedom associated with this separator unit model.
m.fs.sep_1 = Separator(
property_package=m.fs.properties,
split_basis=SplittingType.totalFlow,
outlet_list=["a1", "b1", "c1"], # creates three outlet streams
ideal_separation=False,
has_phase_equilibrium=False,
)
DOF_initial = degrees_of_freedom(m)
print('The initial degrees of freedom are: {0}'.format(DOF_initial))
The initial degrees of freedom are: 7
Fixing input specifications¶
In the following cell, we will be specifying the inlet conditions for the separator block and re-evaluating the degrees of freedom to ensure the problem is square (i.e. DOF=0).
m.fs.sep_1.inlet.flow_mol.fix(10) # converting to mol/s as unit basis is mol/s
m.fs.sep_1.inlet.mole_frac_comp[0, "H2O"].fix(0.9)
m.fs.sep_1.inlet.mole_frac_comp[0, "CO2"].fix(0.1)
m.fs.sep_1.inlet.pressure.fix(101325) # Pa
m.fs.sep_1.inlet.temperature.fix(353) # K
m.fs.sep_1.split_fraction[0, "a1"].fix(0.2)
m.fs.sep_1.split_fraction[0, "b1"].fix(0.5)
# Directly setting the split fraction of c1 will cause the DOF check to fail
DOF_final = degrees_of_freedom(m)
print('The final degrees of freedom is: {0}'.format(DOF_final))
The final degrees of freedom is: 0
Flowsheet Initialization¶
IDAES includes pre-written initialization routines for all unit models. Failing to initialize or having a poor intialization of a flowsheet may result in the problem being unsolvable. The output from initialization can be set to 7 different levels depending on the details required by the user. In general, when a particular output level is set, any information at that level and above gets picked up by logger. The default level taken by the logger is INFO.
More information on these levels can be found in the IDAES documentation: https://idaes-pse.readthedocs.io/en/stable/reference_guides/logging.html
m.fs.sep_1.initialize(outlvl=idaeslog.WARNING)
Obtaining Simulation Results¶
In the following cell, the flowsheet will be solved using the IDAES get_solver tool. Setting tee=True will display the solver output.
solver = get_solver()
result = 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...: 186
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 83
Total number of variables............................: 60
variables with only lower bounds: 16
variables with lower and upper bounds: 39
variables with only upper bounds: 0
Total number of equality constraints.................: 60
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 4.25e+02 1.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 0.0000000e+00 4.25e+00 4.84e-02 -1.0 1.00e-02 - 9.90e-01 9.90e-01h 1
2 0.0000000e+00 4.20e-02 9.79e-02 -1.0 1.00e-04 - 9.90e-01 9.90e-01h 1
3 0.0000000e+00 1.16e-10 9.90e+02 -1.0 9.90e-07 - 9.90e-01 1.00e+00h 1
Number of Iterations....: 3
(scaled) (unscaled)
Objective...............: 0.0000000000000000e+00 0.0000000000000000e+00
Dual infeasibility......: 0.0000000000000000e+00 0.0000000000000000e+00
Constraint violation....: 1.1489298971323445e-13 1.1641532182693481e-10
Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
Overall NLP error.......: 1.1489298971323445e-13 1.1641532182693481e-10
Number of objective function evaluations = 4
Number of objective gradient evaluations = 4
Number of equality constraint evaluations = 4
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 4
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 3
Total CPU secs in IPOPT (w/o function evaluations) = 0.001
Total CPU secs in NLP function evaluations = 0.000
EXIT: Optimal Solution Found.
View Results¶
As expected, the report below shows that the three outlet streams share the same composition as the inlet stream with the only difference being their molar flowrate, which was determined by their respective split fractions.
m.fs.sep_1.report()
====================================================================================
Unit : fs.sep_1 Time: 0.0
------------------------------------------------------------------------------------
Unit Performance
Variables:
Key : Value : Units : Fixed : Bounds
Split Fraction [('a1',)] : 0.20000 : dimensionless : True : (None, None)
Split Fraction [('b1',)] : 0.50000 : dimensionless : True : (None, None)
Split Fraction [('c1',)] : 0.30000 : dimensionless : False : (None, None)
------------------------------------------------------------------------------------
Stream Table
Units Inlet a1 b1 c1
Total Molar Flowrate mole / second 10.000 2.0000 5.0000 3.0000
Total Mole Fraction H2O dimensionless 0.90000 0.90000 0.90000 0.90000
Total Mole Fraction CO2 dimensionless 0.10000 0.10000 0.10000 0.10000
Temperature kelvin 353.00 353.00 353.00 353.00
Pressure pascal 1.0132e+05 1.0132e+05 1.0132e+05 1.0132e+05
====================================================================================
Case 2:¶
In the following cell, we will be creating the separator unit model that splits on a phase flow basis and determining the initial degrees of freedom associated with this separator unit model.
m.fs.sep_2 = Separator(
property_package=m.fs.properties,
split_basis=SplittingType.phaseFlow,
outlet_list=["a2", "b2"],
ideal_separation=False,
has_phase_equilibrium=False,
)
DOF_initial = degrees_of_freedom(m)
print('The initial degrees of freedom are: {0}'.format(DOF_initial))
The initial degrees of freedom are: 7
Fixing input specifications¶
In the following cell, we will be specifying the inlet conditions for the separator block and re-evaluating the degrees of freedom to ensure the problem is square (i.e. DOF=0).
m.fs.sep_2.inlet.flow_mol.fix(10) # converting to mol/s as unit basis is mol/s
m.fs.sep_2.inlet.mole_frac_comp[0, "H2O"].fix(0.9)
m.fs.sep_2.inlet.mole_frac_comp[0, "CO2"].fix(0.1)
m.fs.sep_2.inlet.pressure.fix(101325) # Pa
m.fs.sep_2.inlet.temperature.fix(353) # K
m.fs.sep_2.split_fraction[0, "a2", "Vap"].fix(0.8)
m.fs.sep_2.split_fraction[0, "b2", "Liq"].fix(0.8)
DOF_final = degrees_of_freedom(m)
print('The final degrees of freedom is: {0}'.format(DOF_final))
The final degrees of freedom is: 0
Flowsheet Initialization¶
IDAES includes pre-written initialization routines for all unit models. Failing to initialize or having a poor intialization of a flowsheet may result in the problem being unsolvable. The output from initialization can be set to 7 different levels depending on the details required by the user. In general, when a particular output level is set, any information at that level and above gets picked up by logger. The default level taken by the logger is INFO.
More information on these levels can be found in the IDAES documentation: https://idaes-pse.readthedocs.io/en/stable/reference_guides/logging.html
m.fs.sep_2.initialize(outlvl=idaeslog.WARNING)
Obtaining Simulation Results¶
In the following cell, the flowsheet will be solved using the IDAES get_solver tool. Setting tee=True will display the solver output.
solver = get_solver()
result = 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...: 321
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 144
Total number of variables............................: 105
variables with only lower bounds: 28
variables with lower and upper bounds: 67
variables with only upper bounds: 0
Total number of equality constraints.................: 105
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 4.25e+02 1.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 0.0000000e+00 4.25e+00 4.84e-02 -1.0 1.00e-02 - 9.90e-01 9.90e-01h 1
2 0.0000000e+00 4.20e-02 9.79e-02 -1.0 1.00e-04 - 9.90e-01 9.90e-01h 1
3 0.0000000e+00 1.38e-10 9.90e+02 -1.0 9.90e-07 - 9.90e-01 1.00e+00h 1
Number of Iterations....: 3
(scaled) (unscaled)
Objective...............: 0.0000000000000000e+00 0.0000000000000000e+00
Dual infeasibility......: 0.0000000000000000e+00 0.0000000000000000e+00
Constraint violation....: 1.3643542528446593e-13 1.3824319466948509e-10
Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
Overall NLP error.......: 1.3643542528446593e-13 1.3824319466948509e-10
Number of objective function evaluations = 4
Number of objective gradient evaluations = 4
Number of equality constraint evaluations = 4
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 4
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 3
Total CPU secs in IPOPT (w/o function evaluations) = 0.001
Total CPU secs in NLP function evaluations = 0.000
EXIT: Optimal Solution Found.
View Results¶
As expected, the report below shows that the outlet a2 contains 80% of the gaseous CO2 and outlet b2 contains 80% of the liquid H2O.
m.fs.sep_2.report()
====================================================================================
Unit : fs.sep_2 Time: 0.0
------------------------------------------------------------------------------------
Unit Performance
Variables:
Key : Value : Units : Fixed : Bounds
Split Fraction [('a2', 'Liq')] : 0.20000 : dimensionless : False : (None, None)
Split Fraction [('a2', 'Vap')] : 0.80000 : dimensionless : True : (None, None)
Split Fraction [('b2', 'Liq')] : 0.80000 : dimensionless : True : (None, None)
Split Fraction [('b2', 'Vap')] : 0.20000 : dimensionless : False : (None, None)
------------------------------------------------------------------------------------
Stream Table
Units Inlet a2 b2
Total Molar Flowrate mole / second 10.000 3.1220 6.8780
Total Mole Fraction H2O dimensionless 0.90000 0.74375 0.97092
Total Mole Fraction CO2 dimensionless 0.10000 0.25625 0.029078
Temperature kelvin 353.00 353.00 353.00
Pressure pascal 1.0132e+05 1.0132e+05 1.0132e+05
====================================================================================
Case 3:¶
In the following cell, we will be creating the separator unit model that splits on a component flow basis and determining the initial degrees of freedom associated with this separator unit model.
m.fs.sep_3 = Separator(
property_package=m.fs.properties,
split_basis=SplittingType.componentFlow,
outlet_list=["a3", "b3", "c3", "d3"],
ideal_separation=False,
has_phase_equilibrium=False,
)
DOF_initial = degrees_of_freedom(m)
print('The initial degrees of freedom are: {0}'.format(DOF_initial))
The initial degrees of freedom are: 11
Fixing input specifications¶
In the following cell, we will be specifying the inlet conditions for the separator block and re-evaluating the degrees of freedom to ensure the problem is square (i.e. DOF=0).
m.fs.sep_3.inlet.flow_mol.fix(10) # converting to mol/s as unit basis is mol/s
m.fs.sep_3.inlet.mole_frac_comp[0, "H2O"].fix(0.9)
m.fs.sep_3.inlet.mole_frac_comp[0, "CO2"].fix(0.1)
m.fs.sep_3.inlet.pressure.fix(101325) # Pa
m.fs.sep_3.inlet.temperature.fix(353) # K
m.fs.sep_3.split_fraction[0, "a3", "H2O"].fix(0.25)
m.fs.sep_3.split_fraction[0, "b3", "H2O"].fix(0.5)
m.fs.sep_3.split_fraction[0, "c3", "H2O"].fix(0.1)
m.fs.sep_3.split_fraction[0, "a3", "CO2"].fix(0.1)
m.fs.sep_3.split_fraction[0, "b3", "CO2"].fix(0.2)
m.fs.sep_3.split_fraction[0, "c3", "CO2"].fix(0.3)
DOF_final = degrees_of_freedom(m)
print('The final degrees of freedom is: {0}'.format(DOF_final))
The final degrees of freedom is: 0
Flowsheet Initialization¶
IDAES includes pre-written initialization routines for all unit models. Failing to initialize or having a poor intialization of a flowsheet may result in the problem being unsolvable. The output from initialization can be set to 7 different levels depending on the details required by the user. In general, when a particular output level is set, any information at that level and above gets picked up by logger. The default level taken by the logger is INFO.
More information on these levels can be found in the IDAES documentation: https://idaes-pse.readthedocs.io/en/stable/reference_guides/logging.html
m.fs.sep_3.initialize(outlvl=idaeslog.WARNING)
Obtaining Simulation Results¶
In the following cell, the flowsheet will be solved using the IDAES get_solver tool. Setting tee=True will display the solver output.
solver = get_solver()
result = 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...: 561
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 250
Total number of variables............................: 182
variables with only lower bounds: 48
variables with lower and upper bounds: 117
variables with only upper bounds: 0
Total number of equality constraints.................: 182
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 4.25e+02 1.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 0.0000000e+00 4.25e+00 8.00e-02 -1.0 1.00e-02 - 9.90e-01 9.90e-01h 1
2 0.0000000e+00 4.20e-02 9.79e-02 -1.0 1.00e-04 - 9.90e-01 9.90e-01h 1
3 0.0000000e+00 8.73e-11 9.90e+02 -1.0 9.90e-07 - 9.90e-01 1.00e+00h 1
Number of Iterations....: 3
(scaled) (unscaled)
Objective...............: 0.0000000000000000e+00 0.0000000000000000e+00
Dual infeasibility......: 0.0000000000000000e+00 0.0000000000000000e+00
Constraint violation....: 9.5744158094362128e-14 8.7311491370201111e-11
Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
Overall NLP error.......: 9.5744158094362128e-14 8.7311491370201111e-11
Number of objective function evaluations = 4
Number of objective gradient evaluations = 4
Number of equality constraint evaluations = 4
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 4
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 3
Total CPU secs in IPOPT (w/o function evaluations) = 0.001
Total CPU secs in NLP function evaluations = 0.000
EXIT: Optimal Solution Found.
View Results¶
As expected, the report below shows that the component mole fractions in each of the outlet streams are equivalent to their respective split fractions as specified in the input specifications.
m.fs.sep_3.report()
====================================================================================
Unit : fs.sep_3 Time: 0.0
------------------------------------------------------------------------------------
Unit Performance
Variables:
Key : Value : Units : Fixed : Bounds
Split Fraction [('a3', 'CO2')] : 0.10000 : dimensionless : True : (None, None)
Split Fraction [('a3', 'H2O')] : 0.25000 : dimensionless : True : (None, None)
Split Fraction [('b3', 'CO2')] : 0.20000 : dimensionless : True : (None, None)
Split Fraction [('b3', 'H2O')] : 0.50000 : dimensionless : True : (None, None)
Split Fraction [('c3', 'CO2')] : 0.30000 : dimensionless : True : (None, None)
Split Fraction [('c3', 'H2O')] : 0.10000 : dimensionless : True : (None, None)
Split Fraction [('d3', 'CO2')] : 0.40000 : dimensionless : False : (None, None)
Split Fraction [('d3', 'H2O')] : 0.15000 : dimensionless : False : (None, None)
------------------------------------------------------------------------------------
Stream Table
Units Inlet a3 b3 c3 d3
Total Molar Flowrate mole / second 10.000 2.3500 4.7000 1.2000 1.7500
Total Mole Fraction H2O dimensionless 0.90000 0.95745 0.95745 0.75000 0.77143
Total Mole Fraction CO2 dimensionless 0.10000 0.042553 0.042553 0.25000 0.22857
Temperature kelvin 353.00 353.00 353.00 353.00 353.00
Pressure pascal 1.0132e+05 1.0132e+05 1.0132e+05 1.0132e+05 1.0132e+05
====================================================================================