Compressor¶
Tutorial: Compressor Unit Model with Span-Wagner Property Package for supercritical CO2¶
Learning Outcomes¶
- Demonstrate use of the compressor unit model in IDAES
- Demonstarte use of the Span Wagner EOS for supercritical CO2 cycles
- Demonstrate different simulation options available for the compressor unit model
In this tutorial, we will simulate the main compressor for an indirect supercritical CO2 cycle using the Span-Wagner EOS as the property package. The input specifications for this tutorial are from the NETL report on indirect SCO2 cycles available here. In this example, we will be compressing supercritical CO2 from 9.1 MPa to 34.5 MPa.
It is assumed that the compressor operates at steady state.
The inlet specifications are as follows:
- Flow Rate = 91067 mol/s
- Pressure = 9.1107 MPa
- Temperature = 308.15 K
We will simulate 2 different cases, depending on the compressor specifications fixed by the user:
Case 1: In this case, we will fix the isentropic efficiency and the pressure change across the compressor.
- Pressure Change = 25.51 MPa
- Isentropic Efficiency = 0.85
Case 2: In this case, we will fix the isentropic efficiency and the pressure ratio instead of the pressure change across the compressor.
- Pressure Ratio = 3.8
- Isentropic Efficiency = 0.85
IDAES documentation:https://idaes-pse.readthedocs.io/en/stable/
Setting up the problem in IDAES¶
In the following cell, we will be importing the necessary components from Pyomo and IDAES.
In [1]:
# Import objects from pyomo package
from pyomo.environ import ConcreteModel, SolverFactory, value, units
# 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
# Create the ConcreteModel and the FlowsheetBlock, and attach the flowsheet block to it.
m = ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False) # dynamic or ss flowsheet needs to be specified here
# Import the SWCO2 property package to create a properties block for the flowsheet
from idaes.models.properties.swco2 import SWCO2ParameterBlock, StateVars, htpx
# Add properties parameter block to the flowsheet with specifications
m.fs.properties = SWCO2ParameterBlock()
Case 1: Fix pressure change and isentropic efficiency¶
Add Compressor Unit Model¶
In [2]:
# Import compressor unit model from the model library
from idaes.models.unit_models.pressure_changer import PressureChanger,ThermodynamicAssumption
# Create an instance of the compressor unit, attaching it to the flowsheet
# Specify that the property package to be used with the compressor is the one we created earlier.
m.fs.compr_case_1 = PressureChanger(
dynamic=False,
property_package=m.fs.properties,
compressor=True,
thermodynamic_assumption=ThermodynamicAssumption.isentropic)
# 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
# Call the degrees_of_freedom function, get intitial DOF
DOF_initial = degrees_of_freedom(m)
print("The initial DOF is {0}".format(DOF_initial))
The initial DOF is 5
Fix Inlet Stream Conditions¶
In [3]:
# Fix the stream inlet conditions
m.fs.compr_case_1.inlet.flow_mol[0].fix(91067) # mol/s
# Use htpx method to obtain the molar enthalpy of inlet stream at the given temperature and pressure conditions
m.fs.compr_case_1.inlet.enth_mol[0].fix(value(htpx(T=308.15*units.K, P=9.1107e+06*units.Pa))) # T in K, P in Pa
m.fs.compr_case_1.inlet.pressure[0].fix(9.1107e+06)
Fix Pressure Change and Isentropic Efficiency¶
In [4]:
# Fix compressor conditions
m.fs.compr_case_1.deltaP.fix(2.5510e+07)
m.fs.compr_case_1.efficiency_isentropic.fix(0.85)
# Call the degrees_of_freedom function, get final DOF
DOF_final = degrees_of_freedom(m)
print("The final DOF is {0}".format(DOF_final))
The final DOF is 0
Initialization¶
In [5]:
# Initialize the flowsheet, and set the output at INFO level
m.fs.compr_case_1.initialize(outlvl=idaeslog.INFO)
2023-03-04 01:47:38 [INFO] idaes.init.fs.compr_case_1: Initialization Complete: optimal - Optimal Solution Found
Solve Model¶
In [6]:
# Solve the simulation using ipopt
# Note: If the degrees of freedom = 0, we have a square problem
opt = SolverFactory('ipopt')
solve_status = opt.solve(m, tee=True)
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...: 18
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 8
Total number of variables............................: 9
variables with only lower bounds: 0
variables with lower and upper bounds: 4
variables with only upper bounds: 0
Total number of equality constraints.................: 9
Total number of inequality constraints...............: 0
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 0.0000000e+00 3.12e-11 0.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
Number of Iterations....: 0
(scaled) (unscaled)
Objective...............: 0.0000000000000000e+00 0.0000000000000000e+00
Dual infeasibility......: 0.0000000000000000e+00 0.0000000000000000e+00
Constraint violation....: 3.1150193535722792e-11 3.1150193535722792e-11
Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
Overall NLP error.......: 3.1150193535722792e-11 3.1150193535722792e-11
Number of objective function evaluations = 1
Number of objective gradient evaluations = 1
Number of equality constraint evaluations = 1
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 1
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 0
Total CPU secs in IPOPT (w/o function evaluations) = 0.002
Total CPU secs in NLP function evaluations = 0.000
EXIT: Optimal Solution Found.
View Results¶
In [7]:
# Display Outlet Pressure
m.fs.compr_case_1.outlet.pressure.display()
_pressure_outlet_ref : Size=1, Index=fs._time, ReferenceTo=fs.compr_case_1.control_volume.properties_out[...].component('pressure')
Key : Lower : Value : Upper : Fixed : Stale : Domain
0.0 : 1.0000000000000002e-06 : 34620700.0 : 500000000.0 : False : False : PositiveReals
In [8]:
# Display a readable report
m.fs.compr_case_1.report()
====================================================================================
Unit : fs.compr_case_1 Time: 0.0
------------------------------------------------------------------------------------
Unit Performance
Variables:
Key : Value : Units : Fixed : Bounds
Isentropic Efficiency : 0.85000 : dimensionless : True : (None, None)
Mechanical Work : 1.5934e+08 : watt : False : (None, None)
Pressure Change : 2.5510e+07 : pascal : True : (None, None)
Pressure Ratio : 3.8000 : dimensionless : False : (None, None)
------------------------------------------------------------------------------------
Stream Table
Units Inlet Outlet
Molar Flow mole / second 91067. 91067.
Mass Flow kilogram / second 4007.8 4007.8
T kelvin 308.15 348.81
P pascal 9.1107e+06 3.4621e+07
Vapor Fraction dimensionless 0.0000 0.0000
Molar Enthalpy joule / mole -9215.6 -7465.9
====================================================================================
Case 2: Fix pressure ratio and isentropic efficiency¶
Add Compressor Unit¶
In [9]:
# Create an instance of another compressor unit, attaching it to the flowsheet
# Specify that the property package to be used with the turbine is the one we created earlier.
m.fs.compr_case_2 = PressureChanger(
dynamic=False,
property_package=m.fs.properties,
compressor=True,
thermodynamic_assumption=ThermodynamicAssumption.isentropic)
# Call the degrees_of_freedom function, get intitial DOF
DOF_initial = degrees_of_freedom(m.fs.compr_case_2)
print("The initial DOF is {0}".format(DOF_initial))
The initial DOF is 5
Fix Inlet Stream Conditions¶
In [10]:
# Fix the stream inlet conditions
m.fs.compr_case_2.inlet.flow_mol[0].fix(91067) # converting to mol/s as unit basis is mol/s
# Use htpx method to obtain the molar enthalpy of inlet stream at the given temperature and pressure conditions
m.fs.compr_case_2.inlet.enth_mol[0].fix(value(htpx(T=308.15*units.K, P=9.1107e+06*units.Pa)))
m.fs.compr_case_2.inlet.pressure[0].fix(9.1107e+06)
Fix Compressor Pressure Ratio and Isentropic Efficiency¶
In [11]:
# Fix compressor pressure ratio
m.fs.compr_case_2.ratioP.fix(3.8)
# Fix compressor efficiency
m.fs.compr_case_2.efficiency_isentropic.fix(0.85)
# Call the degrees_of_freedom function, get final DOF
DOF_final = degrees_of_freedom(m.fs.compr_case_2)
print("The final DOF is {0}".format(DOF_final))
The final DOF is 0
Initialization¶
In [12]:
# Initialize the flowsheet, and set the output at INFO level
m.fs.compr_case_2.initialize(outlvl=idaeslog.INFO)
2023-03-04 01:47:38 [INFO] idaes.init.fs.compr_case_2: Initialization Complete: optimal - Optimal Solution Found
Solve Model¶
In [13]:
# Solve the simulation using ipopt
# Note: If the degrees of freedom = 0, we have a square problem
opt = SolverFactory('ipopt')
solve_status = opt.solve(m.fs.compr_case_2, tee=True)
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...: 18
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 8
Total number of variables............................: 9
variables with only lower bounds: 0
variables with lower and upper bounds: 4
variables with only upper bounds: 0
Total number of equality constraints.................: 9
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 1.19e-07 0.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
Number of Iterations....: 0
(scaled) (unscaled)
Objective...............: 0.0000000000000000e+00 0.0000000000000000e+00
Dual infeasibility......: 0.0000000000000000e+00 0.0000000000000000e+00
Constraint violation....: 1.3090284027230638e-10 1.1920928955078125e-07
Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
Overall NLP error.......: 1.3090284027230638e-10 1.1920928955078125e-07
Number of objective function evaluations = 1
Number of objective gradient evaluations = 1
Number of equality constraint evaluations = 1
Number of inequality constraint evaluations = 0
Number of equality constraint Jacobian evaluations = 1
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations = 0
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¶
In [14]:
# Display compressor pressure increase
m.fs.compr_case_2.outlet.pressure[0].display()
pressure : Pressure
Size=1, Index=None, Units=Pa
Key : Lower : Value : Upper : Fixed : Stale : Domain
None : 1.0000000000000002e-06 : 34620660.0 : 500000000.0 : False : False : PositiveReals
In [15]:
# Display a readable report
m.fs.compr_case_2.report()
====================================================================================
Unit : fs.compr_case_2 Time: 0.0
------------------------------------------------------------------------------------
Unit Performance
Variables:
Key : Value : Units : Fixed : Bounds
Isentropic Efficiency : 0.85000 : dimensionless : True : (None, None)
Mechanical Work : 1.5934e+08 : watt : False : (None, None)
Pressure Change : 2.5510e+07 : pascal : False : (None, None)
Pressure Ratio : 3.8000 : dimensionless : True : (None, None)
------------------------------------------------------------------------------------
Stream Table
Units Inlet Outlet
Molar Flow mole / second 91067. 91067.
Mass Flow kilogram / second 4007.8 4007.8
T kelvin 308.15 348.81
P pascal 9.1107e+06 3.4621e+07
Vapor Fraction dimensionless 0.0000 0.0000
Molar Enthalpy joule / mole -9215.6 -7465.9
====================================================================================