###############################################################################
# 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 conjuction 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

2023-11-02 10:29:59 [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 `1.3789905650578088e-06` outside the bounds (None, 0).
    See also https://pyomo.readthedocs.io/en/stable/errors.html#w1002

2023-11-02 10:29:59 [INFO] idaes.init.fs.state_block: Dew and bubble point initialization: optimal - Optimal Solution Found.

2023-11-02 10:29:59 [INFO] idaes.init.fs.state_block: Equilibrium temperature initialization completed.

2023-11-02 10:29:59 [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 10:30:00 [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.

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.

IDAES Examples

Using Parameter Estimation with Modular Property Packages

Contents