Valve¶
Tutorial: Valve Unit Model with IAPWS Property Package¶
Learning Outcomes¶
- Demonstrate use of the valve unit model in IDAES
Problem Statement¶
In this example, we will be passing a liquid stream through a valve.
Stream Inputs:
Flow Rate = 1000 mol/s
Temperature = 298 K
Inlet Pressure = 202650 Pa
Outlet Pressure = 101325 Pa
Valve Opening = 0.5 (fraction)
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 math functions
import math
# Import objects from pyomo package
from pyomo.environ import ConcreteModel, Constraint, value, SolverFactory, units
# 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 Valve unit model
from idaes.models.unit_models import Valve
# Import the option to set the valve function
from idaes.models.unit_models import ValveFunctionType
# Import idaes logger to set output levels
import idaes.logger as idaeslog
# Import the iapws95 property package to create a property block for the flowsheet
from idaes.models.properties import iapws95
# 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 = iapws95.Iapws95ParameterBlock()
In the following cell, we will be creating the valve unit model, assigning the valve function and property package to it, and determining the initial degrees of freedom associated with the valve unit model. The ValveFunctionType determines how the flow coefficient will be calculated.
m.fs.valve = Valve(
valve_function_callback=ValveFunctionType.linear,
property_package=m.fs.properties
)
DOF_initial = degrees_of_freedom(m)
print('The initial degrees of freedom is: {0}'.format(DOF_initial))
The initial degrees of freedom is: 3
Fixing input specifications¶
In the following cell, we will be calculating and specifying the inlet conditions for the valve block and re-evaluating the degrees of freedom to ensure the problem is square (i.e. DOF=0).
# Assign the known inlet conditions to variables
fin = 1000 # mol/s
pin = 202650 # Pa
pout = 101325 # Pa
tin = 298 # K
# Determine inlet enthalpy
hin = iapws95.htpx(T=tin * units.K, P=pin * units.Pa) # J/mol
# Determine flow coefficient - equation depends on the valve function specified earlier
cv = 1000 / math.sqrt(pin - pout) / 0.5
# Fix the inlet conditions
m.fs.valve.inlet.enth_mol[0].fix(hin)
m.fs.valve.inlet.flow_mol[0].fix(fin)
m.fs.valve.inlet.pressure[0].fix(pin)
m.fs.valve.outlet.pressure[0].set_value(pout) # Sets the target value for the outlet pressure, but does not fix it
m.fs.valve.Cv.fix(cv)
m.fs.valve.valve_opening.fix(0.5)
# Call the degrees_of_freedom function, get final DOF
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?highlight=log%20level#idaes-solve-loggers
m.fs.valve.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...: 10
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 3
Total number of variables............................: 6
variables with only lower bounds: 0
variables with lower and upper bounds: 2
variables with only upper bounds: 0
Total number of equality constraints.................: 6
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 0.00e+00 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....: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00
Overall NLP error.......: 0.0000000000000000e+00 0.0000000000000000e+00
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) = 0.000
Total CPU secs in NLP function evaluations = 0.000
EXIT: Optimal Solution Found.
View Results¶
As expected, the report will show that pressure of the stream is halved after going through the valve.
m.fs.valve.report()
====================================================================================
Unit : fs.valve Time: 0.0
------------------------------------------------------------------------------------
Unit Performance
Variables:
Key : Value : Units : Fixed : Bounds
Mechanical Work : 0.0000 : watt : False : (None, None)
Opening : 0.50000 : dimensionless : True : (0, 1)
Pressure Change : -1.0132e+05 : pascal : False : (None, None)
Pressure Ratio : 0.50000 : dimensionless : False : (None, None)
Valve Coefficient : 6.2831 : meter ** 0.5 * mole / kilogram ** 0.5 : True : (None, None)
------------------------------------------------------------------------------------
Stream Table
Units Inlet Outlet
Molar Flow mole / second 1000.0 1000.0
Mass Flow kilogram / second 18.015 18.015
T kelvin 298.00 298.02
P pascal 2.0265e+05 1.0132e+05
Vapor Fraction dimensionless 0.0000 0.0000
Molar Enthalpy joule / mole 1880.6 1880.6
====================================================================================