# Valve¶

This section describes the generic adiabatic valve model. By default the model is based on molar flow, but the pressure-flow equation and the flow basis is configurable. This model inherits the PressureChanger model with the adiabatic options. Beyond the base pressure changer model this provides a pressure flow relation as a function of the valve opening fraction.

## Example¶

from pyomo.environ import ConcreteModel, SolverFactory, TransformationFactory

from idaes.core import FlowsheetBlock
from idaes.models.unit_models import Valve
from idaes.models.properties import iapws95
import idaes.core.util.scaling as iscale

m = ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False)
m.fs.properties = iapws95.Iapws95ParameterBlock()
m.fs.valve = Valve(property_package=m.fs.properties)
fin = 900 # mol/s
pin = 200000 # Pa
pout = 100000 # Pa
tin = 300 # K
hin = iapws95.htpx(T=tin*units.K, P=pin*units.Pa) # J/mol
# Calculate the flow coefficient to give 1000 mol/s flow with given P
cv = 1000/math.sqrt(pin - pout)/0.5
# set inlet
m.fs.valve.inlet.enth_mol[0].fix(hin)
m.fs.valve.inlet.flow_mol[0].fix(fin)
m.fs.valve.inlet.flow_mol[0].unfix()
m.fs.valve.inlet.pressure[0].fix(pin)
m.fs.valve.outlet.pressure[0].fix(pout)
m.fs.valve.Cv.fix(cv)
m.fs.valve.valve_opening.fix(0.5)
iscale.calculate_scaling_factors(m)
m.fs.valve.initialize(outlvl=1)

solver = pyo.SolverFactory("ipopt")
solver.options = {"nlp_scaling_method": "user-scaling"}
solver(m, tee=True)


## Variables¶

Variable

Symbol

Index Sets

Doc

Cv

$$C_v$$

None

Valve coefficient

valve_opening

$$x$$

time

The fraction that the valve is open from 0 to 1

The Cv variable is highly recommended but can be omitted in custom pressure-flow relations.

## Expressions¶

Expression

Symbol

Index Sets

Doc

valve_function

$$f(x)$$

time

This is a valve function that describes how the fraction open affects flow.

### Built-in Valve Functions¶

Standard valve functions can be specified by providing a ValveFunctionType enumerated type to the valve_function_callback argument. Standard functions are given below.

ValveFunctionType.linear

$f(x) = x$

ValveFunctionType.quick_opening

$f(x) = \sqrt{x}$

ValveFunctionType.equal_percentage

$f(x) = \alpha^{x - 1}$

For the equal-percentage valve function an additional variable alpha is defined which by default is fixed and set to 100.

### Custom Valve Functions¶

In general, the valve opening should be restricted to range from 0 to 1. The valve function should be a named expression attached to the valve model called valve_function which takes the valve opening and computes a value that goes from approximately zero when valve opening is 0 to 1 when the valve opening is one. The valve function can have parameters as needed, so custom valve functions are defined using a callback function.

The callback function should take an object of the Valve class as an argument and add the valve_function named expression. Any additional parameters can also be added. The standard equal-percentage valve function is provided below as an example. The callback can be provided for the valve_function_callback configuration option.

def equal_percentage_cb(b):
"""
Equal percentage valve function callback.
"""
# Parameters can be defined as Var or Param.  If Var is used the parameter
# can be included in a parameter estimation problem.
b.alpha = pyo.Var(initialize=100, doc="Valve function parameter")
b.alpha.fix()
@b.Expression(b.flowsheet().config.time)
def valve_function(b2, t):
return b2.alpha ** (b2.valve_opening[t] - 1)


## Constraints¶

The pressure flow relation is added to the inherited constraints from the PressureChanger model.

The default pressure-flow relation is given below where $$F$$ is the molar flow. The default valve function assumes an incompressible fluid of constant density. In this case the fluid specific gravity is included in the flow coefficient. For rigorous modeling of valves with gases, it is recommended that a custom pressure-flow equation be specified.

$F^2 = C_v^2\left(P_{in} - P_{out}\right)f(x)^2$

### Custom Pressure Flow Relations¶

Other pressure-flow equations can be specified via callback supplied to the unit configuration option pressure_flow_callback. The callback allows both the form and flow basis of the pressure-flow equation to be specified.

The callback can add parameters and variables as needed. It is recommended that only the pressure_flow_equation be specified as additional constraints would not be scaled by the valve model’s scaling routines. The pressure flow relation generally should be written in the form below to facilitate scaling where $$F$$ is flow variable.

$f_1(F) = f_2(P_{in}, P_{out})$

The callback takes a Valve model object as an argument. There are three attributes that the pressure_flow_callback should define: 1. flow_var a time indexed reference to the flow variable basis, 2. pressure_flow_equation_scale a function that takes flow_var and defines the form of the flow term 3. pressure_flow_equation the pressure flow relation constraint.

The first two items, flow_var and pressure_flow_equation_scale, are not directly used in the model, but are used by the model scaling routine.

The example callback below is the model default pressure-flow equation.

def pressure_flow_default_callback(b):
"""
Add the default pressure flow relation constraint.  This will be used in the
valve model, a custom callback is provided.
"""

b.Cv = pyo.Var(
initialize=0.1,
doc="Valve flow coefficent",
units=umeta("amount")/umeta("time")/umeta("pressure")**0.5
)
b.Cv.fix()

b.flow_var = pyo.Reference(b.control_volume.properties_in[:].flow_mol)
b.pressure_flow_equation_scale = lambda x : x**2

@b.Constraint(b.flowsheet().config.time)
def pressure_flow_equation(b2, t):
Po = b2.control_volume.properties_out[t].pressure
Pi = b2.control_volume.properties_in[t].pressure
F = b2.control_volume.properties_in[t].flow_mol
Cv = b2.Cv
fun = b2.valve_function[t]
return F ** 2 == Cv ** 2 * (Pi - Po) * fun ** 2


## Initialization¶

This just calls the initialization routine from PressureChanger. Either an outlet pressure value or deltaP can be specified to aid the initialization.

## Valve Class¶

class idaes.models.unit_models.valve.Valve(*args, **kwds)

Parameters
• rule (function) – A rule function or None. Default rule calls build().

• concrete (bool) – If True, make this a toplevel model. Default - False.

• ctype (class) –

Pyomo ctype of the block. Default - pyomo.environ.Block

Config args
dynamic

Indicates whether this model will be dynamic or not, default = useDefault. Valid values: { useDefault - get flag from parent (default = False), True - set as a dynamic model, False - set as a steady-state model.}

has_holdup

Indicates whether holdup terms should be constructed or not. Must be True if dynamic = True, default - False. Valid values: { useDefault - get flag from parent (default = False), True - construct holdup terms, False - do not construct holdup terms}

material_balance_type

Indicates what type of mass balance should be constructed, default - MaterialBalanceType.useDefault. Valid values: { MaterialBalanceType.useDefault - refer to property package for default balance type **MaterialBalanceType.none - exclude material balances, MaterialBalanceType.componentPhase - use phase component balances, MaterialBalanceType.componentTotal - use total component balances, MaterialBalanceType.elementTotal - use total element balances, MaterialBalanceType.total - use total material balance.}

energy_balance_type

Indicates what type of energy balance should be constructed, default - EnergyBalanceType.useDefault. Valid values: { EnergyBalanceType.useDefault - refer to property package for default balance type **EnergyBalanceType.none - exclude energy balances, EnergyBalanceType.enthalpyTotal - single enthalpy balance for material, EnergyBalanceType.enthalpyPhase - enthalpy balances for each phase, EnergyBalanceType.energyTotal - single energy balance for material, EnergyBalanceType.energyPhase - energy balances for each phase.}

momentum_balance_type

Indicates what type of momentum balance should be constructed, default - MomentumBalanceType.pressureTotal. Valid values: { MomentumBalanceType.none - exclude momentum balances, MomentumBalanceType.pressureTotal - single pressure balance for material, MomentumBalanceType.pressurePhase - pressure balances for each phase, MomentumBalanceType.momentumTotal - single momentum balance for material, MomentumBalanceType.momentumPhase - momentum balances for each phase.}

has_phase_equilibrium

Indicates whether terms for phase equilibrium should be constructed, default = False. Valid values: { True - include phase equilibrium terms False - exclude phase equilibrium terms.}

compressor

Indicates whether this unit should be considered a compressor (True (default), pressure increase) or an expander (False, pressure decrease).

thermodynamic_assumption

Flag to set the thermodynamic assumption to use for the unit. - ThermodynamicAssumption.isothermal (default) - ThermodynamicAssumption.isentropic - ThermodynamicAssumption.pump - ThermodynamicAssumption.adiabatic

property_package

Property parameter object used to define property calculations, default - useDefault. Valid values: { useDefault - use default package from parent model or flowsheet, PropertyParameterObject - a PropertyParameterBlock object.}

property_package_args

A ConfigBlock with arguments to be passed to a property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}

support_isentropic_performance_curves

Include a block for performance curves, configure via isentropic_performance_curves.

isentropic_performance_curves

Configuration dictionary for the performance curve block.

build_callback

Optional callback to add performance curve constraints

If true add expressions for ‘head’ and ‘head_isentropic’. These expressions can be used in performance curve constraints.

valve_function_callback

This takes either an enumerated valve function type in: { ValveFunctionType.linear, ValveFunctionType.quick_opening, ValveFunctionType.equal_percentage, ValveFunctionType.custom} or a callback function that takes a valve model object as an argument and adds a time- indexed valve_function expression to it. Any additional required variables, expressions, or constraints required can also be added by the callback.

pressure_flow_callback

This callback function takes a valve model object as an argument and adds a time-indexed valve_function expression to it. Any additional required variables, expressions, or constraints required can also be added by the callback.

• initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries with config arguments as keys.

• idx_map (function) – Function to take the index of a BlockData element and return the index in the initialize dict from which to read arguments. This can be provided to override the default behavior of matching the BlockData index exactly to the index in initialize.

Returns

(Valve) New instance

## ValveData Class¶

class idaes.models.unit_models.valve.ValveData(component)[source]
build()[source]
Parameters

None

Returns

None

calculate_scaling_factors()[source]

Calculate pressure flow constraint scaling from flow variable scale.

initialize_build(state_args=None, outlvl=0, solver=None, optarg=None)[source]

Initialize the valve based on a deltaP guess.

Parameters
• state_args (dict) – Initial state for property initialization

• outlvl – sets output level of initialization routine

• solver (str) – Solver to use for initialization

• optarg (dict) – Solver arguments dictionary