Water/Steam

Two property modules are available for pure water and steam properties. The property modules use the same calculations and yield consistent results, but one uses pressure and molar enthalpy as state variables and the other uses temperature, pressure, and vapor fraction as the state variables.

Theses modules can be imported as:

from idaes.property_models import iapws95_ph

Example

The Heater unit model example, provides a simple example for using water properties.

Since all properties except the state variables are Pyomo Expressions in the water properties module, after solving the problem any property can be calculated in any state block after the problem is solved. To get the viscosity of the water at the heater outlet, for example the line below could be added.

import pyomo.environ as pe
mu_l = pe.value(model.fs.heater.control_volume.properties_out[0].visc_d_phase["Liq"])
mu_v = pe.value(model.fs.heater.control_volume.properties_out[0].visc_d_phase["Vap"])

For more information about how StateBlocks and PropertyParameterBlocks work see the StateBlock documentation.

Units

The water property modules are in SI units (m, kg, s, mol). Temperature is in K.

Methods

These methods use the IAPWS-95 formulation for scientific use for thermodynamic properties (Wagner and Pruss, 2002; IAPWS, 2016). To solve the phase equilibrium, the method of Akasaka (2008) was used. For solving these equations, some relations from the IAPWS-97 formulation for industrial use are used as initial values (Wagner et al., 2002). The industrial formulation is slightly discontinuous between different regions, so it may not be suitable for optimization. In addition to thermodynamic quantities, viscosity and thermal conductivity are calculated (IAPWS, 2008; IAPWS, 2011).

External Functions

The IAPWS-95 formulation uses density and temperature as state variables. For most applications those sate variables are not the most convenient choices. Using other state variables requires solving an equation or two to get density and temperature from the chosen state variables. This can have numerous solutions only one of which is physically meaningful. Rather than solve these equations as part of the full process simulation, external functions were developed that can solve the equations required to change state variables and guarantee the correct roots.

The external property functions are written in C++ and complied such that they can be called by AMPL solvers. See the Installation page for information about compiling these functions. The external functions provide both first and second derivatives for all property function calls, however at phase transitions some of these functions may be non-smooth.

IDAES Framework Wrappers

Wrappers for these function are provided for compatibility with the IDAES framework. Some methods for dealing with non-smoothness may also be included in the IDAES wrappers. The wrappers provide most properties in the form of Pyomo Expressions, with only the chosen set of state variables being Pyomo Vars. The expressions pass the state variables to the external functions and do unit conversion to put the results in SI units. This means that only the state variables can be fixed and other quantities cannot be fixed, but constraints can be added to set them to a specific value.

Since state variables are calculated when solving a model, and the rest of the properties are Expressions, any property available can be easily calculated after the model is solved, whether is was needed in the model or not.

Although not generally used the wrappers provide direct access to the ExternalFunctions also. For more information see section ExternalFunctions

Pressure-Enthalpy

Although Expressions for properties of different phases are available, the pressure-enthalpy formulation treats the fluid as a single mixed phase with a vapor fraction. This bypasses some of the IDAES framework phase equilibrium mechanisms and phase equilibrium is always calculated.

The advantage of this choice of state variables is that it is very robust when phase changes occur, and is especially useful when it is not known if a phase change will occur. The disadvantage of this choice of state variables is that for equations like heat transfer equations that are highly dependent on temperature, a model could be harder to solve near regions with phase change. Temperature is a non-smooth function with a zero derivative with respect to enthalpy in the two-phase region.

The variables for this form are flow_mol (mol/s), pressure (Pa), and enth_mol (J/mol).

Since temperature and vapor fraction are not state variables in this formulation, they are provided by expressions, and cannot be fixed. For example, to set a temperature to a specific value, a constraint could be added which says the temperature expression equals a fixed value.

These expressions are specific to the P-H formulation:

temperature

Expression that calculates temperature by calling an ExternalFunction of enthalpy and pressure. This expression is non-smooth in the transition from single-phase to two-phase and has a zero derivative with respect to enthalpy in the two-phase region.

vapor_frac

Expression that calculates vapor fraction by calling an ExternalFunction of enthalpy and pressure. This expression is non-smooth in the transition from single-phase to two-phase and has a zero derivative with respect to enthalpy in the single-phase region, where the value is 0 (liquid) or 1 (vapor).

Temperature-Pressure-Vapor Fraction

Coming soon.

Expressions

Unless otherwise noted above, the property expressions are common to both the T-P-x and P-H formulations. For phase specific properties, valid phase indexes are "Liq" and "Vap"

Expression	Description
mw	Molecular weight (kg/mol)
tau	Critical temperature divided by temperature (unitless)
temperature_red	Reduced temperature, temperature divided by critical temperature (unitless)
temperature_sat	Saturation temperature (K)
tau_sat	Critical temperature divided by saturation temperature (unitless)
pressure_sat	Saturation pressure (Pa)
dens_mass_phase[phase]	Density phase (kg/m3)
dens_phase_red[phase]	Phase reduced density (\(\delta\)), mass density divided by critical density (unitless)
dens_mass	Total mixed phase mass density (kg/m3)
dens_mol	Total mixed phase mole density (kg/m3)
flow_vol	Total volumetric flow rate (m3/s)
enth_mass	Mass enthalpy (kJ/kg)
enth_mol_sat_phase[phase]	Saturation enthalpy of phase, enthalpy at P and Tsat (kJ/mol)
enth_mol_phase[phase]	Molar enthalpy of phase (kJ/mol)
entr_mol_phase	Molar entropy of phase (kJ/mol/K)
entr_mol	Total mixed phase entropy (kJ/mol/K)
cp_mol_phase[phase]	Constant pressure molar heat capacity of phase (kJ/mol/K)
cv_mol_phase[phase]	Constant pressure volume heat capacity of phase (kJ/mol/K)
cp_mol	Total mixed phase constant pressure heat capacity (kJ/mol/K)
cv_mol	Total mixed phase constant volume heat capacity (kJ/mol/K)
heat_capacity_ratio	cp_mol/cv_mol
speed_sound_phase[phase]	Speed of sound in phase (m/s)
dens_mol_phase[phase]	Mole density of phase (mol/m3)
therm_cond_phase[phase]	Thermal conductivity of phase (W/K/m)
visc_d_phase[phase]	Viscosity of phase (Pa/s)
visc_k_phase[phase]	Kinimatic viscosity of phase (m2/s)
phase_frac[phase]	Phase fraction
flow_mol_comp["H2O"]	Same as total flow since only water (mol/s)

ExternalFunctions

This provides a list of ExternalFuctions available in the wrappers. These functions do not use SI units and are not usually called directly. If these functions are needed, they should be used with caution. Some of these are used in the property expressions, some are just provided to allow easier testing with a Python framework.

All of these functions provide first and second derivative and are generally suited to optimization. Some functions may have non-smoothness at phase transitions. The delta_vap and delta_liq functions return the same values in the critical region. They will also return real values when a phase doesn’t exist, but those values do not necessarily have physical meaning.

There are a few variables that are common to a lot of these functions, so they are summarized here \(tau\) is the critical temperature divided by the temperature \(\frac{T_c}{T}\), \(\delta\) is density divided by the critical density \(\frac{\rho}{\rho_c}\), and \(\phi\) is Helmholtz free energy divided by the ideal gas constant and temperature \(\frac{f}{RT}\).

Pyomo Function	C Function	Returns	Arguments
func_p	p	pressure (kPa)	\(\delta, \tau\)
func_u	u	internal energy (kJ/kg)	\(\delta, \tau\)
func_s	s	entropy (kJ/K/kg)	\(\delta, \tau\)
func_h	h	enthalpy (kJ/kg)	\(\delta, \tau\)
func_hvpt	hvpt	vapor enthalpy (kJ/kg)	P (kPa), \(\tau\)
func_hlpt	hlpt	liquid enthalpy (kJ/kg)	P (kPa), \(\tau\)
func_tau	tau	\(\tau\) (unitless)	h (kJ/kg), P (kPa)
func_vf	vf	vapor fraction (unitless)	h (kJ/kg), P (kPa)
func_g	g	Gibbs free energy (kJ/kg)	\(\delta, \tau\)
func_f	f	Helmholtz free energy (kJ/kg)	\(\delta, \tau\)
func_cv	cv	const. volume heat capacity (kJ/K/kg)	\(\delta, \tau\)
func_cp	cp	const. pressure heat capacity (kJ/K/kg)	\(\delta, \tau\)
func_w	w	speed of sound (m/s)	\(\delta, \tau\)
func_delta_liq	delta_liq	liquid \(\delta\) (unitless)	P (kPa), \(\tau\)
func_delta_vap	delta_vap	vapor \(\delta\) (unitless)	P (kPa), \(\tau\)
func_delta_sat_l	delta_sat_l	sat. liquid \(\delta\) (unitless)	\(\tau\)
func_delta_sat_v	delta_sat_v	sat. vapor \(\delta\) (unitless)	\(\tau\)
func_p_sat	p_sat	sat. pressure (kPa)	\(\tau\)
func_tau_sat	tau_sat	sat. \(\tau\) (unitless)	P (kPa)
func_phi0	phi0	\(\phi\) idaes gas part (unitless)	\(\delta, \tau\)
func_phi0_delta	phi0_delta	\(\frac{\partial \phi_0}{\partial \delta}\)	\(\delta\)
func_phi0_delta2	phi0_delta2	\(\frac{\partial^2 \phi_0}{\partial \delta^2}\)	\(\delta\)
func_phi0_tau	phi0_tau	\(\frac{\partial \phi_0}{\partial \tau}\)	\(\tau\)
func_phi0_tau2	phi0_tau2	\(\frac{\partial^2 \phi_0}{\partial \tau^2}\)	\(\tau\)
func_phir	phir	\(\phi\) real gas part (unitless)	\(\delta, \tau\)
func_phir_delta	phir_delta	\(\frac{\partial \phi_r}{\partial \delta}\)	\(\delta, \tau\)
func_phir_delta2	phir_delta2	\(\frac{\partial^2 \phi_r}{\partial \delta^2}\)	\(\delta, \tau\)
func_phir_tau	phir_tau	\(\frac{\partial \phi_r}{\partial \tau}\)	\(\delta, \tau\)
func_phir_tau2	phir_tau2	\(\frac{\partial^2 \phi_r}{\partial \tau^2}\)	\(\delta, \tau\)
func_phir_delta_tau	phir_delta_tau	\(\frac{\partial^2 \phi_r}{\partial \delta \partial \tau}\)	\(\delta, \tau\)

Initialization

The IAPWS-95 property functions do provide initilaization functions for general compatibility with the IDAES framework, but as long as the state variables are specified to some resonalbe value, initialization is not required. All required solves are handled by external functions.

References

International Association for the Properties of Water and Steam (2016). IAPWS R6-95 (2016), “Revised Release on the IAPWS Formulation 1995 for the Properties of Ordinary Water Substance for General Scientific Use,” URL: http://iapws.org/relguide/IAPWS95-2016.pdf

Wagner, W., A. Pruss (2002). “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use.” J. Phys. Chem. Ref. Data, 31, 387-535.

Wagner, W. et al. (2000). “The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam,” ASME J. Eng. Gas Turbines and Power, 122, 150-182.

Akasaka, R. (2008). “A Reliable and Useful Method to Determine the Saturation State from Helmholtz Energy Equations of State.” Journal of Thermal Science and Technology, 3(3), 442-451.

International Association for the Properties of Water and Steam (2011). IAPWS R15-11, “Release on the IAPWS Formulation 2011 for the Thermal Conductivity of Ordinary Water Substance,” URL: http://iapws.org/relguide/ThCond.pdf.

International Association for the Properties of Water and Steam (2008). IAPWS R12-08, “Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance,” URL: http://iapws.org/relguide/visc.pdf.

Convenience Functions

idaes.property_models.iapws95.iapws95_wrap_ph.htpx(T, P=None, x=None)

Conveneince function to calculate steam enthalpy from temperature and either pressure or vapor fraction. This function can be used for inlet streams and initialization where temperature is known instread of enthalpy. :param T: Temperature [K] :param P: Pressure [Pa], None if saturated steam :param x: Vapor fraction [mol vapor/mol total], None if superheated or subcooled

Returns:Molar enthalpy [J/mol].

Iapws95StateBlock Class

class idaes.property_models.iapws95.iapws95_wrap_ph.Iapws95StateBlock(*args, **kwargs)

This is some placeholder doc.

Parameters:

• rule (function) – A rule function or None. Default rule calls build().
• concrete (bool) – If True, make this a toplevel model. Default - False.
• ctype (str) – Pyomo ctype of the block. Default - “Block”
• default (dict) –

  Default ProcessBlockData config

  Keys

  parameters

  A reference to an instance of the Property Parameter Block associated with this property package.

  defined_state

  Flag indicating whether the state should be considered fully defined, and thus whether constraints such as sum of mass/mole fractions should be included, default - False. Valid values: { True - state variables will be fully defined, False - state variables will not be fully defined.}

  has_phase_equilibrium

  Flag indicating whether phase equilibrium constraints should be constructed in this state block, default - True. Valid values: { True - StateBlock should calculate phase equilibrium, False - StateBlock should not calculate phase equilibrium.}

• initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries described under the “default” argument above.
• 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 overide the default behavior of matching the BlockData index exactly to the index in initialize.

Returns:

(Iapws95StateBlock) New instance

Iapws95StateBlockData Class

class idaes.property_models.iapws95.iapws95_wrap_ph.Iapws95StateBlockData(component)

This is a property package for calcuating thermophysical properties of water

build(*args)

Callable method for Block construction

define_state_vars()

Method that returns a dictionary of state variables used in property package. Implement a placeholder method which returns an Exception to force users to overload this.

get_enthalpy_density_terms(p)

Method which returns a valid expression for enthalpy density to use in the energy balances.

get_enthalpy_flow_terms(p)

Method which returns a valid expression for enthalpy flow to use in the energy balances.

get_material_density_terms(p, j)

Method which returns a valid expression for material density to use in the material balances .

get_material_flow_terms(p, j)

Method which returns a valid expression for material flow to use in the material balances.

Iapws95ParameterBlock Class

class idaes.property_models.iapws95.iapws95_wrap_ph.Iapws95ParameterBlock(*args, **kwargs)

Parameters:

• rule (function) – A rule function or None. Default rule calls build().
• concrete (bool) – If True, make this a toplevel model. Default - False.
• ctype (str) – Pyomo ctype of the block. Default - “Block”
• default (dict) –

  Default ProcessBlockData config

  Keys

  default_arguments

  Default arguments to use with Property Package

• initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries described under the “default” argument above.
• 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 overide the default behavior of matching the BlockData index exactly to the index in initialize.

Returns:

(Iapws95ParameterBlock) New instance

Iapws95ParameterBlockData Class

class idaes.property_models.iapws95.iapws95_wrap_ph.Iapws95ParameterBlockData(component)

build()

General build method for PropertyParameterBlocks. Inheriting models should call super().build.

Parameters:None – Returns:None

classmethod define_metadata(obj)

Set all the metadata for properties and units.

This method should be implemented by subclasses. In the implementation, they should set information into the object provided as an argument.

Parameters:pcm (PropertyClassMetadata) – Add metadata to this object. Returns:None