Species Standard-State Thermodynamic Properties

In this module we describe Cantera's treatment of pressure dependent standard states (PDSS) objects. More...

Collaboration diagram for Species Standard-State Thermodynamic Properties:

Classes
class	PDSS
	Virtual base class for a species with a pressure dependent standard state. More...
class	PDSS_ConstVol
	Class for pressure dependent standard states that use a constant volume model. More...
class	PDSS_HKFT
	Class for pressure dependent standard states corresponding to ionic solutes in electrolyte water. More...
class	PDSS_IdealGas
	Derived class for pressure dependent standard states of an ideal gas species. More...
class	PDSS_IonsFromNeutral
	Derived class for pressure dependent standard states of an ideal gas species. More...
class	PDSS_SSVol
	Class for pressure dependent standard states that uses a standard state volume model of some sort. More...
class	PDSS_Water
	Class for the liquid water pressure dependent standard state. More...

Detailed Description

In this module we describe Cantera's treatment of pressure dependent standard states (PDSS) objects.

These are objects that calculate the standard state of a single species that depends on both temperature and pressure.

To compute the thermodynamic properties of multicomponent solutions, it is necessary to know something about the thermodynamic properties of the individual species present in the solution. Exactly what sort of species properties are required depends on the thermodynamic model for the solution. For a gaseous solution (i.e., a gas mixture), the species properties required are usually ideal gas properties at the mixture temperature and at a reference pressure (almost always at 1 bar). For other types of solutions, however, it may not be possible to isolate the species in a "pure" state. For example, the thermodynamic properties of, say, Na+ and Cl- in saltwater are not easily determined from data on the properties of solid NaCl, or solid Na metal, or chlorine gas. In this case, the solvation in water is fundamental to the identity of the species, and some other reference state must be used. One common convention for liquid solutions is to use thermodynamic data for the solutes in the limit of infinite dilution within the pure solvent; another convention is to reference all properties to unit molality.

In defining these standard states for species in a phase, we make the following definition. A reference state is a standard state of a species in a phase limited to one particular pressure, the reference pressure. The reference state specifies the dependence of all thermodynamic functions as a function of the temperature, in between a minimum temperature and a maximum temperature. The reference state also specifies the molar volume of the species as a function of temperature. The molar volume is a thermodynamic function. A full standard state does the same thing as a reference state, but specifies the thermodynamics functions at all pressures.

Class PDSS is the base class for a family of classes that compute properties of a single species in a phase at its standard states, for a range of temperatures and pressures.

Phases which use the VPSSMGr class must have their respective ThermoPhase objects actually be derivatives of the VPStandardState class. These classes assume that there exists a standard state for each species in the phase, where the Thermodynamic functions are specified as a function of temperature and pressure. Standard state objects for each species in the phase are all derived from the PDSS virtual base class.

The following classes inherit from PDSS. Each of these classes handles just one species.

• PDSS_IdealGas
  • standardState model = "IdealGas"
  • This model assumes that the species in the phase obeys the ideal gas law for their pressure dependence. The manager uses a SimpleThermo object to handle the calculation of the reference state. This object adds the pressure dependencies to the thermo functions.
• PDSS_ConstVol
  • standardState model = "ConstVol"
  • This model assumes that the species in the phase obeys the constant partial molar volume pressure dependence. The manager uses a SimpleThermo object to handle the calculation of the reference state. This object adds the pressure dependencies to these thermo functions.
• PDSS_SSVol
  • standardState model = "constant_incompressible" || model == "constant"
  • standardState model = "temperature_polynomial"
  • standardState model = "density_temperature_polynomial"
  • This model assumes that the species in the phase obey a fairly general equation of state, but one that separates out the calculation of the standard state density and/or volume. Models include a cubic polynomial in temperature for either the standard state volume or the standard state density. The manager uses a SimpleThermo object to handle the calculation of the reference state. This object then adds the pressure dependencies and the volume terms to these thermo functions to complete the representation.
• PDSS_Water
  • standardState model = "Water"
  • This model assumes that Species 0 is assumed to be water, and a real equation of state is used to model the T, P behavior. Note, the model assumes that the species is liquid water, and not steam.
• PDSS_HKFT
  • standardState model = "HKFT"
  • This model assumes that the species follows the HKFT pressure dependent equation of state

The choice of which VPSSMGr object to be used is either implicitly made by Cantera by querying the XML data file for compatibility or it may be explicitly requested in the XML file.

Normally the PDSS object is not called directly. Instead the VPSSMgr object manages the calls to the PDSS object for the entire set of species that comprise a phase. Additionally, sometimes the VPSSMgr object will not call the PDSS object at all to calculate thermodynamic properties, instead relying on its own determination/knowledge for how to calculate thermo quantities quickly given what it knows about the PDSS objects under its control.

The PDSS objects may or may not utilize the SpeciesThermo reference state manager class to calculate the reference state thermodynamics functions in its own calculation. There are some classes, such as PDSS_IdealGas and PDSS+_ConstVol, which utilize the SpeciesThermo object because the calculation is very similar to the reference state calculation, while there are other classes, PDSS_Water and PDSS_HKFT, which don't utilize the reference state calculation at all, because it wouldn't make sense to. For example, using the PDSS_Water module, there isn't anything special about the reference pressure of 1 bar, so the reference state calculation would represent a duplication of work. Additionally, when evaluating thermodynamic properties at higher pressures and temperatures, near the critical point, evaluation of the thermodynamics at a pressure of 1 bar may lead to situations where the liquid is unstable, i.e., beyond the spinodal curve leading to potentially wrong evaluation results.

For cases where the PDSS object doesn't use the SpeciesThermo object, a dummy SpeciesThermoInterpType object is actually installed into the SpeciesThermo object for that species. This dummy SpeciesThermoInterpType object is called a STITbyPDSS object. This object satisfies calls to SpeciesThermo member functions by actually calling the PDSS object at the reference pressure.