optmat.gas.mixture_eos#

The density of a gas mixture at a pressure and temperature (OEP 4, section 7.4).

A mixture’s equation of state is chosen per mixture, by the evidence for its pairs:

multi-fluid: CoolProp’s multi-fluid Helmholtz model of the mixture, where every pair has a binary model fitted to data of that pair. It reduces to each pure fluid’s equation at \(x_s = 1\). It is qualified only where every pair passed the comparison with the measured cross second virials and mixture densities (data/gas/mixture_pairs.toml).
virial: the fallback of section 4.2, each species’ own equation at its partial density plus the curated cross second virial coefficients,

\[p(\rho, T) = \sum_s p_s(x_s\rho, T) + RT\rho^2\sum_{s \ne t} x_s x_t B_{st}(T).\]

It preserves the composition, \(N_s = x_s N\) exactly, and holds while \(|\rho\sum_{s\ne t}x_s x_t B_{st}| \le 10^{-2}\). It is qualified where every pair’s fallback passed the same comparison with the measured densities.
partial-density: the same with every unknown cross coefficient zero: the composition-preserving form of the partial-pressure rule, provisional, which warns when it is built.

The densities follow the CODATA convention of optmat.gas.eos: N = p / (Z k_B T) with the equation’s dimensionless Z.

Module Attributes

`PAIRS_FILE`	The curated pairs of the mixture equations of state.
`METHODS`	The density methods, in the order the default is chosen.
`TRUNCATION_BOUND`	The bound on `\|rho sum_{s != t} x_s x_t B_st\|` within which the fallback holds.

Functions

mixture_equation_of_state(composition, *[, ...])

Return the equation of state of a gas mixture (OEP 4, sections 4.2 and 7.4).

Classes

`MixtureEquationOfState`(material, ...[, ...])	The equation of state of a gas mixture of fixed composition (OEP 4).
`PairDensity`(species, partner, model, kind, ...)	One unlike pair of a mixture equation of state.

optmat.gas.mixture_eos.METHODS: Final = ('multi-fluid', 'virial', 'partial-density')#: The density methods, in the order the default is chosen.

class optmat.gas.mixture_eos.MixtureEquationOfState(material, composition, method, qualified, pairs, constituents, backend, temperature_range, *, status='user', status_reason='', modified=(), base='')[source]#

Bases: Identified

The equation of state of a gas mixture of fixed composition (OEP 4).

Attributes:

materialstr: The composition’s name, or its species and fractions.
compositiontuple of tuple: (species, mole fraction), in the order given, summing to one.
methodstr: One of METHODS.
qualifiedbool: Whether the method holds for this mixture by the evidence of section 7.4.
pairstuple of PairDensity: Every unlike pair.
constituentstuple of EquationOfState: Each species’ own equation of state, in the order of composition.
backendstr: CoolProp’s version.
temperature_rangetuple of float: The temperatures every constituent’s equation covers, K, and for the fallback every cross coefficient’s measured temperatures.
statusstr: validated where qualified, else provisional.

EVALUATES_THROUGH: ClassVar[tuple[str, ...]] = ('optmat.gas.eos',)#

EVALUATION_VERSION: ClassVar[int] = 1#

IDENTITY_KIND: ClassVar[str] = 'mixture_equation_of_state'#

backend: str#

composition: tuple[tuple[str, float], ...]#

compressibility(state)[source]#

Return the mixture’s compressibility factor Z = p / (N k_B T).

Parameters:

stateState: Pressure and temperature.

Returns:

float: Dimensionless.

constituents: tuple[EquationOfState, ...]#

material: str#

method: str#

property molar_mass: float#

The composition’s molar mass, kg/mol.

The constituents’ equation-of-state molar masses (molar_mass) weighted by their mole fractions, for every method. For dry air it is the mean of its composition, not the pseudo-pure air of air_equation_of_state() (TC-832).

Returns:

float: The molar mass, kg/mol.

Examples

>>> mixture_equation_of_state({"Ar": 1.0}).molar_mass
0.039948

number_density(state)[source]#

Return the mixture’s total number density at a state.

Parameters:

stateState: Pressure and temperature.

Returns:

float: The total number density, m^-3.

Raises:

StateError: Outside the constituents’ temperatures, or where the mixture (or, for the fallback, a constituent at its partial density) is not a gas.

Warns:

ModelRangeWarning: Where the fallback is beyond its truncation bound.

Examples

>>> from optmat.conditions import State
>>> eos = mixture_equation_of_state({"He": 0.5, "Ne": 0.5})
>>> eos.method
'virial'
>>> f"{eos.number_density(State(pressure=1e6, temperature=294.0)):.6e}"
'2.451570e+26'

pairs: tuple[PairDensity, ...]#

partial_densities(state)[source]#

Return each species’ number density, x_s N.

Parameters:

stateState: Pressure and temperature.

Returns:

dict: Species to m^-3, the keys MixtureOptics takes.

pressure(number_density, temperature)[source]#

Return the pressure at total number densities and temperatures.

Parameters:

number_densityarray_like or float: Total number density, m^-3, > 0.
temperaturearray_like or float: K; broadcast against number_density.

Returns:

numpy.ndarray: Pa.

Raises:

StateError: At a non-positive density, or where the mixture is not a gas.

Examples

>>> eos = mixture_equation_of_state({"He": 0.5, "Ne": 0.5})
>>> f"{float(eos.pressure(2.451570e26, 294.0)) / 1e6:.6f}"
'1.000000'

qualified: bool#

second_virial(temperature)[source]#

Return the mixture’s second virial coefficient, the method’s own.

Parameters:

temperaturefloat

Returns:

float: B_mix, m^3/mol: the multi-fluid model’s at zero density, or the fallback’s sum_s x_s^2 B_ss + sum_{s != t} x_s x_t B_st.

property species: tuple[str, ...]#

The species, in the order of composition.

Returns:

tuple of str: The species.

temperature_range: tuple[float, float]#

optmat.gas.mixture_eos.PAIRS_FILE: Final = PosixPath('/home/docs/checkouts/optmat/checkouts/7/src/optmat/data/gas/mixture_pairs.toml')#: The curated pairs of the mixture equations of state.

class optmat.gas.mixture_eos.PairDensity(species, partner, model, kind, curated, qualified, cross_virial, reason, fallback_qualified=False, fallback_reason='', prefer_multi_fluid=False)[source]#

Bases: object

One unlike pair of a mixture equation of state.

Attributes:

species, partnerstr: The pair, in sorted order.
modelstr: CoolProp’s reference key of the pair’s binary model, or empty where it has none.
kindstr: fitted, placeholder (every reducing parameter one and no departure function: not fitted to data of the pair) or none.
curatedbool: Whether the pair is in mixture_pairs.toml.
qualifiedbool: Whether its multi-fluid model passed the comparison with the measured data.
cross_virialstr: The curated cross (or excess) second virial dataset, or empty.
reasonstr: The comparison’s result, or why the pair is what it is.
fallback_qualifiedbool: Whether the fallback (method virial) passed the same comparison with the measured mixture densities, within its truncation bound.
fallback_reasonstr: That comparison’s result.
prefer_multi_fluidbool: Whether the author chose the multi-fluid model as this pair’s default even though it is not qualified (dry air’s pairs, TC-796).

cross_virial: str#

curated: bool#

fallback_qualified: bool = False#

fallback_reason: str = ''#

kind: str#

model: str#

partner: str#

prefer_multi_fluid: bool = False#

qualified: bool#

reason: str#

species: str#

optmat.gas.mixture_eos.TRUNCATION_BOUND: Final = 0.01#: The bound on |rho sum_{s != t} x_s x_t B_st| within which the fallback holds.

optmat.gas.mixture_eos.mixture_equation_of_state(composition, *, method=None)[source]#

Return the equation of state of a gas mixture (OEP 4, sections 4.2 and 7.4).

Parameters:

compositionMapping or str: Species to mole fraction, summing to one, or a named composition ("dry air (N2, O2, Ar)").
methodstr, optional: One of METHODS; by default the first the mixture’s pairs qualify for, else partial-density.

Returns:

MixtureEquationOfState: The equation, with its method, qualification and pairs.

Raises:

OptmatError: For an invalid composition or a method the pairs cannot support.
StateError: For a species without an equation of state (ozone).

Warns:

ModelRangeWarning: When the equation is provisional.

Examples

>>> eos = mixture_equation_of_state({"Ar": 1.0})
>>> eos.method, eos.qualified
('multi-fluid', True)