Property packages¶

One object that owns phase equilibrium and energy for a set of components: the PropertyPackage protocol and its cubic, gamma-phi, PC-SAFT, and reference-fluid implementations, plus the generic two-phase properties and energy-specified flashes built on top of them.

See the property-packages guide for the concepts and worked examples.

package ¶

Property packages: one object that owns phase equilibrium and energy.

A process simulator needs two things from its thermodynamics: "what splits?" (fugacities, K-values, flashes) and "how much energy?" (enthalpy, entropy, volume). The equilibrium models in fugacio.thermo.phase answer the first question for the cubic, gamma-phi, and PC-SAFT routes, but the energy side of the engine was, until now, wired to the cubic equation of state alone: a heater, a mixer, an isentropic compressor, or a column energy balance could only be evaluated on Peng-Robinson or SRK. A PropertyPackage closes that gap. It is the single interface every energy-balanced unit operation consumes, and it is implemented for all four method classes Fugacio carries:

CubicPackage: phi-phi on a cubic EOS (PR, SRK, RK, vdW), the default;
GammaPhiPackage: an activity-coefficient liquid (NRTL, UNIQUAC, Wilson, UNIFAC, ...) with an ideal or EOS vapour. Its liquid enthalpy is the pure-liquid enthalpies plus the excess enthalpy obtained by automatic differentiation of the excess Gibbs energy (Gibbs-Helmholtz), so heat of mixing comes for free and stays consistent with the activity coefficients themselves;
SAFTPackage: PC-SAFT with Wertheim association, residual properties from the temperature derivatives of the residual Helmholtz energy;
HelmholtzPackage: a pure reference fluid (IAPWS-95 water, Span-Wagner CO2, ...) wrapped as a one-component package, so steam and refrigerant loops can be simulated with reference-grade properties inside the same flowsheet engine.

Every package exposes the same calls: single-phase ln_phi / enthalpy / entropy / volume at (T, P, x), the isothermal flash_pt and the four saturation calculations, and (implemented once, generically, on top of those) the two-phase-aware mixture_enthalpy / mixture_entropy / mixture_volume and the energy-specified flash_ph / flash_ps / flash_tv. Packages are registered JAX pytrees whose model parameters are differentiable leaves, so a flowsheet built on any of them is differentiable with respect to the thermodynamic parameters as well as the operating conditions.

Every package also satisfies the fugacio.thermo.phase.EquilibriumModel protocol, so it can be passed anywhere an equilibrium model is accepted.

Enthalpy and entropy are relative to the ideal-gas reference at T_REF / P_REF (the reference state of fugacio.thermo.properties), except for HelmholtzPackage, whose reference is the one built into the published formulation. Only differences are physical, and any consistent reference cancels in a balance, so do not mix packages with different references across one energy balance.

Classes:

Name	Description
`EnergySolveResult`	A PH/PS flash state and its independently verified solve report.
`PropertyPackage`	Structural type of a property package (equilibrium + energy + volume).
`CubicPackage`	Phi-phi property package on a cubic equation of state.
`GammaPhiPackage`	Gamma-phi property package: activity-coefficient liquid, ideal or EOS vapour.
`SAFTPackage`	PC-SAFT property package (phi-phi on the molecular equation of state).
`HelmholtzPackage`	One-component package on a reference multiparameter Helmholtz EOS.

Functions:

Name	Description
`excess_enthalpy`	Excess (mixing) enthalpy `h^E = -R T^2 d(g^E/RT)/dT` (J/mol) by autodiff.
`excess_entropy`	Excess entropy `s^E = (h^E - g^E) / T` (J/mol/K).
`cubic_package`	Construct a `CubicPackage` from component constants and `Cp` coefficients.
`gamma_phi_package`	Construct a `GammaPhiPackage` from an activity model and component constants.
`saft_package`	Construct a `SAFTPackage` from PC-SAFT parameters, seeding constants, and `Cp`.
`helmholtz_package`	Wrap a reference fluid as a one-component `HelmholtzPackage`.
`energy_flash_report`	Verify an energy flash independently from its temperature iteration.
`flash_ph_with_info`	PH flash and an independent material/enthalpy verification report.
`flash_ps_with_info`	PS flash and an independent material/entropy verification report.

EnergySolveResult ¶

Bases: NamedTuple

A PH/PS flash state and its independently verified solve report.

PropertyPackage ¶

Bases: Protocol

Structural type of a property package (equilibrium + energy + volume).

Implementations bundle their component constants and model parameters, so callers pass only the state (T, P, composition). phase is "liquid" or "vapor" and selects the phase branch to evaluate.

Methods:

Name	Description
`ln_phi`	Log fugacity coefficients `ln phi_i` of the phase at `(T, P, x)`.
`enthalpy`	Single-phase molar enthalpy (J/mol).
`entropy`	Single-phase molar entropy (J/mol/K).
`volume`	Single-phase molar volume (m^3/mol).
`flash_pt`	Isothermal-isobaric two-phase flash.
`bubble_pressure`	Bubble pressure and incipient vapour `(P, y)` at fixed `T`, `x`.
`dew_pressure`	Dew pressure and incipient liquid `(P, x)` at fixed `T`, `y`.
`bubble_temperature`	Bubble temperature and incipient vapour `(T, y)` at fixed `P`, `x`.
`dew_temperature`	Dew temperature and incipient liquid `(T, x)` at fixed `P`, `y`.
`k_values`	Equilibrium ratios `K_i = phi_i^L(x) / phi_i^V(y)`.
`k_seed`	Composition-light K-value estimate used to initialise staged solvers.
`mixture_enthalpy`	Two-phase-aware molar enthalpy of a feed `z` at `(T, P)` (J/mol).
`mixture_entropy`	Two-phase-aware molar entropy of a feed `z` at `(T, P)` (J/mol/K).
`mixture_volume`	Two-phase-aware molar volume of a feed `z` at `(T, P)` (m^3/mol).
`flash_ph`	Isenthalpic flash: the temperature (and split) at which `H = h`.
`flash_ps`	Isentropic flash: the temperature (and split) at which `S = s`.
`signature`	Hashable description of the package structure (not its values).

Attributes:

Name	Type	Description
`n_components`	`int`	Number of components the package describes.

n_components `property` ¶

n_components: int

Number of components the package describes.

ln_phi ¶

ln_phi(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Log fugacity coefficients ln phi_i of the phase at (T, P, x).

enthalpy ¶

enthalpy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Single-phase molar enthalpy (J/mol).

entropy ¶

entropy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Single-phase molar entropy (J/mol/K).

volume ¶

volume(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Single-phase molar volume (m^3/mol).

flash_pt ¶

flash_pt(
    t: ArrayLike, p: ArrayLike, z: Array
) -> FlashResult

Isothermal-isobaric two-phase flash.

bubble_pressure ¶

bubble_pressure(
    t: ArrayLike, x: Array
) -> tuple[Array, Array]

Bubble pressure and incipient vapour (P, y) at fixed T, x.

dew_pressure ¶

dew_pressure(t: ArrayLike, y: Array) -> tuple[Array, Array]

Dew pressure and incipient liquid (P, x) at fixed T, y.

bubble_temperature ¶

bubble_temperature(
    p: ArrayLike, x: Array
) -> tuple[Array, Array]

Bubble temperature and incipient vapour (T, y) at fixed P, x.

dew_temperature ¶

dew_temperature(
    p: ArrayLike, y: Array
) -> tuple[Array, Array]

Dew temperature and incipient liquid (T, x) at fixed P, y.

k_values ¶

k_values(
    t: ArrayLike, p: ArrayLike, x: Array, y: Array
) -> Array

Equilibrium ratios K_i = phi_i^L(x) / phi_i^V(y).

k_seed ¶

k_seed(t: ArrayLike, p: ArrayLike, x: Array) -> Array

Composition-light K-value estimate used to initialise staged solvers.

mixture_enthalpy ¶

mixture_enthalpy(
    t: ArrayLike, p: ArrayLike, z: Array
) -> Array

Two-phase-aware molar enthalpy of a feed z at (T, P) (J/mol).

mixture_entropy ¶

mixture_entropy(
    t: ArrayLike, p: ArrayLike, z: Array
) -> Array

Two-phase-aware molar entropy of a feed z at (T, P) (J/mol/K).

mixture_volume ¶

mixture_volume(
    t: ArrayLike, p: ArrayLike, z: Array
) -> Array

Two-phase-aware molar volume of a feed z at (T, P) (m^3/mol).

flash_ph ¶

flash_ph(
    p: ArrayLike,
    h: ArrayLike,
    z: Array,
    *,
    t_init: ArrayLike = 300.0,
    t_min: float = 50.0,
    t_max: float = 1500.0,
    tol: float = 1e-08,
    max_iter: int = 100,
) -> EnergyFlashResult

Isenthalpic flash: the temperature (and split) at which H = h.

flash_ps ¶

flash_ps(
    p: ArrayLike,
    s: ArrayLike,
    z: Array,
    *,
    t_init: ArrayLike = 300.0,
    t_min: float = 50.0,
    t_max: float = 1500.0,
    tol: float = 1e-08,
    max_iter: int = 100,
) -> EnergyFlashResult

Isentropic flash: the temperature (and split) at which S = s.

signature ¶

signature() -> tuple[Any, ...]

Hashable description of the package structure (not its values).

CubicPackage `dataclass` ¶

CubicPackage(
    tc: Array,
    pc: Array,
    omega: Array,
    cp: CpCoeffs,
    kij: Array | None = None,
    eos: CubicEOS = PR,
    component_names: tuple[str, ...] = (),
    evidence: PackageEvidence = PackageEvidence(),
)

Bases: _PackageBase

Phi-phi property package on a cubic equation of state.

Attributes:

Name	Type	Description
`tc`	`Array`	Critical temperatures (K).
`pc`	`Array`	Critical pressures (Pa).
`omega`	`Array`	Acentric factors.
`cp`	`CpCoeffs`	Ideal-gas heat-capacity coefficient arrays `(a, b, c, d, e)`.
`kij`	`Array \| None`	Binary interaction matrix (`None` means zeros).
`eos`	`CubicEOS`	Cubic equation of state (static; default Peng-Robinson).

Methods:

Name	Description
`signature`	Class, component count, cubic, and whether a `kij` matrix is present.
`ln_phi`	Log fugacity coefficients from the cubic EOS.
`enthalpy`	Ideal-gas enthalpy plus the cubic residual enthalpy (J/mol).
`entropy`	Ideal-gas entropy (with mixing) plus the cubic residual entropy (J/mol/K).
`volume`	Molar volume `Z R T / P` on the requested cubic root (m^3/mol).
`flash_pt`	Isothermal-isobaric two-phase flash via the cubic EOS.
`bubble_pressure`	Bubble pressure and incipient vapour at fixed `T`, `x`.
`dew_pressure`	Dew pressure and incipient liquid at fixed `T`, `y`.
`stability`	Michelsen tangent-plane stability of feed `z` at `(T, P)`.

n_components `property` ¶

n_components: int

Number of components.

signature ¶

signature() -> tuple[Any, ...]

Class, component count, cubic, and whether a kij matrix is present.

ln_phi ¶

ln_phi(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Log fugacity coefficients from the cubic EOS.

enthalpy ¶

enthalpy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Ideal-gas enthalpy plus the cubic residual enthalpy (J/mol).

entropy ¶

entropy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Ideal-gas entropy (with mixing) plus the cubic residual entropy (J/mol/K).

volume ¶

volume(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Molar volume Z R T / P on the requested cubic root (m^3/mol).

flash_pt ¶

flash_pt(
    t: ArrayLike, p: ArrayLike, z: Array
) -> FlashResult

Isothermal-isobaric two-phase flash via the cubic EOS.

bubble_pressure ¶

bubble_pressure(
    t: ArrayLike, x: Array
) -> tuple[Array, Array]

Bubble pressure and incipient vapour at fixed T, x.

dew_pressure ¶

dew_pressure(t: ArrayLike, y: Array) -> tuple[Array, Array]

Dew pressure and incipient liquid at fixed T, y.

stability ¶

stability(
    t: ArrayLike, p: ArrayLike, z: Array
) -> StabilityResult

Michelsen tangent-plane stability of feed z at (T, P).

GammaPhiPackage `dataclass` ¶

GammaPhiPackage(
    activity: ActivityModel,
    tc: Array,
    pc: Array,
    omega: Array,
    cp: CpCoeffs,
    kij: Array | None = None,
    eos: CubicEOS = PR,
    vapor: str = "ideal",
    poynting: bool = False,
    phi_saturation: bool = False,
    component_names: tuple[str, ...] = (),
    evidence: PackageEvidence = PackageEvidence(),
)

Bases: _PackageBase

Gamma-phi property package: activity-coefficient liquid, ideal or EOS vapour.

The liquid fugacity is x_i gamma_i f_i^{0,L}(T, P) (see fugacio.thermo.reference), expressed here as an effective liquid fugacity coefficient phi_i^L = gamma_i f_i^{0,L} / P so the package presents the same ln_phi interface as the phi-phi routes. The liquid enthalpy is

h^L(T, P, x) = sum_i x_i h_i^{L,pure}(T, P) + h^E(T, x)

with each pure-liquid enthalpy taken from the cubic EOS at that component's saturation point (plus the small v_i^L (P - Psat_i) pressure term that partners the Poynting factor) and the excess enthalpy from excess_enthalpy (autodiff Gibbs-Helmholtz on the activity model). The liquid entropy follows the same construction with the ideal entropy of mixing and s^E.

Components must be subcritical at the conditions of interest (the reference fugacity is saturation-based, the standard gamma-phi limitation).

Attributes:

Name	Type	Description
`activity`	`ActivityModel`	Liquid activity-coefficient model (a differentiable pytree).
`tc`	`Array`	Critical temperatures (K).
`pc`	`Array`	Critical pressures (Pa).
`omega`	`Array`	Acentric factors.
`cp`	`CpCoeffs`	Ideal-gas heat-capacity coefficient arrays `(a, b, c, d, e)`.
`kij`	`Array \| None`	Binary interaction matrix for an EOS vapour (`None` means zeros).
`eos`	`CubicEOS`	Cubic EOS used for the saturation reference and, if selected, the vapour.
`vapor`	`str`	`"ideal"` (phi^V = 1) or `"eos"` (static).
`poynting`	`bool`	Include the Poynting correction in the reference (static).
`phi_saturation`	`bool`	Include the saturation fugacity coefficient (static).

Methods:

Name	Description
`signature`	Class, component count, activity-model class, and the static flags.
`ln_phi`	Effective `ln phi`: `ln gamma + ln f^{0,L} - ln P` (liquid) or the vapour model.
`enthalpy`	Liquid: pure saturated-liquid enthalpies plus `h^E`; vapour: ideal gas (+ EOS).
`entropy`	Liquid: saturated-liquid entropies, ideal mixing, `s^E`; vapour: ideal gas (+ EOS).
`volume`	Liquid: mole-fraction sum of pure saturated-liquid volumes; vapour: ideal gas or EOS.
`flash_pt`	Isothermal-isobaric gamma-phi flash.
`k_seed`	`gamma_i(x) Psat_i / P`: the modified Raoult K-values (ideal vapour).
`bubble_pressure`	Bubble pressure and incipient vapour at fixed `T`, `x`.
`dew_pressure`	Dew pressure and incipient liquid at fixed `T`, `y`.
`bubble_temperature`	Bubble temperature and incipient vapour at fixed `P`, `x` (native gamma-phi).
`dew_temperature`	Dew temperature and incipient liquid at fixed `P`, `y` (native gamma-phi solve).

n_components `property` ¶

n_components: int

Number of components.

signature ¶

signature() -> tuple[Any, ...]

Class, component count, activity-model class, and the static flags.

ln_phi ¶

ln_phi(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Effective ln phi: ln gamma + ln f^{0,L} - ln P (liquid) or the vapour model.

enthalpy ¶

enthalpy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Liquid: pure saturated-liquid enthalpies plus h^E; vapour: ideal gas (+ EOS).

entropy ¶

entropy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Liquid: saturated-liquid entropies, ideal mixing, s^E; vapour: ideal gas (+ EOS).

volume ¶

volume(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Liquid: mole-fraction sum of pure saturated-liquid volumes; vapour: ideal gas or EOS.

flash_pt ¶

flash_pt(
    t: ArrayLike, p: ArrayLike, z: Array
) -> FlashResult

Isothermal-isobaric gamma-phi flash.

k_seed ¶

k_seed(t: ArrayLike, p: ArrayLike, x: Array) -> Array

gamma_i(x) Psat_i / P: the modified Raoult K-values (ideal vapour).

bubble_pressure ¶

bubble_pressure(
    t: ArrayLike, x: Array
) -> tuple[Array, Array]

Bubble pressure and incipient vapour at fixed T, x.

dew_pressure ¶

dew_pressure(t: ArrayLike, y: Array) -> tuple[Array, Array]

Dew pressure and incipient liquid at fixed T, y.

bubble_temperature ¶

bubble_temperature(
    p: ArrayLike,
    x: Array,
    *,
    t_min: float = 150.0,
    t_max: float = 700.0,
) -> tuple[Array, Array]

Bubble temperature and incipient vapour at fixed P, x (native gamma-phi).

dew_temperature ¶

dew_temperature(
    p: ArrayLike,
    y: Array,
    *,
    t_min: float = 150.0,
    t_max: float = 700.0,
) -> tuple[Array, Array]

Dew temperature and incipient liquid at fixed P, y (native gamma-phi solve).

SAFTPackage `dataclass` ¶

SAFTPackage(
    params: SaftParameters,
    tc: Array,
    pc: Array,
    omega: Array,
    cp: CpCoeffs,
    component_names: tuple[str, ...] = (),
    evidence: PackageEvidence = PackageEvidence(),
)

Bases: _PackageBase

PC-SAFT property package (phi-phi on the molecular equation of state).

Residual enthalpy and entropy come from the temperature derivatives of the reduced residual Helmholtz energy (fugacio.thermo.saft.properties), so association effects on the heat of mixing and vaporisation are captured.

Attributes:

Name	Type	Description
`params`	`SaftParameters`	PC-SAFT parameter set (a differentiable pytree).
`tc`	`Array`	Critical temperatures (K), used to seed the flash K-values.
`pc`	`Array`	Critical pressures (Pa), used to seed the flash K-values.
`omega`	`Array`	Acentric factors, used to seed the flash K-values.
`cp`	`CpCoeffs`	Ideal-gas heat-capacity coefficient arrays `(a, b, c, d, e)`.

Methods:

Name	Description
`signature`	Class and component count.
`ln_phi`	Log fugacity coefficients on the PC-SAFT density branch `phase`.
`enthalpy`	Ideal-gas enthalpy plus the PC-SAFT residual enthalpy (J/mol).
`entropy`	Ideal-gas entropy (with mixing) plus the PC-SAFT residual entropy (J/mol/K).
`volume`	Molar volume `1 / rho` on the requested density branch (m^3/mol).
`flash_pt`	Isothermal-isobaric two-phase flash via PC-SAFT.
`bubble_pressure`	Bubble pressure and incipient vapour at fixed `T`, `x`.
`dew_pressure`	Dew pressure and incipient liquid at fixed `T`, `y`.
`stability`	Michelsen tangent-plane stability of feed `z` at `(T, P)`.

n_components `property` ¶

n_components: int

Number of components.

signature ¶

signature() -> tuple[Any, ...]

Class and component count.

ln_phi ¶

ln_phi(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Log fugacity coefficients on the PC-SAFT density branch phase.

enthalpy ¶

enthalpy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Ideal-gas enthalpy plus the PC-SAFT residual enthalpy (J/mol).

entropy ¶

entropy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Ideal-gas entropy (with mixing) plus the PC-SAFT residual entropy (J/mol/K).

volume ¶

volume(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Molar volume 1 / rho on the requested density branch (m^3/mol).

flash_pt ¶

flash_pt(
    t: ArrayLike, p: ArrayLike, z: Array
) -> FlashResult

Isothermal-isobaric two-phase flash via PC-SAFT.

bubble_pressure ¶

bubble_pressure(
    t: ArrayLike, x: Array
) -> tuple[Array, Array]

Bubble pressure and incipient vapour at fixed T, x.

dew_pressure ¶

dew_pressure(t: ArrayLike, y: Array) -> tuple[Array, Array]

Dew pressure and incipient liquid at fixed T, y.

stability ¶

stability(
    t: ArrayLike, p: ArrayLike, z: Array
) -> StabilityResult

Michelsen tangent-plane stability of feed z at (T, P).

HelmholtzPackage `dataclass` ¶

HelmholtzPackage(
    fluid: HelmholtzFluid,
    component_names: tuple[str, ...] = (),
    evidence: PackageEvidence = PackageEvidence(),
)

Bases: _PackageBase

One-component package on a reference multiparameter Helmholtz EOS.

Wraps a fugacio.thermo.helmholtz.HelmholtzFluid (IAPWS-95 water, Span-Wagner CO2, ...) so a pure utility or working fluid can flow through the ordinary unit operations with reference-grade properties. Compositions are the one-element vector [1.0]; the "flash" is the saturation-line test of a pure substance (vapour fraction 0 or 1 away from the dome, the quality on it), and the energy flashes resolve directly to the steam-table state functions state_ph / state_ps.

Enthalpy and entropy carry the reference state of the published formulation (not the ideal-gas T_REF reference of the mixture packages).

Attributes:

Name	Type	Description
`fluid`	`HelmholtzFluid`	The reference fluid.

Methods:

Name	Description
`signature`	Class and fluid name.
`ln_phi`	Pure-fluid `ln phi` on the requested density branch, as a length-1 vector.
`enthalpy`	Molar enthalpy on the requested branch (J/mol).
`entropy`	Molar entropy on the requested branch (J/mol/K).
`volume`	Molar volume `1 / rho` on the requested branch (m^3/mol).
`flash_pt`	Pure-fluid phase test: all vapour below `Psat(T)` (or above `Tc`), else liquid.
`k_seed`	`Psat(T) / P` as a length-1 vector.
`mixture_enthalpy`	Stable-branch molar enthalpy at `(T, P)` (J/mol).
`mixture_entropy`	Stable-branch molar entropy at `(T, P)` (J/mol/K).
`mixture_volume`	Stable-branch molar volume at `(T, P)` (m^3/mol).
`flash_ph`	Steam-table `(P, h)` state: saturation temperature and quality inside the dome.
`flash_ps`	Steam-table `(P, s)` state: saturation temperature and quality inside the dome.
`bubble_pressure`	Saturation pressure at `T` (pure fluid).
`dew_pressure`	Saturation pressure at `T` (pure fluid).
`bubble_temperature`	Saturation temperature at `P` (pure fluid).
`dew_temperature`	Saturation temperature at `P` (pure fluid).

n_components `property` ¶

n_components: int

Always one.

signature ¶

signature() -> tuple[Any, ...]

Class and fluid name.

ln_phi ¶

ln_phi(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Pure-fluid ln phi on the requested density branch, as a length-1 vector.

enthalpy ¶

enthalpy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Molar enthalpy on the requested branch (J/mol).

entropy ¶

entropy(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Molar entropy on the requested branch (J/mol/K).

volume ¶

volume(
    t: ArrayLike, p: ArrayLike, x: Array, *, phase: str
) -> Array

Molar volume 1 / rho on the requested branch (m^3/mol).

flash_pt ¶

flash_pt(
    t: ArrayLike, p: ArrayLike, z: Array
) -> FlashResult

Pure-fluid phase test: all vapour below Psat(T) (or above Tc), else liquid.

k_seed ¶

k_seed(t: ArrayLike, p: ArrayLike, x: Array) -> Array

Psat(T) / P as a length-1 vector.

mixture_enthalpy ¶

mixture_enthalpy(
    t: ArrayLike, p: ArrayLike, z: Array
) -> Array

Stable-branch molar enthalpy at (T, P) (J/mol).

mixture_entropy ¶

mixture_entropy(
    t: ArrayLike, p: ArrayLike, z: Array
) -> Array

Stable-branch molar entropy at (T, P) (J/mol/K).

mixture_volume ¶

mixture_volume(
    t: ArrayLike, p: ArrayLike, z: Array
) -> Array

Stable-branch molar volume at (T, P) (m^3/mol).

flash_ph ¶

flash_ph(
    p: ArrayLike, h: ArrayLike, z: Array, **kwargs: Any
) -> EnergyFlashResult

Steam-table (P, h) state: saturation temperature and quality inside the dome.

flash_ps ¶

flash_ps(
    p: ArrayLike, s: ArrayLike, z: Array, **kwargs: Any
) -> EnergyFlashResult

Steam-table (P, s) state: saturation temperature and quality inside the dome.

bubble_pressure ¶

bubble_pressure(
    t: ArrayLike, x: Array
) -> tuple[Array, Array]

Saturation pressure at T (pure fluid).

dew_pressure ¶

dew_pressure(t: ArrayLike, y: Array) -> tuple[Array, Array]

Saturation pressure at T (pure fluid).

bubble_temperature ¶

bubble_temperature(
    p: ArrayLike,
    x: Array,
    *,
    t_min: float = 150.0,
    t_max: float = 700.0,
) -> tuple[Array, Array]

Saturation temperature at P (pure fluid).

dew_temperature ¶

dew_temperature(
    p: ArrayLike,
    y: Array,
    *,
    t_min: float = 150.0,
    t_max: float = 700.0,
) -> tuple[Array, Array]

Saturation temperature at P (pure fluid).

excess_enthalpy ¶

excess_enthalpy(
    activity: ActivityModel, x: Array, t: ArrayLike
) -> Array

Excess (mixing) enthalpy h^E = -R T^2 d(g^E/RT)/dT (J/mol) by autodiff.

The Gibbs-Helmholtz relation turns the temperature derivative of the excess Gibbs energy into the heat of mixing. Taking that derivative with automatic differentiation keeps h^E exactly consistent with the activity coefficients (and their temperature dependence), with no separate correlation to maintain.

Parameters:

Name	Type	Description	Default
`activity`	`ActivityModel`	Liquid activity-coefficient model.	required
`x`	`Array`	Liquid mole fractions.	required
`t`	`ArrayLike`	Temperature (K).	required

Returns:

Type	Description
`Array`	The molar excess enthalpy of the liquid mixture.

excess_entropy ¶

excess_entropy(
    activity: ActivityModel, x: Array, t: ArrayLike
) -> Array

Excess entropy s^E = (h^E - g^E) / T (J/mol/K).

cubic_package ¶

cubic_package(
    tc: Array,
    pc: Array,
    omega: Array,
    cp: CpCoeffs,
    *,
    kij: Array | None = None,
    eos: CubicEOS = PR,
) -> CubicPackage

Construct a CubicPackage from component constants and Cp coefficients.

gamma_phi_package ¶

gamma_phi_package(
    activity: ActivityModel,
    tc: Array,
    pc: Array,
    omega: Array,
    cp: CpCoeffs,
    *,
    kij: Array | None = None,
    eos: CubicEOS = PR,
    vapor: str = "ideal",
    poynting: bool = False,
    phi_saturation: bool = False,
) -> GammaPhiPackage

Construct a GammaPhiPackage from an activity model and component constants.

saft_package ¶

saft_package(
    params: SaftParameters,
    tc: Array,
    pc: Array,
    omega: Array,
    cp: CpCoeffs,
) -> SAFTPackage

Construct a SAFTPackage from PC-SAFT parameters, seeding constants, and Cp.

helmholtz_package ¶

helmholtz_package(
    fluid: HelmholtzFluid,
) -> HelmholtzPackage

Wrap a reference fluid as a one-component HelmholtzPackage.

energy_flash_report ¶

energy_flash_report(
    pkg: PropertyPackage,
    result: EnergyFlashResult,
    p: ArrayLike,
    target: ArrayLike,
    z: Array,
    *,
    prop: str = "enthalpy",
    tol: float = 1e-07,
) -> SolveReport

Verify an energy flash independently from its temperature iteration.

The residual checks component closure, composition normalization, phase fractions, and the specified molar property. The iteration count is zero because this is a verification of the returned state, not its iteration log.

flash_pt_with_info ¶

flash_pt_with_info(
    pkg: PropertyPackage,
    t: ArrayLike,
    p: ArrayLike,
    z: Array,
    **options: Any,
) -> Any

PT flash and its actual iteration report for cubic, gamma-phi, and PC-SAFT.

Reference-fluid and custom packages use independent state verification with zero reported iterations. Physical stability and applicability are assessed by fugacio.thermo.acceptance.flash_pt_checked.

flash_ph_with_info ¶

flash_ph_with_info(
    pkg: PropertyPackage,
    p: ArrayLike,
    h: ArrayLike,
    z: Array,
    **options: Any,
) -> EnergySolveResult

PH flash and an independent material/enthalpy verification report.

flash_ps_with_info ¶

flash_ps_with_info(
    pkg: PropertyPackage,
    p: ArrayLike,
    s: ArrayLike,
    z: Array,
    **options: Any,
) -> EnergySolveResult

PS flash and an independent material/entropy verification report.

Property packages¶

package ¶

EnergySolveResult ¶

PropertyPackage ¶

n_components property ¶

ln_phi ¶

enthalpy ¶

entropy ¶

volume ¶

flash_pt ¶

bubble_pressure ¶

dew_pressure ¶

bubble_temperature ¶

dew_temperature ¶

k_values ¶

k_seed ¶

mixture_enthalpy ¶

mixture_entropy ¶

mixture_volume ¶

flash_ph ¶

flash_ps ¶

signature ¶

CubicPackage dataclass ¶

n_components property ¶

signature ¶

ln_phi ¶

enthalpy ¶

entropy ¶

volume ¶

flash_pt ¶

bubble_pressure ¶

dew_pressure ¶

stability ¶

GammaPhiPackage dataclass ¶

n_components property ¶

signature ¶

ln_phi ¶

enthalpy ¶

entropy ¶

volume ¶

flash_pt ¶

k_seed ¶

bubble_pressure ¶

dew_pressure ¶

bubble_temperature ¶

dew_temperature ¶

SAFTPackage dataclass ¶

n_components property ¶

signature ¶

ln_phi ¶

enthalpy ¶

entropy ¶

volume ¶

flash_pt ¶

bubble_pressure ¶

dew_pressure ¶

stability ¶

HelmholtzPackage dataclass ¶

n_components property ¶

signature ¶

ln_phi ¶

enthalpy ¶

entropy ¶

volume ¶

flash_pt ¶

k_seed ¶

mixture_enthalpy ¶

mixture_entropy ¶

mixture_volume ¶

flash_ph ¶

flash_ps ¶

bubble_pressure ¶

dew_pressure ¶

bubble_temperature ¶

dew_temperature ¶

excess_enthalpy ¶

excess_entropy ¶

cubic_package ¶

gamma_phi_package ¶

saft_package ¶

n_components `property` ¶

CubicPackage `dataclass` ¶

n_components `property` ¶

GammaPhiPackage `dataclass` ¶

n_components `property` ¶

SAFTPackage `dataclass` ¶

n_components `property` ¶

HelmholtzPackage `dataclass` ¶

n_components `property` ¶