PC-SAFT (molecular SAFT)¶

The perturbed-chain statistical associating fluid theory (PC-SAFT) of Gross and Sadowski, implemented as one scalar reduced residual Helmholtz energy whose every property, the density and saturation solvers, and the Wertheim association site-fraction solve are exact jax.grad derivatives, differentiable in both state and the molecular parameters themselves. SAFTModel exposes the same flash_pt, bubble, and dew calls as a cubic EOSModel or a GammaPhiModel, so a flowsheet adopts a molecular EOS by swapping one object.

See the molecular SAFT guide for worked examples.

saft ¶

PC-SAFT: a molecular-based, differentiable equation of state.

The perturbed-chain statistical associating fluid theory (PC-SAFT) of Gross & Sadowski is the third major class of thermodynamic method in Fugacio, alongside the cubic equations of state (fugacio.thermo.eos) and the gamma-phi activity models (fugacio.thermo.gammaphi). It models a fluid as chains of spherical segments with dispersion attraction and optional short-range association, which captures associating species (water, alcohols, amines), polymers, and refrigerant mixtures far better than a cubic EOS.

As with the reference multiparameter EOS (fugacio.thermo.helmholtz), PC-SAFT is one scalar reduced Helmholtz energy (fugacio.thermo.saft.pcsaft.alpha_residual) and every property is an autodiff derivative of it, so the whole model, including the Wertheim association site-fraction solve, is differentiable in both state and parameters.

The public surface is:

parameters: SaftParameters, saft_parameters, saft_parameters_for (named components from the curated bank);
energy & properties: alpha_residual, compressibility_factor, pressure, molar_density, ln_fugacity_coefficients, residual_properties, and site_fractions;
phase equilibrium: flash_pt_saft, bubble_pressure_saft, dew_pressure_saft, psat_saft, stability_saft;
model: the unified SAFTModel / saft_model;
regression: fit_saft_pure, fit_saft_kij.

Modules:

Name	Description
`association`	Wertheim (TPT1) association for PC-SAFT, with a differentiable site solve.
`equilibrium`	PC-SAFT phase equilibrium: flash, bubble/dew points, saturation, stability.
`model`	`SAFTModel`: PC-SAFT behind the unified `EquilibriumModel` interface.
`parameters`	The differentiable PC-SAFT parameter set and its combining rules.
`pcsaft`	The PC-SAFT reduced residual Helmholtz energy `alpha_res(rho, T, x)`.
`properties`	PC-SAFT properties at `(rho, T, x)` and `(T, P, x)` from `alpha_res`.
`regression`	Differentiable PC-SAFT parameter estimation.

Classes:

Name	Description
`SAFTModel`	PC-SAFT (phi-phi) equilibrium model.
`SaftParameters`	PC-SAFT parameters of a mixture as a differentiable pytree.
`ResidualProperties`	Residual (departure) molar properties at `(T, P)` relative to the ideal gas.

Functions:

Name	Description
`alpha_association`	Association contribution `alpha_assoc` to the reduced residual Helmholtz energy.
`association_strength`	Association strength matrix `Delta_ij` (m^3) for every component pair.
`site_fractions`	Bonded-site fractions `(X_A, X_B)` per component at `(rho, T, x)`.
`bubble_pressure_saft`	Bubble-point pressure and incipient vapour `(P, y)` at fixed `T`, `x`.
`dew_pressure_saft`	Dew-point pressure and incipient liquid `(P, x)` at fixed `T`, `y`.
`flash_pt_saft`	Isothermal-isobaric two-phase flash on PC-SAFT by accelerated substitution.
`psat_saft`	Pure-component saturation pressure (Pa) by equifugacity, from a guess `p_guess`.
`stability_saft`	Michelsen tangent-plane stability test for feed `z` at `(T, P)` on PC-SAFT.
`saft_model`	Construct a `SAFTModel` from a PC-SAFT parameter set and seeding constants.
`saft_parameters`	Assemble a `SaftParameters` pytree from raw parameter arrays.
`saft_parameters_for`	Build a `SaftParameters` set for named components from the curated bank.
`segment_diameter`	Temperature-dependent segment diameter `d_i(T)` (metres).
`alpha_dispersion`	Dispersion contribution `alpha_disp` (Gross-Sadowski eqs. 16-19).
`alpha_hard_chain`	Hard-chain contribution `alpha_hc` to the reduced residual Helmholtz energy.
`alpha_residual`	Total PC-SAFT reduced residual Helmholtz energy `A_res / (n R T)`.
`compressibility_factor`	Compressibility factor `Z = 1 + rho (d alpha_res / d rho)` at `(rho, T, x)`.
`ln_fugacity_coefficients`	Log fugacity coefficients `ln phi_i` of every component at `(T, P, x)`.
`molar_density`	Molar density `rho(T, P, x)` (mol/m^3) on the requested phase branch.
`pressure`	Pressure (Pa) at molar density `rho` (mol/m^3), temperature `t` (K), comp. `x`.
`residual_properties`	All residual molar properties at `(T, P, x)` on a phase branch.
`fit_saft_kij`	Fit a single binary correction `k_ij` to isothermal bubble-pressure data.
`fit_saft_pure`	Fit pure `(m, sigma, epsilon)` to saturation pressure and liquid density.

SAFTModel `dataclass` ¶

SAFTModel(
    params: SaftParameters,
    tc: Array,
    pc: Array,
    omega: Array,
)

PC-SAFT (phi-phi) equilibrium model.

Attributes:

Name	Type	Description
`params`	`SaftParameters`	PC-SAFT parameter set (a differentiable pytree).
`tc,`	`(pc, omega)`	Component critical constants and acentric factors, used to seed the Wilson K-values that initialise the flashes.

Methods:

Name	Description
`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`.
`bubble_temperature`	Bubble temperature and incipient vapour at fixed `P`, `x`.
`dew_temperature`	Dew temperature and incipient liquid at fixed `P`, `y`.
`stability`	Michelsen tangent-plane stability of feed `z` at `(T, P)`.

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.

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.

Found by inverting bubble_pressure for the temperature whose bubble pressure equals P (saturation pressure rises monotonically with temperature), then returning the incipient vapour there.

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.

stability ¶

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

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

SaftParameters `dataclass` ¶

SaftParameters(
    m: Array,
    sigma: Array,
    epsilon: Array,
    kappa_ab: Array,
    epsilon_ab: Array,
    n_sites_a: Array,
    n_sites_b: Array,
    kij: Array,
    associating: bool,
    names: tuple[str, ...] | None,
)

PC-SAFT parameters of a mixture as a differentiable pytree.

Attributes:

Name	Type	Description
`m`	`Array`	Segment number per component, shape `(n,)` (dimensionless).
`sigma`	`Array`	Segment diameter per component, shape `(n,)` (metres).
`epsilon`	`Array`	Dispersion energy `epsilon/k` per component, `(n,)` (kelvin).
`kappa_ab`	`Array`	Association volume per component, `(n,)` (0 if non-associating).
`epsilon_ab`	`Array`	Association energy `epsilon_AB/k` per component, `(n,)` (kelvin).
`n_sites_a`	`Array`	Number of type-A (electron-acceptor) sites per component, `(n,)`.
`n_sites_b`	`Array`	Number of type-B (electron-donor) sites per component, `(n,)`.
`kij`	`Array`	Symmetric binary dispersion correction, shape `(n, n)` (zero diagonal).
`associating`	`bool`	Whether any A-B association is active in the mixture (static).
`names`	`tuple[str, ...] \| None`	Optional component labels (static), for diagnostics.

n_components `property` ¶

n_components: int

Number of components in the parameter set.

ResidualProperties ¶

Bases: NamedTuple

Residual (departure) molar properties at (T, P) relative to the ideal gas.

Attributes:

Name	Type	Description
`z`	`Array`	Compressibility factor.
`enthalpy`	`Array`	Residual molar enthalpy `H - H^ig` (J/mol).
`entropy`	`Array`	Residual molar entropy `S - S^ig` (J/mol/K).
`gibbs`	`Array`	Residual molar Gibbs energy `G - G^ig` (J/mol).
`cp`	`Array`	Residual molar isobaric heat capacity `cp - cp^ig` (J/mol/K).

alpha_association ¶

alpha_association(
    params: SaftParameters,
    rho: ArrayLike,
    t: ArrayLike,
    x: Array,
) -> Array

Association contribution alpha_assoc to the reduced residual Helmholtz energy.

sum_i x_i [ n_{A,i}(ln X_{A,i} - X_{A,i}/2) + n_{B,i}(ln X_{B,i} - X_{B,i}/2) + (n_{A,i} + n_{B,i}) / 2 ] (Chapman-Gubbins-Jackson-Radosz).

association_strength ¶

association_strength(
    params: SaftParameters,
    rho: ArrayLike,
    t: ArrayLike,
    x: Array,
) -> Array

Association strength matrix Delta_ij (m^3) for every component pair.

Delta_ij = g_ij^hs sigma_ij^3 kappa_ij [exp(epsilon_ij^AB / T) - 1] with the contact radial distribution at the mixture packing fraction and the CR-1 combining rules for the unlike association parameters.

Parameters:

Name	Type	Description	Default
`params`	`SaftParameters`	PC-SAFT parameter set.	required
`rho`	`ArrayLike`	Molar density (mol/m^3).	required
`t`	`ArrayLike`	Temperature (K).	required
`x`	`Array`	Mole fractions, shape `(n,)`.	required

Returns:

Type	Description
`Array`	The symmetric `(n, n)` association-strength matrix.

site_fractions ¶

site_fractions(
    params: SaftParameters,
    rho: ArrayLike,
    t: ArrayLike,
    x: Array,
) -> tuple[Array, Array]

Bonded-site fractions (X_A, X_B) per component at (rho, T, x).

Parameters:

Name	Type	Description	Default
`params`	`SaftParameters`	PC-SAFT parameter set.	required
`rho`	`ArrayLike`	Molar density (mol/m^3).	required
`t`	`ArrayLike`	Temperature (K).	required
`x`	`Array`	Mole fractions, shape `(n,)`.	required

Returns:

Type	Description
`Array`	`(X_A, X_B)`: the fraction of type-A and type-B sites not bonded, each
`Array`	shape `(n,)`. Differentiable with respect to state and parameters.

bubble_pressure_saft ¶

bubble_pressure_saft(
    params: SaftParameters,
    t: ArrayLike,
    x: Array,
    tc: Array,
    pc: Array,
    omega: Array,
    *,
    tol: float = 1e-12,
    max_iter: int = 300,
) -> tuple[Array, Array]

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

Solved as a coupled fixed point in (ln P, y) so the result is differentiable in temperature, composition, and the PC-SAFT parameters.

dew_pressure_saft ¶

dew_pressure_saft(
    params: SaftParameters,
    t: ArrayLike,
    y: Array,
    tc: Array,
    pc: Array,
    omega: Array,
    *,
    tol: float = 1e-12,
    max_iter: int = 300,
) -> tuple[Array, Array]

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

Differentiable in temperature, composition, and the PC-SAFT parameters.

flash_pt_saft ¶

flash_pt_saft(
    params: SaftParameters,
    t: ArrayLike,
    p: ArrayLike,
    z: Array,
    tc: Array,
    pc: Array,
    omega: Array,
    *,
    tol: float = 1e-12,
    max_iter: int = 300,
) -> FlashResult

Isothermal-isobaric two-phase flash on PC-SAFT by accelerated substitution.

Solves the equal-fugacity conditions phi_i^L x_i = phi_i^V y_i with the Rachford-Rice material balance, seeded from Wilson K-values. The converged (beta, x, y) is differentiable in (T, P, z) and the PC-SAFT parameters through implicit differentiation of the fixed point.

psat_saft ¶

psat_saft(
    params: SaftParameters,
    t: ArrayLike,
    p_guess: ArrayLike,
    *,
    tol: float = 1e-11,
    max_iter: int = 100,
) -> Array

Pure-component saturation pressure (Pa) by equifugacity, from a guess p_guess.

Solves ln phi^L(T, P) = ln phi^V(T, P) for P with a Newton iteration in ln P (keeping the pressure positive). params must hold a single component. Differentiable in T and the PC-SAFT parameters through the Clapeyron-like implicit derivative.

Parameters:

Name	Type	Description	Default
`params`	`SaftParameters`	Single-component PC-SAFT parameter set.	required
`t`	`ArrayLike`	Temperature (K).	required
`p_guess`	`ArrayLike`	Initial pressure estimate (Pa); a Wilson/Antoine value is fine.	required
`tol`	`float`	Residual tolerance on `ln phi^L - ln phi^V`.	`1e-11`
`max_iter`	`int`	Newton iteration cap.	`100`

Returns:

Type	Description
`Array`	The saturation pressure (Pa).

stability_saft ¶

stability_saft(
    params: SaftParameters,
    t: ArrayLike,
    p: ArrayLike,
    z: Array,
    tc: Array,
    pc: Array,
    omega: Array,
    *,
    iters: int = 40,
) -> StabilityResult

Michelsen tangent-plane stability test for feed z at (T, P) on PC-SAFT.

Runs vapour-like and liquid-like trial-phase searches; a modified tangent-plane distance below zero for either means the feed splits.

saft_model ¶

saft_model(
    params: SaftParameters,
    tc: Array,
    pc: Array,
    omega: Array,
) -> SAFTModel

Construct a SAFTModel from a PC-SAFT parameter set and seeding constants.

saft_parameters ¶

saft_parameters(
    m: Array,
    sigma: Array,
    epsilon: Array,
    *,
    kappa_ab: Array | None = None,
    epsilon_ab: Array | None = None,
    n_sites_a: Array | None = None,
    n_sites_b: Array | None = None,
    kij: Array | None = None,
    names: Sequence[str] | None = None,
    sigma_in_angstrom: bool = False,
) -> SaftParameters

Assemble a SaftParameters pytree from raw parameter arrays.

Parameters:

Name	Type	Description	Default
`m`	`Array`	Segment number per component, shape `(n,)`.	required
`sigma`	`Array`	Segment diameter per component, `(n,)` (metres, unless `sigma_in_angstrom`).	required
`epsilon`	`Array`	Dispersion energy `epsilon/k` per component, `(n,)` (kelvin).	required
`kappa_ab`	`Array \| None`	Association volume per component (`None` => no association).	`None`
`epsilon_ab`	`Array \| None`	Association energy `epsilon_AB/k` per component (kelvin).	`None`
`n_sites_a`	`Array \| None`	Type-A site count per component (`None` => zeros).	`None`
`n_sites_b`	`Array \| None`	Type-B site count per component (`None` => zeros).	`None`
`kij`	`Array \| None`	Symmetric `(n, n)` binary correction (`None` => zeros).	`None`
`names`	`Sequence[str] \| None`	Optional component labels.	`None`
`sigma_in_angstrom`	`bool`	If `True`, `sigma` is given in angstrom and is converted to metres.	`False`

Returns:

Type	Description
`SaftParameters`	A registered `SaftParameters` pytree.

saft_parameters_for ¶

saft_parameters_for(
    components: Sequence[str],
    *,
    kij: Array | None = None,
    use_database_kij: bool = True,
) -> SaftParameters

Build a SaftParameters set for named components from the curated bank.

Parameters:

Name	Type	Description	Default
`components`	`Sequence[str]`	Component names present in the PC-SAFT parameter bank (`fugacio.thermo.saft._data.PURE_SAFT_PARAMS`).	required
`kij`	`Array \| None`	Explicit `(n, n)` binary-correction matrix; takes precedence over the curated bank.	`None`
`use_database_kij`	`bool`	Fill the binary corrections from the curated `fugacio.thermo.saft._data.SAFT_KIJ` set when `kij` is not given; pairs without a curated value stay at zero.	`True`

Returns:

Type	Description
`SaftParameters`	The assembled `SaftParameters` pytree.

Raises:

Type	Description
`KeyError`	If any component lacks curated PC-SAFT parameters.

segment_diameter ¶

segment_diameter(
    params: SaftParameters, t: ArrayLike
) -> Array

Temperature-dependent segment diameter d_i(T) (metres).

The Chen-Kreglewski soft-repulsion diameter d_i = sigma_i [1 - 0.12 exp(-3 epsilon_i / (k T))] used by PC-SAFT.

Parameters:

Name	Type	Description	Default
`params`	`SaftParameters`	PC-SAFT parameter set.	required
`t`	`ArrayLike`	Temperature (K).	required

Returns:

Type	Description
`Array`	The per-component effective hard-sphere diameter, shape `(n,)`.

alpha_dispersion ¶

alpha_dispersion(
    params: SaftParameters,
    rho: ArrayLike,
    t: ArrayLike,
    x: Array,
) -> Array

Dispersion contribution alpha_disp (Gross-Sadowski eqs. 16-19).

alpha_hard_chain ¶

alpha_hard_chain(
    params: SaftParameters,
    rho: ArrayLike,
    t: ArrayLike,
    x: Array,
) -> Array

Hard-chain contribution alpha_hc to the reduced residual Helmholtz energy.

The BMCSL hard-sphere reference scaled by the mean segment number, less the chain term sum_i x_i (m_i - 1) ln g_ii^hs (Gross-Sadowski eqs. 5-8).

alpha_residual ¶

alpha_residual(
    params: SaftParameters,
    rho: ArrayLike,
    t: ArrayLike,
    x: Array,
) -> Array

Total PC-SAFT reduced residual Helmholtz energy A_res / (n R T).

The sum of the hard-chain, dispersion, and (where active) association contributions, evaluated at molar density rho (mol/m^3), temperature t (K), and mole fractions x.

Parameters:

Name	Type	Description	Default
`params`	`SaftParameters`	PC-SAFT parameter set.	required
`rho`	`ArrayLike`	Molar density (mol/m^3).	required
`t`	`ArrayLike`	Temperature (K).	required
`x`	`Array`	Mole fractions, shape `(n,)`.	required

Returns:

Type	Description
`Array`	The dimensionless residual Helmholtz energy; every PC-SAFT property is an
`Array`	autodiff derivative of this scalar.

compressibility_factor ¶

compressibility_factor(
    params: SaftParameters,
    rho: ArrayLike,
    t: ArrayLike,
    x: Array,
) -> Array

Compressibility factor Z = 1 + rho (d alpha_res / d rho) at (rho, T, x).

ln_fugacity_coefficients ¶

ln_fugacity_coefficients(
    params: SaftParameters,
    t: ArrayLike,
    p: ArrayLike,
    x: Array,
    *,
    phase: str = "liquid",
) -> Array

Log fugacity coefficients ln phi_i of every component at (T, P, x).

Parameters:

Name	Type	Description	Default
`params`	`SaftParameters`	PC-SAFT parameter set.	required
`t`	`ArrayLike`	Temperature (K).	required
`p`	`ArrayLike`	Pressure (Pa).	required
`x`	`Array`	Mole fractions, shape `(n,)`.	required
`phase`	`str`	Density branch (see `molar_density`).	`'liquid'`

Returns:

Type	Description
`Array`	The vector of `ln phi_i`, differentiable in `(T, P, x)` and the
`Array`	PC-SAFT parameters.

molar_density ¶

molar_density(
    params: SaftParameters,
    t: ArrayLike,
    p: ArrayLike,
    x: Array,
    *,
    phase: str = "liquid",
) -> Array

Molar density rho(T, P, x) (mol/m^3) on the requested phase branch.

Parameters:

Name	Type	Description	Default
`params`	`SaftParameters`	PC-SAFT parameter set.	required
`t`	`ArrayLike`	Temperature (K).	required
`p`	`ArrayLike`	Pressure (Pa).	required
`x`	`Array`	Mole fractions, shape `(n,)`.	required
`phase`	`str`	`"liquid"` or `"vapor"` seed the Newton solve from a dense packing fraction or the ideal gas; `"stable"` runs a bracketed bisection over the whole density range and returns the root with the lower molar Gibbs energy when more than one branch exists.	`'liquid'`

Returns:

Type	Description
`Array`	The converged molar density, differentiable in `T`, `P`, `x`, and
`Array`	the PC-SAFT parameters.

pressure ¶

pressure(
    params: SaftParameters,
    rho: ArrayLike,
    t: ArrayLike,
    x: Array,
) -> Array

Pressure (Pa) at molar density rho (mol/m^3), temperature t (K), comp. x.

residual_properties ¶

residual_properties(
    params: SaftParameters,
    t: ArrayLike,
    p: ArrayLike,
    x: Array,
    *,
    phase: str = "liquid",
) -> ResidualProperties

All residual molar properties at (T, P, x) on a phase branch.

Parameters:

Name	Type	Description	Default
`params`	`SaftParameters`	PC-SAFT parameter set.	required
`t`	`ArrayLike`	Temperature (K).	required
`p`	`ArrayLike`	Pressure (Pa).	required
`x`	`Array`	Mole fractions, shape `(n,)`.	required
`phase`	`str`	Density branch (see `molar_density`).	`'liquid'`

Returns:

Type	Description
`ResidualProperties`	A `ResidualProperties` of `Z` and the enthalpy/entropy/Gibbs/cp
`ResidualProperties`	departures, each differentiable in `(T, P, x)` and the parameters.

fit_saft_kij ¶

fit_saft_kij(
    base: SaftParameters,
    t: ArrayLike,
    x: Array,
    p_exp: Array,
    tc: Array,
    pc: Array,
    omega: Array,
    *,
    max_iter: int = 40,
) -> tuple[Array, Array]

Fit a single binary correction k_ij to isothermal bubble-pressure data.

Parameters:

Name	Type	Description	Default
`base`	`SaftParameters`	Binary PC-SAFT parameter set (its `kij` is overwritten by the fit).	required
`t`	`ArrayLike`	Temperature of the isotherm (K).	required
`x`	`Array`	Liquid mole fractions of component 0 at each point, shape `(k,)`; the second component is `1 - x`.	required
`p_exp`	`Array`	Measured bubble pressures (Pa), shape `(k,)`.	required
`tc`	`Array`	Critical temperatures of the two components, K (for Wilson seeding).	required
`pc`	`Array`	Critical pressures of the two components, Pa (for Wilson seeding).	required
`omega`	`Array`	Acentric factors of the two components (for Wilson seeding).	required
`max_iter`	`int`	Levenberg-Marquardt iteration cap.	`40`

Returns:

Type	Description
`tuple[Array, Array]`	`(kij, cost)`: the fitted scalar binary correction and the final cost.

fit_saft_pure ¶

fit_saft_pure(
    base: SaftParameters,
    t: Array,
    psat_exp: Array,
    rho_liquid_exp: Array,
    *,
    density_weight: float = 1.0,
    max_iter: int = 60,
) -> tuple[SaftParameters, Array]

Fit pure (m, sigma, epsilon) to saturation pressure and liquid density.

Parameters:

Name	Type	Description	Default
`base`	`SaftParameters`	Single-component PC-SAFT parameter set; its current values seed the fit and any association parameters are held fixed.	required
`t`	`Array`	Temperatures of the data points (K), shape `(k,)`.	required
`psat_exp`	`Array`	Experimental saturation pressures (Pa), shape `(k,)`.	required
`rho_liquid_exp`	`Array`	Experimental saturated-liquid molar densities (mol/m^3), shape `(k,)`.	required
`density_weight`	`float`	Relative weight of the density residuals against the pressure residuals.	`1.0`
`max_iter`	`int`	Levenberg-Marquardt iteration cap.	`60`

Returns:

Type	Description
`SaftParameters`	`(params, cost)`: the fitted single-component `SaftParameters` and the
`Array`	final half-sum-of-squares cost.

PC-SAFT (molecular SAFT)¶

saft ¶

SAFTModel dataclass ¶

flash_pt ¶

bubble_pressure ¶

dew_pressure ¶

bubble_temperature ¶

dew_temperature ¶

stability ¶

SaftParameters dataclass ¶

n_components property ¶

ResidualProperties ¶

alpha_association ¶

association_strength ¶

site_fractions ¶

bubble_pressure_saft ¶

dew_pressure_saft ¶

flash_pt_saft ¶

psat_saft ¶

stability_saft ¶

saft_model ¶

saft_parameters ¶

saft_parameters_for ¶

segment_diameter ¶

alpha_dispersion ¶

alpha_hard_chain ¶

alpha_residual ¶

compressibility_factor ¶

ln_fugacity_coefficients ¶

molar_density ¶

pressure ¶

residual_properties ¶

fit_saft_kij ¶

fit_saft_pure ¶

SAFTModel `dataclass` ¶

SaftParameters `dataclass` ¶

n_components `property` ¶