saturation_pressure(model::EoSModel, T)
saturation_pressure(model::EoSModel,T,method::SaturationMethod)
saturation_pressure(model,T,x0::Union{Tuple,Vector})

Performs a single component saturation equilibrium calculation, at the specified temperature T, of one mol of pure sustance specified by model. Returns (p₀, Vₗ, Vᵥ) where p₀ is the saturation pressure (in [Pa]), Vₗ is the liquid saturation volume (in [m³]) and Vᵥ is the vapour saturation volume (in [m³]).

If the calculation fails, returns (NaN, NaN, NaN)

By default, it uses ChemPotVSaturation

Examples:

julia> pr = PR(["water"])
PR{BasicIdeal, PRAlpha, NoTranslation, vdW1fRule} with 1 component:
  "water"
Contains parameters: a, b, Tc, Pc, Mw

julia> p,vl,vv = saturation_pressure(pr,373.15) #default, uses Clapeyron.ChemPotVSaturation
(96099.38979351855, 2.2674781912892906e-5, 0.03201681565699426)

julia> p,vl,vv = saturation_pressure(pr,373.15,IsoFugacitySaturation()) #iso fugacity
(96099.38979351871, 2.2674781912892933e-5, 0.03201681565699359)

julia> p,vl,vv = saturation_pressure(pr,373.15,IsoFugacitySaturation(p0 = 1.0e5)) #iso fugacity, with starting point
(96099.38979351871, 2.2674781912892933e-5, 0.03201681565699547)

saturation_temperature(model::EoSModel, p, kwargs...)
saturation_temperature(model::EoSModel, p, method::SaturationMethod)
saturation_temperature(model, p, T0::Number)

Performs a single component saturation temperature equilibrium calculation, at the specified temperature T, of one mol of pure sustance specified by model. Returns (T₀, Vₗ, Vᵥ) where T₀ is the saturation Temperature (in [K]), Vₗ is the liquid saturation volume (in [m³]) and Vᵥ is the vapour saturation volume (in [m³]).

If the calculation fails, returns (NaN, NaN, NaN)

By default, it uses AntoineSaturation

Examples:

julia-repl

julia> pr = PR(["water"])
PR{BasicIdeal, PRAlpha, NoTranslation, vdW1fRule} with 1 component:
  "water"
Contains parameters: a, b, Tc, Pc, Mw

julia> Ts,vl,vv = saturation_temperature(pr,1e5) # AntoineSaturation by default
(374.24014010712983, 2.269760164801948e-5, 0.030849387955737825)

julia> saturation_pressure(pr,Ts)
(100000.00004314569, 2.269760164804427e-5, 0.03084938795785433)

enthalpy_vap(model::EoSModel, T,method = ChemPotVSaturation(x0_sat_pure(model,T)))

Calculates ΔH, the difference between saturated vapour and liquid enthalpies at temperature T [K], in [J]

acentric_factor(model::EoSModel;crit = crit_pure(model), satmethod = ChemPotVSaturation())

Calculates the acentric factor using its definition:

ω = -log10(psatᵣ) -1, at Tᵣ = 0.7

To do so, it calculates the critical temperature (using crit_pure) and performs a saturation calculation (with saturation_pressure(model,0.7Tc,satmethod))

pm,vs,vl = melting_pressure(model::CompositeModel,T;v0=x0_melting_pressure(model,T))

Calculates the melting pressure of a CompositeModel containing a solid and fluid phase EoS, at a specified temperature T. You can pass a tuple of initial values for the volumes (vs0,vl0).

returns:

• pm is melting Pressure [Pa]
• vs is melting solid volume at specified temperature [m³]
• vl is melting liquid volume at specified temperature [m³]

pm,vs,vl = melting_temperature(model::CompositeModel,p;v0=x0_melting_pressure(model,T))

Calculates the melting temperature of a CompositeModel containing a solid and fluid phase EoS, at a specified pressure p. You can pass a tuple of initial values for the volumes (vs0,vl0).

returns:

• Melting Temperature [K]
• melting solid volume at specified pressure [m³]
• melting liquid volume at specified pressure [m³]

psub,vs,vv = sublimation_pressure(model::CompositeModel,T;v0=x0_sublimation_pressure(model,T))

Calculates the sublimation pressure psub of a CompositeModel containing a solid and fluid phase EoS, at a specified temperature T. You can pass a tuple of initial values for the volumes (vs0,vv0).

returns:

• Sublimation Pressure [Pa]
• Sublimation solid volume at specified temperature [m³]
• Sublimation vapour volume at specified temperature [m³]

pm,vs,vv = sublimation_temperature(model::CompositeModel,p;v0=x0_sublimation_pressure(model,T))

Calculates the sublimation temperature of a CompositeModel containing a solid and fluid phase EoS, at a specified pressure p. You can pass a tuple of initial values for the volumes (vs0,vv0).

returns:

• Sublimation Temperature [K]
• Sublimation solid volume at specified pressure [m³]
• Sublimation vapour volume at specified pressure [m³]

Tt,pt,vs,vl,vv = triple_point(model::CompositeModel;v0 = x0_triple_point(model))

Calculates the triple point of a CompositeModel containing solid and fluid phase EoS.

returns:

• Triple point Temperature [K]
• Triple point Pressure [Pa]
• Solid volume at Triple Point [m³]
• Liquid volume at Triple Point [m³]
• Vapour volume at Triple Point [m³]

ChemPotVSaturation <: SaturationMethod
ChemPotVSaturation(V0)
ChemPotVSaturation(;vl = nothing,
                    vv = nothing,
                    crit = nothing,
                    crit_retry = true
                    f_limit = 0.0,
                    atol = 1e-8,
                    rtol = 1e-12,
                    max_iters = 10^4)

Default saturation_pressure Saturation method used by Clapeyron.jl. It uses equality of Chemical Potentials with a volume basis. If no volumes are provided, it will use x0_sat_pure. If those initial guesses fail and the specification is near critical point, it will try one more time, using Corresponding States instead. when crit_retry is true, if the initial solve fail, it will try to obtain a better estimate by calculating the critical point. f_limit, atol, rtol, max_iters are passed to the non linear system solver.

ChemPotDensitySaturation <: SaturationMethod
ChemPotDensitySaturation(;vl = nothing,
                        vv = nothing,
                        crit = nothing,
                        f_limit = 0.0,
                        atol = 1e-8,
                        rtol = 1e-12,
                        max_iters = 10^4)

Saturation method for saturation_pressure. It uses equality of Chemical Potentials with a density basis. If no volumes are provided, it will use x0_sat_pure. vl and vl are initial guesses for the liquid and vapour volumes. f_limit, atol, rtol, max_iters are passed to the non linear system solver.

IsoFugacitySaturation <: SaturationMethod
IsoFugacitySaturation(;p0 = nothing,
    vl = nothing,
    vv = nothing,
    crit = nothing,
    max_iters = 20,
    p_tol = sqrt(eps(Float64)))

Saturation method for saturation_pressure. Uses the isofugacity criteria. Ideal for Cubics or other EoS where the volume calculations are cheap. If p0 is not provided, it will be calculated via x0_psat.

ClapeyronSaturation <: SaturationMethod
ClapeyronSaturation(T0 = nothing, crit = nothing, satmethod = ChemPotVSaturation())

Saturation method for saturation_temperature. It solves iteratively saturation_temperature(model,Ti,satmethod) until convergence, by using the Clapeyron equation:

dp/dT = ΔS/ΔV

It descends from the critical point (or T0, if provided). Reliable, but slow.

It is recommended that T0 > Tsat, as the temperature decrease iteration series is more stable. Default method for saturation_temperature until Clapeyron 0.3.7

AntoineSaturation <: SaturationMethod
AntoineSaturation(;T0 = nothing,
                    vl = nothing,
                    vv = nothing,
                    f_limit = 0.0,
                    atol = 1e-8,
                    rtol = 1e-12,
                    max_iters = 10^4,
                    crit = nothing,
                    crit_retry = false)

Saturation method for saturation_temperature. Default method for saturation temperature from Clapeyron 0.3.7. It solves the Volume-Temperature system of equations for the saturation condition.

If only T0 is provided, vl and vv are obtained via x0_sat_pure. If T0 is not provided, it will be obtained via x0_saturation_temperature. It is recommended to overload x0_saturation_temperature, as the default starting point calls crit_pure, resulting in slower than ideal times. f_limit, atol, rtol, max_iters are passed to the non linear system solver.