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 pressure T, of one mol of pure sustance specified by model

Returns (T₀, Vₗ, Vᵥ) where p₀ 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, in J

crit_pure(model::EoSModel,x0=nothing)

Calculates the critical point of a single component modelled by model. Returns (Tc, pc, Vc) where Tc is the critical temperature (in K), pc is the critical pressure (in Pa) and Vc is the critical volume (in m³)

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 pressure. You can pass a tuple of initial values for the volumes (vs0,vl0).

returns:

• Melting Pressure [Pa]
• melting solid volume at specified temperature [m³]
• melting liquid volume at specified temperature [m³]

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

Calculates the melting temperature of a CompositeModel containing a solid and fluid phase EoS, at a specified pressure. 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 of a CompositeModel containing a solid and fluid phase EoS, at a specified pressure. 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,vl = sublimation_temperature(model::CompositeModel,T;v0=x0_sublimation_pressure(model,T))

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

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.