Index

Correlation Models

Correlation models are, as their name says, fitted equations that express one property of a compound. They meant to be used in conjunction with other models (like Activity models that require a saturated liquid volume), or via a CompositeModel. Because they only overload one property, the way to define a correlation is different than normal EoSModels.

Saturation Correlations

Saturation Correlations are any EoSModel that are subtypes of SaturationModel return psat(T) and the upper limit (Tc,Pc) pair. To define saturation correlations, you need to overload:

function crit_pure(model::MySaturationModel <: SaturationModel)
    ...
    return (Tc,Pc,NaN)
end

function Clapeyron.saturation_pressure_impl(model::MySaturationModel <: SaturationModel,T,::SaturationCorrelation)
    ...
    return (psat,NaN,NaN)
end

Saturation Models and Types

Clapeyron.SaturationModel — Type

SaturationModel <: EoSModel

Abstract type for Saturation correlation models.

Clapeyron.SaturationCorrelation — Type

SaturationCorrelation <: SaturationMethod

Saturation method used for dispatch on saturation correlations.

Clapeyron.LeeKeslerSat — Type

LeeKeslerSat <: SaturationModel

LeeKeslerSat(components;
userlocations = String[],
verbose::Bool=false)

Input Parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
acentricfactor: Single Parameter (Float64) - acentric factor

Description

Lee-Kesler correlation for saturation pressure:

psat(T) = f₀ + ω•f₁
Tr = T/Tc
f₀ = 5.92714 - 6.09648/Tr - 1.28862•log(Tr) + 0.169347•Tr⁶
f₁ = 15.2518 - 15.6875/Tr - 13.4721•log(Tr) + 0.43577•Tr⁶

Model Construction Examples

# Using the default database
sat = LeeKeslerSat("water") #single input
sat = LeeKeslerSat(["water","ethanol"]) #multiple components

# User-provided parameters, passing files or folders
sat = LeeKeslerSat(["neon","hydrogen"]; userlocations = ["path/to/my/db","critical.csv"])

# User-provided parameters, passing parameters directly

sat = LeeKeslerSat(["neon","hydrogen"];
        userlocations = (;Tc = [44.492,33.19],
                        Pc = [2679000, 1296400],
                        acentricfactor = [-0.03,-0.21])
                    )

References

Lee, B. I., & Kesler, M. G. (1975). A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE journal. American Institute of Chemical Engineers, 21(3), 510–527. doi:10.1002/aic.690210313

Clapeyron.DIPPR101Sat — Type

DIPPR101Sat <: SaturationModel

DIPPR101Sat(components;
userlocations = String[],
verbose::Bool=false)

Input Parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
A: Single Parameter (Float64)
B: Single Parameter (Float64)
C: Single Parameter (Float64)
D: Single Parameter (Float64)
E: Single Parameter (Float64)
Tmin: Single Parameter (Float64) - mininum Temperature range [K]
Tmax: Single Parameter (Float64) - maximum Temperature range [K]

Model Parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
A: Single Parameter (Float64)
B: Single Parameter (Float64)
C: Single Parameter (Float64)
D: Single Parameter (Float64)
E: Single Parameter (Float64)
Tmin: Single Parameter (Float64) - mininum Temperature range [K]
Tmax: Single Parameter (Float64) - maximum Temperature range [K]

Description

DIPPR 101 Equation for saturation pressure:

psat(T) = exp(A + B/T + C•log(T) + D•T^E)

References

Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE

Clapeyron.AntoineEqSat — Type

AntoineEqSat <: SaturationModel

AntoineEqSat(components;
userlocations = String[],
verbose::Bool=false)

Input Parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
A: Single Parameter (Float64) - First coefficient [dimensionless]
B: Single Parameter (Float64) - Second coefficent [°C]
C: Single Parameter (Float64) - Third coefficent [°C]
Tmin: Single Parameter (Float64) - Mininum Temperature range [K]
Tmax: Single Parameter (Float64) - Maximum Temperature range [K]

Model Parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
A: Single Parameter (Float64) - First coefficient [dimensionless]
B: Single Parameter (Float64) - Second coefficent [°C]
C: Single Parameter (Float64) - Third coefficent [°C]
Tmin: Single Parameter (Float64) - Mininum Temperature range [K]
Tmax: Single Parameter (Float64) - Maximum Temperature range [K]

Description

Antoine Equation for saturation pressure:

psat(T) = 10^(A + B/(T + C))

Returns saturation pressure of a pure substance, given temperature T.

Temperature T [K]
Saturation Pressure psat [Pa]

References

Antoine, C. (1888), «Tensions des vapeurs; nouvelle relation entre les tensions et les températures», Comptes Rendus des Séances de l'Académie des Sciences 107: 681-684, 778-780, 836-837.

Liquid Volume Correlations

Liquid Volume Correlations are any EoSModel that are subtypes of LiquidVolumeModel.

Most Liquid volume correlations are only defined by a volume equation, but some models are defined in terms of the gibbs free energy.

Clapeyron.RackettLiquid — Type

RackettLiquid(components;
userlocations::Vector{String}=String[],
verbose::Bool=false)

Input parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
Vc: Single Parameter (Float64) - Critical Volume [m³·mol⁻¹]

Model Parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
Zc: Single Parameter (Float64) - Critical Compressibility Factor

Description

Rackett Equation of State for saturated liquids. It is independent of the pressure.

Tr = T/Tc
V = (R̄Tc/Pc)Zc^(1+(1-Tr)^(2/7))

Model Construction Examples

# Using the default database
model = RackettLiquid("water") #single input
model = RackettLiquid(["water","ethanol"]) #multiple components

# User-provided parameters, passing files or folders
model = RackettLiquid(["neon","hydrogen"]; userlocations = ["path/to/my/db","critical.csv"])

# User-provided parameters, passing parameters directly

model = RackettLiquid(["neon","hydrogen"];
        userlocations = (;Tc = [44.492,33.19],
                        Vc = [4.25e-5, 6.43e-5],
                        Pc = [2679000, 1296400])
                    )

References

Rackett, H. G. (1970). Equation of state for saturated liquids. Journal of Chemical and Engineering Data, 15(4), 514–517. doi:10.1021/je60047a012

Clapeyron.YamadaGunnLiquid — Function

YamadaGunnLiquid(components;
            userlocations::Vector{String}=String[],
            verbose::Bool=false)::RackettLiquid

Input parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
acentricfactor: Single Parameter (Float64) - Acentric Factor

Model Parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
Zc: Single Parameter (Float64) - Critical Compressibility Factor

Description

The Yamada-Gunn equation of state is a modification of the Rackett equation of state that uses a different approach to calculate the compressibility factor Zc:

Tr = T/Tc
Zc = 0.29056 - 0.08775ω
V = (R̄Tc/Pc)Zc^(1+(1-Tr)^(2/7))

It can be used as a substitute of RackettLiquid when Vc is not known.

Model Construction Examples

# Using the default database
model = YamadaGunnLiquid("water") #single input
model = YamadaGunnLiquid(["water","ethanol"]) #multiple components

# User-provided parameters, passing files or folders
model = YamadaGunnLiquid(["neon","hydrogen"]; userlocations = ["path/to/my/db","critical.csv"])

# User-provided parameters, passing parameters directly

model = YamadaGunnLiquid(["neon","hydrogen"];
        userlocations = (;Tc = [44.492,33.19],
                        Pc = [2679000, 1296400],
                        acentricfactor = [-0.03,-0.21])
                    )

References

Rackett, H. G. (1970). Equation of state for saturated liquids. Journal of Chemical and Engineering Data, 15(4), 514–517. doi:10.1021/je60047a012
Gunn, R. D., & Yamada, T. (1971). A corresponding states correlation of saturated liquid volumes. AIChE Journal. American Institute of Chemical Engineers, 17(6), 1341–1345. doi:10.1002/aic.690170613

Clapeyron.COSTALD — Type

COSTALD(components; 
            userlocations::Vector{String}=String[], 
            verbose::Bool=false)

Input parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Vc: Single Parameter (Float64) - Critical Volume [m³·mol⁻¹]
acentricfactor: Single Parameter (Float64) - Acentric Factor

Description

COSTALD Equation of State for saturated liquids. It is independent of the pressure.

Model Construction Examples

# Using the default database
model = COSTALD("water") #single input
model = COSTALD(["water","ethanol"]) #multiple components

# User-provided parameters, passing files or folders
model = COSTALD(["neon","hydrogen"]; userlocations = ["path/to/my/db","critical.csv"])

# User-provided parameters, passing parameters directly

model = COSTALD(["neon","hydrogen"];
        userlocations = (;Tc = [44.492,33.19],
                        Vc = [4.25e-5, 6.43e-5],
                        acentricfactor = [-0.03,-0.21])
                    )

References

Hankinson, R. W., & Thomson, G. H. (1979). A new correlation for saturated densities of liquids and their mixtures. AIChE Journal. American Institute of Chemical Engineers, 25(4), 653–663. doi:10.1002/aic.690250412

Missing docstring.

Missing docstring for GrenkeElliotWater. Check Documenter's build log for details.

Clapeyron.HoltenWater — Type

GrenkeElliottWater <: GibbsBasedModel
GrenkeElliottWater()

Input parameters

None

Description

Holten's model for liquid water at low temperatures (homogeneous ice nucleation temperature up to 300 K) and high pressures (up to 400 MPa, but can be extrapolated up to 1000 MPa).

g(P,T) = R*Tc*ĝ
ĝ = ĝᴬ + T̂*(x*L + x*log(x) + (1 - x)*log(1 - x) + ω*x*(1-x))
x: solution of L + log(x) - log(1 - x) + ω*(1 - 2*x) = 0
L = L₀*K₂*(1 + k₀*k₂ + k₁*(p + k₂*t) - K₁)/(2*k₁*k₂)
K₁ = sqrt((1 + k₀*k₂ + k₁*(p - k₂*t))^2 - 4*k₀*k₁*k₂*(p - k₂*t))
K₂ = sqrt(1 + k₂*k₂)
t = (T - Tc)/Tc
p = P/(R*Tc*ρ0)
ω = 2 + ω₀*p
ĝᴬ = ∑(cᵢ * τ^aᵢ * π^bᵢ * exp(-dᵢ*π))

Where x is the fraction of water molecules in with low-density structure.

References

Holten, V., Sengers, J. V., & Anisimov, M. A. (2014). Equation of state for supercooled water at pressures up to 400 MPa. Journal of Physical and Chemical Reference Data, 43(4), 043101. doi:10.1063/1.4895593

Virial Models

Virial models are defined in terms of the second virial coefficient, B(T,z). The reduced residual Helmholtz energy is defined as:

$\frac{A_\mathrm{res}}{Nk_\mathrm{B}T} = \frac{B}{V}$,

To implement a virial model, it is necessary to overload Clapeyron.second_virial_coefficient_impl(model::<:SecondVirialModel,T,z).

Clapeyron.AbbottVirial — Type

AbbottVirial <: SecondVirialModel
AbbottVirial(components;
            idealmodel = BasicIdeal,
            userlocations = String[],
            ideal_userlocations = String[],
            verbose = false)

Input parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
acentricfactor: Single Parameter (Float64) - Acentric Factor
Mw: Single Parameter (Float64) - Molecular Weight [g·mol⁻¹]

Input models

idealmodel: Ideal Model

Description

Virial model using Corresponding State Principles:

B = ∑xᵢxⱼBᵢⱼ
Bᵢⱼ = BrᵢⱼRTcᵢⱼ/Pcᵢⱼ
Brᵢⱼ = B₀ + ωᵢⱼB₁
B₀ = 0.083 + 0.422/Trᵢⱼ^1.6
B₁ = 0.139 - 0.172/Trᵢⱼ^4.2
Trᵢⱼ = T/Tcᵢⱼ
Tcᵢⱼ = √TcᵢTcⱼ
Pcᵢⱼ = (Pcᵢ + Pcⱼ)/2
ωᵢⱼ = (ωᵢ + ωⱼ)/2

Model Construction Examples

# Using the default database
model = AbbottVirial("water") #single input
model = AbbottVirial(["water","ethanol"]) #multiple components
model = AbbottVirial(["water","ethanol"], idealmodel = ReidIdeal) #modifying ideal model

# Passing a prebuilt model

my_idealmodel = MonomerIdeal(["neon","hydrogen"];userlocations = (;Mw = [20.17, 2.]))
model = AbbottVirial(["neon","hydrogen"],idealmodel = my_idealmodel)

# User-provided parameters, passing files or folders
model = AbbottVirial(["neon","hydrogen"]; userlocations = ["path/to/my/db","critical.csv"])

# User-provided parameters, passing parameters directly

model = AbbottVirial(["neon","hydrogen"];
        userlocations = (;Tc = [44.492,33.19],
                        Pc = [2679000, 1296400],
                        Mw = [20.17, 2.],
                        acentricfactor = [-0.03,-0.21])
                    )

References

Smith, H. C. Van Ness Joseph M. Introduction to Chemical Engineering Thermodynamics 4E 1987.

Clapeyron.TsonopoulosVirial — Type

TsonopoulosVirial <: SecondVirialModel
TsonopoulosVirial(components;
        idealmodel = BasicIdeal,
        userlocations = String[],
        ideal_userlocations = String[],
        verbose = false)

Input parameters

Tc: Single Parameter (Float64) - Critical Temperature [K]
Pc: Single Parameter (Float64) - Critical Pressure [Pa]
acentricfactor: Single Parameter (Float64) - Acentric Factor
Mw: Single Parameter (Float64) - Molecular Weight [g·mol⁻¹]

Input models

idealmodel: Ideal Model

Description

Virial model using Corresponding State Principles:

B = ∑xᵢxⱼBᵢⱼ
Bᵢⱼ = BrᵢⱼRTcᵢⱼ/Pcᵢⱼ
Brᵢⱼ = B₀ + ωᵢⱼB₁
B₀ = 0.1445 - 0.330/Trᵢⱼ - 0.1385/Trᵢⱼ^2 - 0.0121/Trᵢⱼ^3 - 0.000607/Trᵢⱼ^8
B₁ = 0.0637 + 0.331/Trᵢⱼ - 0.423/Trᵢⱼ^2 - 0.423/Trᵢⱼ^3 - 0.008/Trᵢⱼ^8
Trᵢⱼ = T/Tcᵢⱼ
Tcᵢⱼ = √TcᵢTcⱼ
Pcᵢⱼ = (Pcᵢ + Pcⱼ)/2
ωᵢⱼ = (ωᵢ + ωⱼ)/2

Model Construction Examples

# Using the default database
model = TsonopoulosVirial("water") #single input
model = TsonopoulosVirial(["water","ethanol"]) #multiple components
model = TsonopoulosVirial(["water","ethanol"], idealmodel = ReidIdeal) #modifying ideal model

# Passing a prebuilt model

my_idealmodel = MonomerIdeal(["neon","hydrogen"];userlocations = (;Mw = [20.17, 2.]))
model = TsonopoulosVirial(["neon","hydrogen"],idealmodel = my_idealmodel)

# User-provided parameters, passing files or folders
model = TsonopoulosVirial(["neon","hydrogen"]; userlocations = ["path/to/my/db","critical.csv"])

# User-provided parameters, passing parameters directly

model = TsonopoulosVirial(["neon","hydrogen"];
        userlocations = (;Tc = [44.492,33.19],
                        Pc = [2679000, 1296400],
                        Mw = [20.17, 2.],
                        acentricfactor = [-0.03,-0.21])
                    )

References

Tsonopoulos, C. (1974). An empirical correlation of second virial coefficients. AIChE Journal. American Institute of Chemical Engineers, 20(2), 263–272. doi:10.1002/aic.690200209

Clapeyron.EoSVirial2 — Type

EoSVirial2 <: SecondVirialModel
EoSVirial2(model;idealmodel = idealmodel(model))

Input models

model: Model providing second virial coefficient is obtained
idealmodel: Ideal Model

Description

Virial model, that just calls the second virial coefficient of the underlying model.

B(T,z) = B(model,T,z)

Solid Models

Solid models provide simple approximations to the excess chemical potential in the solid phase. Intended to be used in conjunction with a liquid model within a CompositeModel.

Clapeyron.SolidHfus — Type

SolidHfusModel <: EoSModel

SolidHfus(components;
userlocations = String[],
verbose::Bool=false)

Parameters

Hfus: Single Parameter (Float64) - Enthalpy of Fusion at 1 bar [J·mol⁻¹]
Tm: Single Parameter (Float64) - Melting Temperature [K]
CpSL: Single Parameter (Float64) (optional) - Heat Capacity of the Solid-Liquid Phase Transition [J·mol⁻¹·K⁻¹]

Description

Approximation of the excess chemical potential in the solid phase (CpSL is not necessary by default):

ln(xᵢγᵢ) = Hfusᵢ*T*(1/Tmᵢ-1/T)-CpSLᵢ/R̄*(Tmᵢ/T-1-log(Tmᵢ/T))

Clapeyron.SolidKs — Type

SolidKsModel <: EoSModel

SolidKs(components;
userlocations = String[],
verbose::Bool=false)

Parameters

Gform: Single Parameter (Float64) - Formation Gibbs energy in water at infinite dilution 1 bar and the reference temperature[J·mol⁻¹]
Hform: Single Parameter (Float64) -Formation enthalpy in water at infinite dilution 1 bar and the reference temperature[J·mol⁻¹]
Tref: Single Parameter (Float64) - Reference temperature [K]

Description

Approximation of the excess chemical potential in the solid phase, using enthalpies and gibbs energies of formation where the liquid reference is at infinite dilution in water:

ln(xᵢγᵢ) = -Gformᵢ*T/Trefᵢ - Hformᵢ*(1 - T/Trefᵢ)

Clapeyron.IAPWS06 — Type

IAPWS06 <: EmpiricHelmholtzModel
IAPWS06()

Input parameters

None

Description

IAPWS (International Association for the Properties of Water and Steam) Pure water Model for ice Ih, 2009 update.

References

Feistel, R., & Wagner, W. (2006). A new equation of state for H2O ice Ih. Journal of Physical and Chemical Reference Data, 35(2), 1021–1047. doi:10.1063/1.2183324
IAPWS R10-06 (2009). Revised Release on the Equation of State 2006 for H2O Ice Ih