Empiric Helmholtz Models

SingleFluid(components;
        userlocations = String[],
        ancillaries = nothing,
        ancillaries_userlocations = String[],
        estimate_pure = false,
        coolprop_userlocations = true,
        Rgas = nothing,
        verbose = false)

Input parameters

• JSON data (CoolProp and teqp format)

Input models

• ancillaries: a model that provides initial guesses for saturation calculations. if nothing, then they will be parsed from the input JSON.

Description

Instantiates a single-component Empiric EoS model. Rgas can be used to set the value of the gas constant that is used during property calculations.

If coolprop_userlocations is true, then Clapeyron will try to look if the fluid is present in the CoolProp library.

The properties, ideal and residual terms can be accessed via the properties, ideal and residual fields respectively:

julia> model = SingleFluid("water")
MultiParameter Equation of state for water:
 Polynomial power terms: 7
 Exponential terms: 44
 Gaussian bell-shaped terms: 3
 Non Analytic terms: 2

julia> model.ideal
Ideal MultiParameter coefficients:
 Lead terms: -8.3204464837497 + 6.6832105275932*τ + 3.00632*log(τ)
 Plank-Einstein terms: 5

julia> model.residual
Residual MultiParameter coefficients:
 Polynomial power terms: 7
 Exponential terms: 44
 Gaussian bell-shaped terms: 3
 Non Analytic terms: 2

SingleFluidIdeal(components;
    userlocations = String[],
    Rgas = nothing,
    verbose = false,
    coolprop_userlocations = true)

Input parameters

• JSON data (CoolProp and teqp format)

Input models

• ancillaries: a model that provides initial guesses for saturation calculations. if nothing, then they will be parsed from the input JSON.

Description

Instantiates the ideal part of a single-component Empiric EoS model. Rgas can be used to set the value of the gas constant that is used during property calculations.

If coolprop_userlocations is true, then Clapeyron will try to look if the fluid is present in the CoolProp library.

The properties and ideal terms can be accessed via the properties and ideal fields respectively:

julia> model = SingleFluidIdeal("water")
Ideal MultiParameter Equation of state for water:
 Lead terms: -8.3204464837497 + 6.6832105275932*τ + 3.00632*log(τ)
 Plank-Einstein terms: 5

julia> model.ideal
Ideal MultiParameter coefficients:
 Lead terms: -8.3204464837497 + 6.6832105275932*τ + 3.00632*log(τ)
 Plank-Einstein terms: 5

MultiFluid(components;
    idealmodel = nothing,
    ideal_userlocations = String[],
    pure_userlocations = String[],
    mixing = AsymmetricMixing,
    departure = EmpiricDeparture,
    mixing_userlocations = String[],
    departure_userlocations = String[],
    estimate_pure = false,
    estimate_mixing = :off,
    coolprop_userlocations = true,
    Rgas = nothing,
    reference_state = nothing,
     verbose = false)

Input parameters

• JSON data (CoolProp and teqp format)

Input models

• idealmodel: Ideal Model. if it is nothing, then it will parse the ideal model from the input JSON.
• mixing: mixing model for temperature and volume.
• departure: departure model

Description

Instantiates a multi-component Empiric EoS model. Rgas can be used to set the value of the gas constant that is used during property calculations.

If coolprop_userlocations is true, then Clapeyron will try to look if the fluid is present in the CoolProp library.

If estimate_pure is true, then, if a JSON is not found, the pure model will be estimated, using the XiangDeiters model

estimate_mixing is used to fill missing mixing values in the case of using AsymmetricMixing. on other mixing models it has no effect.

• estimate_mixing = :off will perform no calculation of mixing parameter, throwing an error if missing values are found.
• estimate_mixing = :lb will perform Lorentz-Berthelot estimation of missing mixing parameters. (γT = βT = γv = βv = 1.0). additionally, you can pass LorentzBerthelotMixing to use k and l BIP instead.
• estimate_mixing = :linear will perform averaging of γT and γv so that T(x) = ∑xᵢTᵢ and V(x) = ∑xᵢVᵢ on missing mixing parameters. Additionally, you can use LinearMixing to perform this directly.

Rgas sets the value of the gas constant to be used by the multifluid. The default is the following:

• If Rgas is not specified and the input is a single component model, then the value of Rgas will be taken from the fluid json file.
• If Rgas is not specified and the input is a multi-component model, then the value of Rgas will be set to Clapeyron.R̄ = Rgas() = 8.31446261815324 (2019 defined constant value)

EmpiricIdeal(components;
pure_userlocations = String[],
estimate_pure = false,
coolprop_userlocations = true,
Rgas = R̄,
verbose = false)

Input parameters

• JSON data (CoolProp and teqp format)

Description

Instantiates the ideal part of a multi-component Empiric EoS model. Rgas can be used to set the value of the gas constant that is used during property calculations.

If coolprop_userlocations is true, then Clapeyron will try to look if the fluid is present in the CoolProp library.

If estimate_pure is true, then, if a JSON is not found, the pure model will be estimated, using the XiangDeiters model

XiangDeiters::SingleFluid
XiangDeiters(component;
    idealmodel = BasicIdeal,
    userlocations = String[],
    ideal_userlocations = String[],
    Rgas = nothing,
    verbose = 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]
• Mw: Single Parameter (Float64) - Molecular Weight [g/mol]
• acentricfactor: Single Parameter (Float64)

Input models

• idealmodel: Ideal Model

Description

Xiang-Deiters model. estimates a single component Empiric EoS Model from critical values and the acentric factor.

Zc = PcVc/RTc
θ = (Zc - 0.29)^2
aᵣ = a₀(δ,τ) + ω*a₁(δ,τ) + θ*a₂(δ,τ)

Rgas can be used to set the value of the gas constant that is used during property calculations.

Model Construction Examples

# Using the default database
model = XiangDeiters("water") #single input
model = XiangDeiters(["water"]) #single input, as a vector
model = XiangDeiters(["water"], idealmodel = ReidIdeal) #modifying ideal model

# Passing a prebuilt model

my_idealmodel = MonomerIdeal(["ethane"])
model = XiangDeiters(["ethane"],idealmodel = my_idealmodel)

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

# User-provided parameters, passing parameters directly

model = XiangDeiters(["hydrogen"];
        userlocations = (;Tc = [44.492],
                        Pc = [2679000],
                        Vc = [4.25e-5],
                        Mw = [2.0],
                        acentricfactor = [-0.21])
                    )

references

1. Xiang, H. W., & Deiters, U. K. (2008). A new generalized corresponding-states equation of state for the extension of the Lee–Kesler equation to fluids consisting of polar and larger nonpolar molecules. Chemical Engineering Science, 63(6), 1490–1496. doi:10.1016/j.ces.2007.11.029

IAPWS95 <: EmpiricHelmholtzModel
IAPWS95()

Input parameters

None

Description

IAPWS95 (International Association for the Properties of Water and Steam) Pure water Model, 2018 update.

δ = ρ/ρc
τ = T/Tc
a⁰(δ,τ) = log(δ) + n⁰₁ + n⁰₂τ + n⁰₃log(τ) + ∑n⁰ᵢ(1-exp(-γ⁰ᵢτ)), i ∈ 4:8
aʳ(δ,τ)  = aʳ₁+ aʳ₂ + aʳ₃ + aʳ₄
aʳ₁(δ,τ)  = ∑nᵢδ^(dᵢ)τ^(tᵢ), i ∈ 1:7
aʳ₂(δ,τ)  = ∑nᵢexp(-δ^cᵢ)δ^(dᵢ)τ^(tᵢ), i ∈ 8:51
aʳ₃(δ,τ)  = ∑nᵢexp(-αᵢ(δ - εᵢ)^2 - βᵢ(τ - γᵢ)^2)δ^(dᵢ)τ^(tᵢ), i ∈ 52:54
aʳ₄(δ,τ) = ∑nᵢδΨΔ^(bᵢ), i ∈ 55:56
Δ = θ^2 + Bᵢ[(δ - 1)^2]^aᵢ
θ = (1 - τ) + Aᵢ[(δ - 1)^2]^(1/2βᵢ)
Ψ = exp(-Cᵢ(δ - 1)^2 - Dᵢ(τ - 1)^2)

parameters n⁰,γ⁰,n,t,d,c,α,β,γ,ε,A,B,C,D where obtained via fitting.

References

1. Wagner, W., & Pruß, A. (2002). The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of physical and chemical reference data, 31(2), 387–535. doi:10.1063/1.1461829
2. IAPWS R6-95 (2018). Revised Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use

PropaneRef <: EmpiricHelmholtzModel
PropaneRef()

Input parameters

None

Description

Propane Reference Equation of State

δ = ρ/ρc
τ = T/Tc
a⁰(δ,τ) = log(δ) + n⁰₁ + n⁰₂τ + n⁰₃log(τ) + ∑n⁰ᵢ(1-exp(-γ⁰ᵢτ)), i ∈ 4:7
aʳ(δ,τ)  = aʳ₁+ aʳ₂ + aʳ₃
aʳ₁(δ,τ)  = ∑nᵢδ^(dᵢ)τ^(tᵢ), i ∈ 1:5
aʳ₂(δ,τ)  = ∑nᵢexp(-δ^cᵢ)δ^(dᵢ)τ^(tᵢ), i ∈ 6:11
aʳ₃(δ,τ)  = ∑nᵢexp(-ηᵢ(δ - εᵢ)^2 - βᵢ(τ - γᵢ)^2)δ^(dᵢ)τ^(tᵢ), i ∈ 12:18

parameters n⁰,γ⁰,n,t,d,c,η,β,γ,ε where obtained via fitting.

References

1. Lemmon, E. W., McLinden, M. O., & Wagner, W. (2009). Thermodynamic properties of propane. III. A reference equation of state for temperatures from the melting line to 650 K and pressures up to 1000 MPa. Journal of Chemical and Engineering Data, 54(12), 3141–3180. doi:10.1021/je900217v

TholLJ()

Lennard-Jones Reference equation of state. valid from 0.5 < T/Tc < 7 and pressures up to p/pc = 500. ``` τᵢ = 1.32/T δᵢ = n/0.31V a⁰ᵢ(δ,τ) = log(δᵢ) + 1.5log(τᵢ) - 1.515151515τᵢ + 6.262265814 a⁰(δ,τ,z) = ∑xᵢ(a⁰ᵢ + log(xᵢ)) aʳ(δ,τ) = aʳ₁+ aʳ₂ + aʳ₃ + aʳ₄ aʳ₁(δ,τ) = ∑nᵢδ^(dᵢ)τ^(tᵢ), i ∈ 1:6 aʳ₂(δ,τ) = ∑nᵢexp(-δ^cᵢ)δ^(dᵢ)τ^(tᵢ), i ∈ 7:12 aʳ₃(δ,τ) = ∑nᵢexp(-ηᵢ(δ - εᵢ)^2 - βᵢ(τ - γᵢ)^2)δ^(dᵢ)τ^(tᵢ), i ∈ 13:23

Ammonia2023 <: EmpiricHelmholtzModel
Ammonia2023()

Input parameters

None

Description

Ammonia Reference Equation of State (2023)

δ = ρ/ρc
τ = T/Tc
a⁰(δ,τ) = log(δ) + n⁰₁ + n⁰₂τ + n⁰₃log(τ) + ∑n⁰ᵢ(1-exp(-γ⁰ᵢτ)), i ∈ 4:7
aʳ(δ,τ)  = aʳ₁+ aʳ₂ + aʳ₃
aʳ₁(δ,τ)  = ∑nᵢδ^(dᵢ)τ^(tᵢ), i ∈ 1:5
aʳ₂(δ,τ)  = ∑nᵢexp(-δ^cᵢ)δ^(dᵢ)τ^(tᵢ), i ∈ 6:8
aʳ₃(δ,τ)  = ∑nᵢexp(-ηᵢ(δ - εᵢ)^2 - βᵢ(τ - γᵢ)^2)δ^(dᵢ)τ^(tᵢ), i ∈ 9:18
aʳ₃(δ,τ)  = ∑nᵢexp(-ηᵢ(δ - εᵢ)^2 - 1/(βᵢ*(τ -γᵢ)^2 + bᵢ))δ^(dᵢ)τ^(tᵢ), i ∈ 19:20

parameters n⁰,γ⁰,n,t,d,c,η,β,γ,ε where obtained via fitting.

References

1. Gao, K., Wu, J., Bell, I. H., Harvey, A. H., & Lemmon, E. W. (2023). A reference equation of state with an associating term for the thermodynamic properties of ammonia. Journal of Physical and Chemical Reference Data, 52(1), 013102. doi:10.1063/5.0128269

LJRef <: EmpiricHelmholtzModel
LJRef(components;
userlocations = String[],
verbose = false)

Input parameters

• sigma: Single Parameter (Float64) - particle size [Å]
• epsilon: Single Parameter (Float64) - dispersion energy [K]
• Mw: Single Parameter (Float64) - Molecular Weight [g/mol]
• k: Pair Parameter (Float64) (optional) - sigma mixing coefficient

Model Parameters

• sigma: Pair Parameter (Float64) - particle size [m]
• epsilon: Pair Parameter (Float64) - dispersion energy [K]
• Mw: Single Parameter (Float64) - Molecular Weight [g/mol]

Description

Lennard-Jones Reference equation of state. valid from 0.5 < T/Tc < 7 and pressures up to p/pc = 500.

σᵢⱼ = (σᵢ + σⱼ)/2
ϵᵢⱼ = (1-kᵢⱼ)√(ϵⱼϵⱼ)
σ^3 = Σxᵢxⱼσᵢⱼ^3
ϵ = Σxᵢxⱼϵᵢⱼσᵢⱼ^3/σ^3
τᵢ = 1.32ϵᵢ/T
δᵢ = n(Nₐσᵢ^3)/0.31V
a⁰ᵢ(δ,τ) = log(δᵢ) + 1.5log(τᵢ) - 1.515151515τᵢ + 6.262265814
a⁰(δ,τ,z) = ∑xᵢ(a⁰ᵢ + log(xᵢ))
τ = 1.32ϵ/T
δ = n(Nₐσ^3)/0.31V
aʳ(δ,τ)  = aʳ₁+ aʳ₂ + aʳ₃ + aʳ₄
aʳ₁(δ,τ)  = ∑nᵢδ^(dᵢ)τ^(tᵢ), i ∈ 1:6
aʳ₂(δ,τ)  = ∑nᵢexp(-δ^cᵢ)δ^(dᵢ)τ^(tᵢ), i ∈ 7:12
aʳ₃(δ,τ)  = ∑nᵢexp(-ηᵢ(δ - εᵢ)^2 - βᵢ(τ - γᵢ)^2)δ^(dᵢ)τ^(tᵢ), i ∈ 13:23

parameters n,t,d,c,η,β,γ,ε where obtained via fitting.

References

1. Thol, M., Rutkai, G., Köster, A., Lustig, R., Span, R., & Vrabec, J. (2016). Equation of state for the Lennard-Jones fluid. Journal of physical and chemical reference data, 45(2), 023101. doi:10.1063/1.4945000

GERG2008::MultiFluid

GERG2008(components;
        Rgas = 8.314472,
        reference_state = nothing,
        verbose = false)

input Parameters

None

Description

The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures. valid for 21 compounds (Clapeyron.GERG2008_names).

a = a⁰ + aʳ

a⁰ = ∑xᵢ(a⁰ᵢ(τᵢ,δᵢ) + ln(xᵢ))
δᵢ = ρ/ρcᵢ
τᵢ = Tcᵢ/T
a⁰ᵢ = ln(δᵢ) + R∗/R[n⁰ᵢ₋₁ + n⁰ᵢ₋₂τᵢ + n⁰ᵢ₋₃ln(τᵢ) + ∑n⁰ᵢ₋ₖln(abs(sinh(ϑ₀ᵢ₋ₖτᵢ))) + ∑n⁰ᵢ₋ₖln(cosh(ϑ₀ᵢ₋ₖτᵢ))]
R∗ = 8.314510
R = 8.314472

τ = Tᵣ/T
δ = ρ/ρᵣ
(1/ρᵣ) = ∑∑xᵢxⱼβᵥ₋ᵢⱼγᵥ₋ᵢⱼ[(xᵢ+xⱼ)/(xᵢβᵥ₋ᵢⱼ^2 + xⱼ)]•1/8(1/∛ρcᵢ + 1/∛ρcⱼ)^2
Tᵣ = ∑∑xᵢxⱼβₜ₋ᵢⱼγₜ₋ᵢⱼ[(xᵢ+xⱼ)/(xᵢβₜ₋ᵢⱼ^2 + xⱼ)]•√(TcᵢTcⱼ)
aʳ = ∑xᵢaᵣᵢ(τ,δ) + ∑∑xᵢxⱼFᵢⱼaʳᵢⱼ(τ,δ)
aʳᵢ = ∑nᵢ₋ₖδ^(dᵢ₋ₖ)τ^(tᵢ₋ₖ)  + ∑nᵢ₋ₖδ^(dᵢ₋ₖ)τ^(tᵢ₋ₖ)exp(-δ^cᵢ₋ₖ)
aʳᵢⱼ = ∑nᵢⱼ₋ₖδ^(dᵢⱼ₋ₖ)τ^(tᵢⱼ₋ₖ)  + ∑nᵢⱼ₋ₖδ^(dᵢⱼ₋ₖ)τ^(tᵢⱼ₋ₖ)exp(ηᵢⱼ₋ₖ(δ-εᵢⱼ₋ₖ)^2 + βᵢⱼ₋ₖ(δ-γᵢⱼ₋ₖ))

References

1. Kunz, O., & Wagner, W. (2012). The GERG-2008 wide-range equation of state for natural gases and other mixtures: An expansion of GERG-2004. Journal of Chemical and Engineering Data, 57(11), 3032–3091. doi:10.1021/je300655b

EOS_LNG::MultiFluid

EOS_LNG(components::Vector{String};
Rgas = 8.314472,
reference_state = nothing,
verbose = false)

input Parameters

None

Description

EOS-LNG: A Fundamental Equation of State for the Calculation of Thermodynamic Properties of Liquefied Natural Gases. valid for 21 compounds (Clapeyron.GERG2008_names). the EoS has new binary-specific parameters for methane + n-butane, methane + isobutane, methane + n-pentane, and methane + isopentane.

It uses the same functional form as GERG2008.

References

1. Thol, M., Richter, M., May, E. F., Lemmon, E. W., & Span, R. (2019). EOS-LNG: A fundamental equation of state for the calculation of thermodynamic properties of liquefied natural gases. Journal of Physical and Chemical Reference Data, 48(3), 033102. doi:10.1063/1.5093800
2. Kunz, O., & Wagner, W. (2012). The GERG-2008 wide-range equation of state for natural gases and other mixtures: An expansion of GERG-2004. Journal of Chemical and Engineering Data, 57(11), 3032–3091. doi:10.1021/je300655b

EOS_LNG::MultiFluid

EOS_LNG(components::Vector{String};
Rgas = R̄,
reference_state = nothing,
verbose = false)

input Parameters

None

Description

EOS-LNG: A Fundamental Equation of State for the Calculation of Thermodynamic Properties of Liquefied Natural Gases. valid for 21 compounds (Clapeyron.GERG2008_names). the EoS has new binary-specific parameters for methane + n-butane, methane + isobutane, methane + n-pentane, and methane + isopentane.

It uses the same functional form as GERG2008.

References

EOS-CG: : A Mixture Model for the Calculation of Thermodynamic Properties of CCS Mixtures

It uses the same functional form as GERG2008.

References

1. Neumann, T., Herrig, S., Bell, I. H., Beckmüller, R., Lemmon, E. W., Thol, M., & Span, R. (2023). EOS-CG-2021: A mixture model for the calculation of thermodynamic properties of CCS mixtures. International Journal of Thermophysics, 44(12). doi:10.1007/s10765-023-03263-6

HelmAct::MultiFluid
HelmAct(components;
    pure_userlocations = String[],
    activity = PSRKUNIFAC,
    activity_userlocations = String[],
    estimate_pure = false,
    coolprop_userlocations = false,
    Rgas = R̄,
    reference_state = nothing,
    verbose = verbose)

input Parameters

• CoolProp JSON pure fluid files

Input Models

• activity: activity model.

Description

Creates a Helmholtz + Activity (HelmAct) model:

aᵣ = ∑xᵢaᵣᵢ(δ,τ) + Δa
Δa = gᴱᵣ/RT - log(1+bρ)/log(1+bρref) * ∑xᵢ(aᵣᵢ(δref,τ) - aᵣᵢ(δrefᵢ,τᵢ))
τᵢ = Tcᵢ/T
δref = ρref/ρr
δrefᵢ = ρrefᵢ/ρcᵢ
b = 1/1.17ρref

where gᴱᵣ is the residual part of the excess gibbs free energy obtained from an activity model.

References

1. Jäger, A., Breitkopf, C., & Richter, M. (2021). The representation of cross second virial coefficients by multifluid mixture models and other equations of state. Industrial & Engineering Chemistry Research, 60(25), 9286–9295. doi:10.1021/acs.iecr.1c01186

LinearMixing <: MultiFluidDepartureModel
LinearMixing(components;
userlocations = String[],
verbose = false)

Input parameters

none

Description

Linear mixing rule for MultiParameter EoS models:

τ = T̄/T
δ = V̄/V
V̄ = ∑xᵢVcⱼ
T̄ = ∑xᵢTcᵢ

Model Construction Examples

# Because this model does not have parameters, all those constructors are equivalent:
mixing = LinearMixing()
mixing = LinearMixing("water")
mixing = LinearMixing(["water","carbon dioxide"])

AsymmetricMixing <: MultiFluidDepartureModel
AsymmetricMixing(components;
userlocations = String[],
verbose = false)

Input parameters

• beta_v: Pair Parameter (Float64) - binary interaction parameter (no units)
• gamma_v: Pair Parameter (Float64) - binary interaction parameter (no units)
• beta_T: Pair Parameter (Float64) - binary interaction parameter (no units)
• gamma_T: Pair Parameter (Float64) - binary interaction parameter (no units)

Description

Asymmetric mixing rule for MultiParameter EoS models:

τ = T̄/T
δ = V̄/V
V̄ = ∑xᵢxⱼ * βᵛᵢⱼ * γᵛᵢⱼ * (xᵢ + xⱼ)/(xᵢ*βᵛᵢⱼ^2 + xⱼ) * Vᵣᵢⱼ
T̄ = ∑xᵢxⱼ * βᵛᵢⱼ * γᵀᵢⱼ * (xᵢ + xⱼ)/(xᵢ*βᵀᵢⱼ^2 + xⱼ) * Tᵣᵢⱼ
Vᵣᵢⱼ = 0.125*(∛Vcᵢ + ∛Vcⱼ)^3
Tᵣᵢⱼ = √(Tcᵢ*Tcⱼ)

With the asymmetry present in the β parameters:

βᵛᵢⱼ = 1/βᵛⱼᵢ
βᵀᵢⱼ = 1/βᵀⱼᵢ

If there is no data present, the parameters can be estimated:

• Linear estimation:

βᵛᵢⱼ = βᵛᵢⱼ = 1
γᵛᵢⱼ = 4*(Vcᵢ + Vcⱼ)/(∛Vcᵢ + ∛Vcⱼ)^3
γᵀᵢⱼ = 0.5*(Tcᵢ + Tcⱼ)/√(Tcᵢ*Tcⱼ)

• Lorentz-Berthelot Estimation:

βᵛᵢⱼ = βᵛᵢⱼ = γᵛᵢⱼ = γᵀᵢⱼ = 1

References

1. R. Klimeck, Ph.D. dissertation, Ruhr-Universit¨at Bochum, 2000

LorentzBerthelotMixing::AsymmetricMixing
LorentzBerthelotMixing(components;
userlocations = String[],
verbose = false)

Input parameters

• k: Pair Parameter (Float64) - binary interaction parameter for temperature (no units)
• l: Pair Parameter (Float64) - binary interaction parameter for volume (no units)

Description

Lorentz-Berthelot Mixing for MultiParameter EoS models:

τ = T̄/T
δ = V̄/V
V̄ = ∑xᵢxⱼ * Vᵣᵢⱼ * (1 - lᵢⱼ)
T̄ = ∑xᵢxⱼ * Tᵣᵢⱼ * (1 - kᵢⱼ)
Vᵣᵢⱼ = 0.125*(∛Vcᵢ + ∛Vcⱼ)^3
Tᵣᵢⱼ = √(Tcᵢ*Tcⱼ)

missing parameters will be assumed kᵢⱼ = lᵢⱼ = 0

EmpiricDeparture <: MultiFluidDepartureModel EmpiricDeparture(components; userlocations = String[], verbose = false)

Input parameters

none

• F: Pair Parameter (Float64) - binary interaction parameter (no units)
• parameters: Pair Parameter (String) - JSON data containing the departure terms for the binary pair

Description

Departure that uses empiric departure functions:

aᵣ = ∑xᵢaᵣᵢ(δ,τ) + Δa
Δa = ∑xᵢxⱼFᵢⱼaᵣᵢⱼ(δ,τ)

aᵣᵢⱼ = ∑nᵢⱼ₋ₖδ^(dᵢⱼ₋ₖ)*τ^(tᵢⱼ₋ₖ) +
    ∑nᵢⱼ₋ₖδ^(dᵢⱼ₋ₖ)τ^(tᵢⱼ₋ₖ)*exp(-gᵢⱼ₋ₖδ^lᵢⱼ₋ₖ) +
    ∑nᵢⱼ₋ₖδ^(dᵢⱼ₋ₖ)τ^(tᵢⱼ₋ₖ)*exp(ηᵢⱼ₋ₖ(δ-εᵢⱼ₋ₖ)^2 + βᵢⱼ₋ₖ(τ-γᵢⱼ₋ₖ)^2)

departure_functions(model::MultiFluid)

if the model is using a EmpiricDeparture departure model, return the matrix of departure functions. you can set a departure in the following way:

using CoolProp #load CoolProp models
model = MultiFluid(["helium","methanol"],mixing = LorentzBerthelotMixing)
dep_mat = departure_functions(model)

dep = Dict(
    #reduced CoolProp Departure format, you only need the type and parameters.
    #ResidualHelmholtzPower would work too.
    type => "Exponential",
    n => [1,1,1,1],
    t => [1,1,1,1],
    d => [1,1,1,1],
    l => [1,1,1,1],
)


dep_mat[1,2] = create_departure(dep,F)

#if you want to delete a departure model:

dep_mat[1,2] = nothing
using SparseArrays

create_departure(data,F = 1.0;verbose = false)

Creates a departure model for use in a MultiFluid model with EmpiricDeparture.

If data is a String and starts with { or [, it will be recognized as JSON text. the text will be parsed as a file location otherwise. You can pass a Dict or NamedTuple if you want to skip the JSON parsing.

Examples

d1 = create_departure("/data/EthanePropane.json",0.9) # reading from a file

dep = Dict(
    #reduced CoolProp Departure format, you only need the type and parameters.
    #ResidualHelmholtzPower would work too.
    :type => "Exponential",
    :n => [1,1,1,1],
    :t => [1,1,1,1],
    :d => [1,1,1,1],
    :l => [1,1,1,1],
)

d2 = create_departure(dep) #F is set to 1.0

GEDeparture <: MultiFluidDepartureModel GEDeparture(components; activity = UNIFAC, userlocations = String[], verbose = false)

Input parameters

none

• k1: Pair Parameter (Float64) - binary, T-dependent interaction parameter [K^-1]

Model parameters

• vref: Single Parameter (Float64, calculated) - Reference pure molar volume [m3/mol]

Input models

• activity: activity model

Description

Departure that uses the residual excess gibbs energy from an activity model:

aᵣ = ∑xᵢaᵣᵢ(δ,τ) + Δa
Δa = gᴱᵣ/RT - log(1+bρ)/log(1+bρref) * ∑xᵢ(aᵣᵢ(δref,τ) - aᵣᵢ(δrefᵢ,τᵢ))
τᵢ = Tcᵢ/T
δref = ρref/ρr
δrefᵢ = ρrefᵢ/ρcᵢ
b = 1/1.17ρref

References

1. Jäger, A., Breitkopf, C., & Richter, M. (2021). The representation of cross second virial coefficients by multifluid mixture models and other equations of state. Industrial & Engineering Chemistry Research, 60(25), 9286–9295. doi:10.1021/acs.iecr.1c01186

QuadraticDeparture <: MultiFluidDepartureModel
QuadraticDeparture(components;
userlocations = String[],
verbose = false)

Input parameters

• k0: Pair Parameter (Float64) - binary interaction parameter (no units)
• k1: Pair Parameter (Float64) - binary, T-dependent interaction parameter [K^-1]

Description

Departure that uses a quadratic mixing rule:

aᵣ = ∑xᵢxⱼaᵣᵢⱼ
aᵣᵢⱼ = 0.5*(aᵣᵢ + aᵣⱼ)*(1 - (k₀ + k₁T))

References

1. Jäger, A., Breitkopf, C., & Richter, M. (2021). The representation of cross second virial coefficients by multifluid mixture models and other equations of state. Industrial & Engineering Chemistry Research, 60(25), 9286–9295. doi:10.1021/acs.iecr.1c01186