Index
Clapeyron.JobackGCClapeyron.AlyLeeIdealClapeyron.BasicIdealClapeyron.CPLNGEstIdealClapeyron.GlennJLClapeyron.JobackIdealClapeyron.LJRefIdealClapeyron.MonomerIdealClapeyron.PPDSIdealClapeyron.ReidIdealClapeyron.ShomateIdealClapeyron.WalkerIdeal
Ideal Models
All Clapeyron.jl models can be separated between an ideal and a residual contribution. The ideal contribution can be obtained via integration of the ideal isobaric heat capacity:
$\frac{A_{\mathrm{ideal}}}{Nk_\mathrm{B}T} = \sum_{i=1}^{N_{\mathrm{Component}}} x_i\left[\ln{\frac{\rho_i}{\rho_0}} + \frac{1}{Nk_\mathrm{B}T} \int_{T_0}^T \!\!C_{p,i}^0 dT + \frac{H_{0,i}}{Nk_\mathrm{B}T}- \frac{1}{Nk_{B}}\!\!\int_{T_0}^T \frac{C_{p,i}^0}{T} dT -\ln{\frac{T}{T_0}}-\frac{S_{0,i}}{Nk_\mathrm{B}} - 1\right]$
Normally, EoS models contain an ideal model. This model can be accessed by using Clapeyron.idealmodel.
Clapeyron.BasicIdeal — Type
BasicIdeal <: IdealModel
BasicIdeal(components;
userlocations = String[],
reference_state = nothing,
verbose = false)Input parameters
None
Description
Default Ideal Model. Constant specific heat capacity equal to 5R/2. It's Helmholtz energy is equal to:
a₀ = A₀/nRT = ∑(xᵢlog(nxᵢ/V)) - 1 - 1.5log(T)Model Construction Examples
# Because this model does not have parameters, all those constructors are equivalent:
idealmodel = BasicIdeal()
idealmodel = BasicIdeal("water")
idealmodel = BasicIdeal(["water","carbon dioxide"])Clapeyron.ReidIdeal — Type
ReidIdeal <: IdealModel
ReidIdeal(components;
userlocations = String[],
reference_state = nothing,
verbose = false)Input parameters
a: Single Parameter (Float64) - polynomial coefficientb: Single Parameter (Float64) - polynomial coefficientc: Single Parameter (Float64) - polynomial coefficientd: Single Parameter (Float64) - polynomial coefficiente: Single Parameter (optional) (Float64) - polynomial coefficientMw: Single Parameter (Float64) (Optional) - Molecular Weight[g·mol⁻¹]
Model parameters
a: Single Parameter (Float64) - polynomial coefficientb: Single Parameter (Float64) - polynomial coefficientc: Single Parameter (Float64) - polynomial coefficientd: Single Parameter (Float64) - polynomial coefficiente: Single Parameter (optional) (Float64) - polynomial coefficient for 1/T^2coeffs: Single Parameter (NTuple{5,Float64})Mw: Single Parameter (Float64) (Optional) - Molecular Weight[g·mol⁻¹]
Description
Reid Ideal Model. Helmholtz energy obtained via integration of specific heat capacity:
Cpᵢ(T) = aᵢ + bᵢT + cᵢT^2 + dᵢT^3 + eᵢT^4
Cp(T) = ∑CpᵢxᵢModel Construction Examples
# Using the default database
idealmodel = ReidIdeal("water") #single input
idealmodel = ReidIdeal(["water","ethanol"]) #multiple components
# Using user-provided parameters
# Passing files or folders
idealmodel = ReidIdeal(["neon","hydrogen"]; userlocations = ["path/to/my/db","reid.csv"])
# Passing parameters directly
idealmodel = ReidIdeal(["water","butane"];
userlocations = (a = [32.24, 9.487],
b = [0.00192, 0.3313],
c = [1.06e-5, -0.0001108],
d = [-3.6e-9, -2.822e-9],
Mw = [18.01, 58.12])
) #e is not usedClapeyron.JobackIdeal — Type
JobackIdeal <: JobackIdealModel
JobackIdeal(components;
userlocations = String[],
reference_state = nothing,
verbose = false)Input parameters
Mw: Single Parameter (Float64) - Molecular Weight[g·mol⁻¹]N_a: Single Parameter (Float64)T_c: Single Parameter (Float64)P_c: Single Parameter (Float64)V_c: Single Parameter (Float64)T_b: Single Parameter (Float64)T_m: Single Parameter (Float64)H_form: Single Parameter (Float64)G_form: Single Parameter (Float64)a: Single Parameter (Float64)b: Single Parameter (Float64)c: Single Parameter (Float64)d: Single Parameter (Float64)H_fusion: Single Parameter (Float64)H_vap: Single Parameter (Float64)eta_a: Single Parameter (Float64)eta_b: Single Parameter (Float64)
Description
Joback Group Contribution Ideal Model. GC version of ReidIdeal. Helmholtz energy obtained via integration of specific heat capacity:
aᵢ = ∑(νᵢₖbₖ) - 37.93
bᵢ = ∑(νᵢₖbₖ) + 0.210
cᵢ = ∑(νᵢₖcₖ) - 3.91e-4
dᵢ = ∑(νᵢₖbₖ) + 2.06e-7
Cpᵢ(T) = aᵢ + bᵢT + cᵢT^2 + dᵢT^3The GC-averaged Reid Model is available by using ReidIdeal(model::JobackIdeal). The estimated critical point of a single component can be obtained via crit_pure(model::JobackIdeal)
Molecule fragmentation into functional groups is available in GCIdentifier.jl, using JobackGroups
References
- Joback, K. G., & Reid, R. C. (1987). Estimation of pure-component properties from group-contributions. Chemical Engineering Communications, 57(1–6), 233–243. doi:10.1080/00986448708960487
List of available groups
| Name | Description |
|---|---|
| -CH3 | Methyl |
| -CH2- | Methylene |
| >CH- | |
| >C< | |
| CH2=CH- | |
| -CH=CH- | |
| =C< | |
| =C= | |
| CH | |
| C | |
| ring-CH2- | Cyclic alkane |
| ring>CH- | |
| ring>C< | |
| ring=CH- | Aromatic group |
| ring=C< | |
| -F | Fluoride |
| -Cl | Chloride |
| -Br | Bromide |
| -I | Iodide |
| -OH (alcohol) | Hydroxyl group |
| -OH (phenol) | |
| -O- (non-ring) | |
| -O- (ring) | |
| >C=O (non-ring) | Ketone |
| >C=O (ring) | |
| O=CH- (aldehyde) | Aldehyde |
| -COOH (acid) | Carboxylic acid |
| -COO- (ester) | Ester |
| O (other than above) | Ketone |
| -NH2 | Amine |
| >NH (non-ring) | |
| >NH (ring) | |
| >N- (non-ring) | |
| -N= (non-ring) | |
| -N= (ring) | |
| =NH | |
| -CN | Nitrile |
| -NO3 | Nitroxide |
| -SH | |
| -S- (non-ring) | |
| -S- (ring) |
Clapeyron.MonomerIdeal — Type
MonomerIdeal <: MonomerIdealModel
MonomerIdeal(components;
userlocations = String[],
reference_state = nothing,
verbose = false)Input parameters
Mw: Single Parameter (Float64) - Molecular Weight[g·mol⁻¹]
Model Parameters
None
Description
Monomer Ideal Model, result obtained from statistical mechanics Λ
Λᵢ = h/√(kᵦTMwᵢ/Nₐ)
a₀ = A₀/nRT = ∑xᵢlog(ρᵢΛᵢ^3)Model Construction Examples
# Using the default database
idealmodel = MonomerIdeal("water") #single input
idealmodel = MonomerIdeal(["water","ethanol"]) #multiple components
# Using user-provided parameters
# Passing files or folders
idealmodel = MonomerIdeal(["neon","hydrogen"]; userlocations = ["path/to/my/db","mw.csv"])
# Passing parameters directly
idealmodel = MonomerIdeal(["neon","hydrogen"];userlocations = (;Mw = [20.17, 2.]))Clapeyron.WalkerIdeal — Type
WalkerIdeal <: WalkerIdealModel
WalkerIdeal(components;
userlocations = String[],
group_userlocations = String[]
verbose = false)Input parameters
Mw: Single Parameter (Float64) - Molecular Weight[g·mol⁻¹]Nrot: Single Parameter (Int)theta1: Single Parameter (Float64)theta2: Single Parameter (Float64)theta3: Single Parameter (Float64)theta4: Single Parameter (Float64)deg1: Single Parameter (Int)deg2: Single Parameter (Int)deg3: Single Parameter (Int)deg4: Single Parameter (Int)
Description
Walker [1] Group Contribution Ideal Model.
Cpᵢ(T)/R = (5+NRot)/2 ∑νᵢₖ∑gₖᵥ(θₖᵥ/T)^2*exp(θₖᵥ/T)/(1-exp(θₖᵥ/T)) , v ∈ 1:4 Molecule fragmentation into functional groups is available in GCIdentifier.jl, using WalkerGroups
References
- Walker, P. J., & Haslam, A. J. (2020). A new predictive group-contribution ideal-heat-capacity model and its influence on second-derivative properties calculated using a free-energy equation of state. Journal of Chemical and Engineering Data, 65(12), 5809–5829. doi:10.1021/acs.jced.0c00723
Clapeyron.LJRefIdeal — Type
LJRefIdeal <: IdealModel
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⁻¹]
Description
Lennard-Jones Reference equation of state. Ideal Part. Valid from 0.5 < T/Tc < 7 and pressures up to p/pc = 500.
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))
LJRefIdeal acts as a wrapper of LJRef model, you can access it with LJRef(model::LJRefIdeal).
The original model was done with only one component in mind. To support multiple components, a VDW 1-fluid mixing rule (shown above) is implemented, but it is not tested.
References
- 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
Clapeyron.AlyLeeIdeal — Type
AlyLeeIdeal <: AlyLeeIdealModel
AlyLeeIdeal(components;
userlocations = String[],
reference_state = nothing,
verbose = false)Input parameters
A: Single Parameter (Float64) - Model CoefficientB: Single Parameter (Float64) - Model CoefficientC: Single Parameter (Float64) - Model CoefficientD: Single Parameter (Float64) - Model CoefficientE: Single Parameter (Float64) - Model CoefficientF: Single Parameter (Float64) - Model CoefficientG: Single Parameter (Float64) - Model CoefficientH: Single Parameter (Float64) - Model CoefficientI: Single Parameter (Float64) - Model CoefficientMw: Single Parameter (Float64) (Optional) - Molecular Weight[g·mol⁻¹]
Description
Aly-Lee Ideal Model (extended):
Cpᵢ(T)/R = A + B(CT⁻¹/sinh(CT⁻¹))² + D(ET⁻¹/cosh(ET⁻¹))² + F(GT⁻¹/sinh(GT⁻¹))² + H(IT⁻¹/cosh(IT⁻¹))²Model Construction Examples
# Using the default database
idealmodel = AlyLeeIdeal("water") #single input
idealmodel = AlyLeeIdeal(["water","ethanol"]) #multiple components
# Using user-provided parameters
# Passing files or folders
idealmodel = AlyLeeIdeal(["neon","hydrogen"]; userlocations = ["path/to/my/db","alylee.csv"])
# Passing parameters directly
idealmodel = AlyLeeIdeal(["water","carbon dioxide"];
userlocations = (A = [4.004, 3.5],
B = [0.01, 2.044],
C = [268.8, 919.3],
D = [0.99, -1.06],
E = [1141.4, -865.1],
F = [3.07, 2.034],
G = [2507.37, 483.55],
H = [0.0, 0.0139],
I = [0.0, 341.11])
)References
- Aly, F. A., & Lee, L. L. (1981). Self-consistent equations for calculating the ideal gas heat capacity, enthalpy, and entropy. Fluid Phase Equilibria, 6(3–4), 169–179. doi:10.1016/0378-3812(81)85002-9
Clapeyron.PPDSIdeal — Type
PPDSIdeal <: PPDSIdealModel
PPDSIdeal(components;
userlocations = String[],
reference_state = nothing,
verbose = false)Input parameters
A: Single Parameter (Float64) - Model CoefficientB: Single Parameter (Float64) - Model CoefficientC: Single Parameter (Float64) - Model CoefficientD: Single Parameter (Float64) - Model CoefficientE: Single Parameter (Float64) - Model CoefficientF: Single Parameter (Float64) - Model CoefficientG: Single Parameter (Float64) - Model CoefficientMw: Single Parameter (Float64) (Optional) - Molecular Weight[g·mol⁻¹]
Description
PPDS Ideal Model:
Cpᵢ(T)/R = B + (C - B)y²[1 + (y − 1)(D + Ey + Fy² + Gy³)]
y = T/(A + T)Model Construction Examples
# Using the default database
idealmodel = PPDSIdeal("water") #single input
idealmodel = PPDSIdeal(["water","ethanol"]) #multiple components
# Using user-provided parameters
# Passing files or folders
idealmodel = PPDSIdeal(["neon","hydrogen"]; userlocations = ["path/to/my/db","alylee.csv"])
# Passing parameters directly
idealmodel = PPDSIdeal(["water","carbon dioxide"];
userlocations = (A = [4.004, 3.5],
B = [0.01, 2.044],
C = [268.8, 919.3],
D = [0.99, -1.06],
E = [1141.4, -865.1],
F = [3.07, 2.034],
G = [2507.37, 483.55],
H = [0.0, 0.0139],
I = [0.0, 341.11])
)References
- Gmehling, J., Kleiber, M., Kolbe, B., & Rarey, J. (2019). Chemical thermodynamics for process simulation (2nd ed.). Berlin, Germany: Blackwell Verlag.
Clapeyron.ShomateIdeal — Type
ShomateIdeal <: ShomateIdealModel
ShomateIdeal(components;
userlocations = String[],
reference_state = nothing,
verbose = false)Input parameters
a: Single Parameter (Float64) - polynomial coefficientb: Single Parameter (Float64) - polynomial coefficientc: Single Parameter (Float64) - polynomial coefficientd: Single Parameter (Float64) - polynomial coefficiente: Single Parameter (optional) (Float64) - polynomial coefficient for 1/T^2Mw: Single Parameter (Float64) (Optional) - Molecular Weight[g·mol⁻¹]
Model parameters
a: Single Parameter (Float64) - polynomial coefficientb: Single Parameter (Float64) - polynomial coefficientc: Single Parameter (Float64) - polynomial coefficientd: Single Parameter (Float64) - polynomial coefficiente: Single Parameter (optional) (Float64) - polynomial coefficient for 1/T^2coeffs: Single Parameter (NTuple{5,Float64})Mw: Single Parameter (Float64) (Optional) - Molecular Weight[g·mol⁻¹]
Description
Shomate Ideal Model. Helmholtz energy obtained via integration of specific heat capacity:
Cpᵢ(T) = aᵢ + bᵢT + cᵢT^2 + dᵢT^3 + eᵢT^-2
Cp(T) = ∑CpᵢxᵢModel Construction Examples
# Using the default database
idealmodel = ShomateIdeal("water") #single input
idealmodel = ShomateIdeal(["water","ethanol"]) #multiple components
# Using user-provided parameters
# Passing files or folders
idealmodel = ShomateIdeal(["neon","hydrogen"]; userlocations = ["path/to/my/db","shomate.csv"])
# Passing parameters directly
idealmodel = ShomateIdeal(["water","butane"];
userlocations = (a = [32.24, 9.487],
b = [0.00192, 0.3313],
c = [1.06e-5, -0.0001108],
d = [-3.6e-9, -2.822e-9],
Mw = [18.01, 58.12])
) #e is not usedClapeyron.CPLNGEstIdeal — Type
CPLNGEstIdeal <: ReidIdealModel
CPLNGEstIdeal(components;
userlocations = String[],
reference_state = nothing,
verbose = false)Input parameters
Mw: Single Parameter (Float64) - Molecular Weight[g·mol⁻¹]
Model parameters
Mw: Single Parameter (Float64) - Molecular Weight[g·mol⁻¹]coeffs: Single Parameter (NTuple{5,Float64}) - polynomial coefficients
Description
Estimation of Reid polynomial, using the molecular weight as input:
Cpᵢ(T) = aᵢ + bᵢT + cᵢT^2 + dᵢT^3
Cp(T) = ∑Cpᵢxᵢ
a = -10.9602 * γ₀ + 25.9033
b = 2.1517e-1 * γ₀ - 6.8687e-2
c = -1.3337e-4 * γ₀ + 8.6387e-5
d = 3.1474e-8 * γ₀ -2.8396e-8
γ₀ = Mw/Mw(air)Model Construction Examples
# Using the default database
idealmodel = CPLNGEstIdeal("water") #single input
idealmodel = CPLNGEstIdeal(["water","ethanol"]) #multiple components
# Using user-provided parameters
# Passing files or folders
idealmodel = CPLNGEstIdeal(["neon","hydrogen"]; userlocations = ["path/to/my/db","mw.csv"])
# Passing parameters directly
idealmodel = CPLNGEstIdeal(["neon","hydrogen"];userlocations = (;Mw = [20.17, 2.]))References
- Kareem, L. A., Iwalewa, T. M., & Omeke, J. E. (2014). Isobaric specific heat capacity of natural gas as a function of specific gravity, pressure and temperature. Journal of Natural Gas Science and Engineering, 19, 74–83. doi:10.1016/j.jngse.2014.04.011
Clapeyron.GlennJL — Type
GlennJL <: IdealModel
GlennJL(calc::Union{Glenn.Calculator,Glenn.ThermoDB}, input;
Rgas = Clapeyron.Rgas(),
R0 = 8.314510,
reference_state = nothing,
verbose = false,
strict = true)Input arguments
calc: a database of Glenn.jl parametersinput: input species, it can be strings, integers (ID of the database),Glenn.SpeciesInfoor a vector of those elements.Rgas: molar gas constant used by the model.R0: molar gas constant used in the fitting of each species. by default it used the original R constant used in the fitting of NASA-7 polynomials.reference_state: if a change of reference state is needed.verbose: if set totrue, displays additional information to the REPL.strict: if set totrue, check if all components have the same phase and if their temperature ranges do not intersect
Description
Ideal model using the NASA-7 polynomial coefficients provided by the Glenn.jl package. the polynomials are standarized to fit specific values of enthalpy and entropy at 1 bar, 298.15K.
Clapeyron.GlennJL requires the package Glenn.jl to be loaded in the enviroment.
Model Construction Examples
# Using the default database
calc = Calculator()
# Using a string
idealmodel = GlennJL(calc,"o2")
# Using the ID of O2 in the default database
idealmodel = GlennJL(calc,931)
# Using a SpeciesInfo to search the database
o2 = only(get_available_species(calc, "O2", exact_match = true))
idealmodel = GlennJL(calc,o2)
# Multiple components, any of the types above can be used instead of strings
idealmodel = GlennJL(calc,["o2","n2"])Glenn.jl integrations
the model GlennJL has the following integrations with Glenn.jl package:
Glenn.calculate_h(model::GlennJL,T,z = [1.0])Glenn.calculate_s(model::GlennJL,T,z = [1.0])Glenn.calculate_cp(model::GlennJL,T,z = [1.0])Glenn.calculate_formation_enthalpy(model::GlennJL,T,z = [1.0])Glenn.calculate_enthalpy_change(model::GlennJL,T1,T2,z = [1.0])Glenn.calculate_properties(model::GlennJL,T,z = [1.0])Glenn.get_properties_range(model::GlennJL,T,z = [1.0])
get_properties and get_properties_range will return NaN for properties outside their ranges. in particular, get_properties_range will return a vector of the same size as the input, with NaN on invalid inputs.
References
- NASA TP-2002-211556, “NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species,” by B.J. McBride, M.J. Zehe, and S. Gordon. September 2002.
Joback GC Utilities
Clapeyron.JobackGC — Module
JobackGCModule containing group contribution calculations using the joback method. The available functions are:
JobackGC.T_c(model::JobackModel): critical temperature (in[K])JobackGC.P_c(model::JobackModel): critical pressure (in[Pa])JobackGC.V_c(model::JobackModel): critical volume (in[m³·mol⁻¹])JobackGC.T_b(model::JobackModel): normal boiling point (in[K])JobackGC.H_form(model::JobackModel): enthalpy of formation at 298 K, ideal gas (in[J·mol⁻¹])JobackGC.G_form(model::JobackModel): Gibbs energy of formation at 298 K, ideal gas (in[J·mol⁻¹])JobackGC.S_form(model::JobackModel): entropy of formation at 298 K, ideal gas (in[J·mol⁻¹·K⁻¹])JobackGC.H_fusion(model::JobackModel): enthalpy of fusion (in[J·mol⁻¹], at 1 atm)JobackGC.H_vap(model::JobackModel): molar enthalpy of vaporization (in[J·mol⁻¹], at normal boiling point)JobackGC.C_p(model::JobackModel, T): ideal gas isobaric heat capacity (in[J·mol⁻¹·K⁻¹])JobackGC.Visc(model::JobackModel, T): liquid dynamic viscocity (in[Pa·s])