ArModel Derived Type

type, public, abstract, extends(BaseModel) :: ArModel

Abstract residual Helmholtz model.

This derived type defines the basics needed for the calculation of residual properties. The basics of a residual Helmholtz model is a routine that calculates all the needed derivatives of residual_helmholtz and a volume initializer function, that is used to initialize a Newton solver of volume when specifying pressure.


Inherits

type~~armodel~~InheritsGraph type~armodel ArModel type~basemodel BaseModel type~armodel->type~basemodel type~substances Substances type~basemodel->type~substances components

Inherited by

type~~armodel~~InheritedByGraph type~armodel ArModel type~armodeladiff ArModelAdiff type~armodeladiff->type~armodel type~armodeltapenade ArModelTapenade type~armodeltapenade->type~armodel type~cubiceos CubicEoS type~cubiceos->type~armodel type~gerg2008 Gerg2008 type~gerg2008->type~armodeladiff type~gerg2008->type~cubiceos srk type~pcsaft PcSaft type~pcsaft->type~armodeladiff

Components

Type Visibility Attributes Name Initial
type(Substances), public :: components

Substances contained in the module
character(len=:), public, allocatable :: name

Name of the model

Type-Bound Procedures

procedure, public :: Cp_residual_pt

  • private subroutine Cp_residual_pt(eos, n, P, T, root_type, Cp)

    Calculate residual heat capacity at constant pressure given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out) :: Cp

    Residual heat capacity at constant pressure [bar L K^-1]

procedure, public :: Cp_residual_vt

  • private subroutine Cp_residual_vt(eos, n, V, T, Cp)

    Calculate residual heat capacity pressure constant given V and T.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: V

    Volume [L]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out) :: Cp

    heat capacity P constant [bar L / K]

procedure, public :: Cv_residual_pt

  • private subroutine Cv_residual_pt(eos, n, P, T, root_type, Cv)

    Calculate residual heat capacity at constant volume given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out) :: Cv

    Residual heat capacity at constant volume [bar L K^-1]

procedure, public :: Cv_residual_vt

  • private subroutine Cv_residual_vt(eos, n, V, T, Cv)

    Calculate residual heat capacity volume constant given V and T.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: V

    Volume [L]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out) :: Cv

    heat capacity V constant [bar L / K]

procedure, public :: Psat_pure

  • private function Psat_pure(eos, ncomp, T)

    Calculation of saturation pressure of a pure component using the secant method.

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model that will be used
    integer, intent(in) :: ncomp

    Number of component in the mixture from which the saturation pressure will be calculated
    real(kind=pr), intent(in) :: T

    Temperature [K]

    Return Value real(kind=pr)

procedure, public :: enthalpy_excess

  • private subroutine enthalpy_excess(eos, n, P, T, root_type, He)

    Calculate excess enthalpy given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out) :: He

    Excess enthalpy [bar L]

procedure, public :: enthalpy_residual_pt

  • private subroutine enthalpy_residual_pt(eos, n, P, T, root_type, Hr, HrP, HrT, Hrn)

    Calculate residual enthalpy given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out), optional :: Hr

    Residual enthalpy [bar L]
    real(kind=pr), intent(out), optional :: HrP

    real(kind=pr), intent(out), optional :: HrT

    real(kind=pr), intent(out), optional :: Hrn(size(n))

procedure, public :: enthalpy_residual_vt

  • private subroutine enthalpy_residual_vt(eos, n, V, T, Hr, HrV, HrT, Hrn)

    Calculate residual enthalpy given volume and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: V

    Volume [L]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out), optional :: Hr

    Residual enthalpy [bar L]
    real(kind=pr), intent(out), optional :: HrV

    real(kind=pr), intent(out), optional :: HrT

    real(kind=pr), intent(out), optional :: Hrn(size(n))

procedure, public :: entropy_excess

  • private subroutine entropy_excess(eos, n, P, T, root_type, Se)

    Calculate excess entropy given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out) :: Se

    Excess entropy [bar L K^-1]

procedure, public :: entropy_residual_pt

  • private subroutine entropy_residual_pt(eos, n, P, T, root_type, Sr, SrP, SrT, Srn)

    Calculate residual entropy given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out), optional :: Sr

    Residual entropy [bar L K^-1]
    real(kind=pr), intent(out), optional :: SrP

    real(kind=pr), intent(out), optional :: SrT

    real(kind=pr), intent(out), optional :: Srn(size(n))

procedure, public :: entropy_residual_vt

  • private subroutine entropy_residual_vt(eos, n, V, T, Sr, SrV, SrT, Srn)

    Calculate residual entropy given volume and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: V

    Volume [L]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out), optional :: Sr

    Entropy [bar L / K]
    real(kind=pr), intent(out), optional :: SrV

    real(kind=pr), intent(out), optional :: SrT

    real(kind=pr), intent(out), optional :: Srn(size(n))

procedure(abs_volume_initializer), public, deferred :: get_v0

  • function abs_volume_initializer(self, n, p, t) Prototype

    Function that provides an initializer value for the liquid-root of newton solver of volume. In the case the model will use the volume_michelsen routine this value should provide the co-volume of the model.

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: self

    Ar Model
    real(kind=pr), intent(in) :: n(:)

    Moles vector
    real(kind=pr), intent(in) :: p

    Pressure [bar]
    real(kind=pr), intent(in) :: t

    Temperature [K]

    Return Value real(kind=pr)

    Initial volume [L]

procedure, public :: gibbs_excess

  • private subroutine gibbs_excess(eos, n, P, T, root_type, Ge, GeP, GeT, Gen)

    Calculate excess Gibbs energy and its derivatives given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out), optional :: Ge

    Excess Gibbs energy [bar L]
    real(kind=pr), intent(out), optional :: GeP

    real(kind=pr), intent(out), optional :: GeT

    real(kind=pr), intent(out), optional :: Gen(size(n))

procedure, public :: gibbs_residual_pt

  • private subroutine gibbs_residual_pt(eos, n, P, T, root_type, Gr, GrP, GrT, Grn)

    Calculate residual Gibbs energy given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out), optional :: Gr

    Residual Gibbs energy [bar L]
    real(kind=pr), intent(out), optional :: GrP

    real(kind=pr), intent(out), optional :: GrT

    real(kind=pr), intent(out), optional :: Grn(size(n))

procedure, public :: gibbs_residual_vt

  • private subroutine gibbs_residual_vt(eos, n, V, T, Gr, GrV, GrT, Grn)

    Calculate residual Gibbs energy given volume and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: V

    Volume [L]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out), optional :: Gr

    Gibbs energy [bar L]
    real(kind=pr), intent(out), optional :: GrV

    real(kind=pr), intent(out), optional :: GrT

    real(kind=pr), intent(out), optional :: Grn(size(n))

procedure, public :: helmholtz_excess

  • private subroutine helmholtz_excess(eos, n, P, T, root_type, Ae)

    Calculate excess Helmholtz energy given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out) :: Ae

    Excess Helmholtz energy [bar L]

procedure, public :: helmholtz_residual_pt

  • private subroutine helmholtz_residual_pt(eos, n, P, T, root_type, Ar, ArP, ArT, Arn)

    Calculate residual Helmholtz energy given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out), optional :: Ar

    Residual Helmholtz energy [bar L]
    real(kind=pr), intent(out), optional :: ArP

    real(kind=pr), intent(out), optional :: ArT

    real(kind=pr), intent(out), optional :: Arn(size(n))

procedure, public :: internal_energy_excess

  • private subroutine internal_energy_excess(eos, n, P, T, root_type, Ue)

    Calculate excess internal energy given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out) :: Ue

    Excess internal energy [bar L]

procedure, public :: internal_energy_residual_pt

  • private subroutine internal_energy_residual_pt(eos, n, P, T, root_type, Ur, UrP, UrT, Urn)

    Calculate residual internal energy given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out), optional :: Ur

    Residual internal energy [bar L]
    real(kind=pr), intent(out), optional :: UrP

    real(kind=pr), intent(out), optional :: UrT

    real(kind=pr), intent(out), optional :: Urn(size(n))

procedure, public :: internal_energy_residual_vt

  • private subroutine internal_energy_residual_vt(eos, n, V, T, Ur, UrV, UrT, Urn)

    Calculate residual internal energy given volume and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: V

    Volume [L]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out), optional :: Ur

    Internal energy [bar L]
    real(kind=pr), intent(out), optional :: UrV

    real(kind=pr), intent(out), optional :: UrT

    real(kind=pr), intent(out), optional :: Urn(size(n))

procedure, public :: ln_activity_coefficient

  • private subroutine ln_activity_coefficient(eos, n, P, T, root_type, lngamma, dlngammadP, dlngammadT, dlngammadn)

    Calculate natural logarithm of activity coefficients and its derivatives given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out), optional :: lngamma(size(n))

    Natural logarithm of activity coefficient
    real(kind=pr), intent(out), optional :: dlngammadP(size(n))

    real(kind=pr), intent(out), optional :: dlngammadT(size(n))

    real(kind=pr), intent(out), optional :: dlngammadn(size(n),size(n))

procedure, public :: lnfug_vt

  • private subroutine lnfug_vt(eos, n, V, T, P, lnf, dlnfdV, dlnfdT, dlnfdn, dPdV, dPdT, dPdn)

    Calculate natural logarithm of fugacity given volume and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Mixture mole numbers
    real(kind=pr), intent(in) :: V

    Volume [L]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out), optional :: P

    Pressure [bar]
    real(kind=pr), intent(out), optional :: lnf(size(n))

    vector
    real(kind=pr), intent(out), optional :: dlnfdV(size(n))

    Volume derivative
    real(kind=pr), intent(out), optional :: dlnfdT(size(n))

    Temp derivative
    real(kind=pr), intent(out), optional :: dlnfdn(size(n),size(n))

    compositional derivative
    real(kind=pr), intent(out), optional :: dPdV

    real(kind=pr), intent(out), optional :: dPdT

    real(kind=pr), intent(out), optional :: dPdn(:)

procedure, public :: lnphi_pt

  • private subroutine lnphi_pt(eos, n, P, T, V, root_type, lnPhi, dlnPhidP, dlnPhidT, dlnPhidn, dPdV, dPdT, dPdn, lnPhiP)

    Calculate natural logarithm of fugacity given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Mixture mole numbers
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out), optional :: V

    Volume [L]
    character(len=*), intent(in) :: root_type

    Type of root desired [“liquid”, “vapor”, “stable”]
    real(kind=pr), intent(out), optional :: lnPhi(size(n))

    vector
    real(kind=pr), intent(out), optional :: dlnPhidP(size(n))

    ln(phi) Presssure derivative
    real(kind=pr), intent(out), optional :: dlnPhidT(size(n))

    ln(phi) Temperature derivative
    real(kind=pr), intent(out), optional :: dlnPhidn(size(n),size(n))

    ln(phi) compositional derivative
    real(kind=pr), intent(out), optional :: dPdV

    real(kind=pr), intent(out), optional :: dPdT

    real(kind=pr), intent(out), optional :: dPdn(size(n))

    real(kind=pr), intent(out), optional :: lnPhiP(:)

    . It is useful to calculate fugacity coefficients at negatives pressures.

procedure, public :: lnphi_vt

  • private subroutine lnphi_vt(eos, n, V, T, P, lnPhi, dlnPhidP, dlnPhidT, dlnPhidn, dPdV, dPdT, dPdn, lnPhiP)

    Calculate natural logarithm of fugacity coefficent.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Mixture mole numbers
    real(kind=pr), intent(in) :: V

    Volume [L]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out), optional :: P

    Pressure [bar]
    real(kind=pr), intent(out), optional :: lnPhi(size(n))

    vector
    real(kind=pr), intent(out), optional :: dlnPhidP(size(n))

    Presssure derivative
    real(kind=pr), intent(out), optional :: dlnPhidT(size(n))

    Temp derivative
    real(kind=pr), intent(out), optional :: dlnPhidn(size(n),size(n))

    compositional derivative
    real(kind=pr), intent(out), optional :: dPdV

    real(kind=pr), intent(out), optional :: dPdT

    real(kind=pr), intent(out), optional :: dPdn(:)

    real(kind=pr), intent(out), optional :: lnPhiP(:)

    . It is useful to calculate fugacity coefficients at negatives pressures.

procedure, public :: pressure

  • private subroutine pressure(eos, n, V, T, P, dPdV, dPdT, dPdn)

    Calculate pressure.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: V

    Volume [L]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out) :: P

    Pressure [bar]
    real(kind=pr), intent(out), optional :: dPdV

    real(kind=pr), intent(out), optional :: dPdT

    real(kind=pr), intent(out), optional :: dPdn(:)

procedure(abs_residual_helmholtz), public, deferred :: residual_helmholtz

  • subroutine abs_residual_helmholtz(self, n, v, t, Ar, ArV, ArT, ArTV, ArV2, ArT2, Arn, ArVn, ArTn, Arn2) Prototype

    Residual Helmholtz model generic interface.

    This interface represents how an Ar model should be implemented. By our standard, a Resiudal Helmholtz model takes as input:

    • The mixture’s number of moles vector.
    • Volume, by default in liters.
    • Temperature, by default in Kelvin.

    All the output arguments are optional. While this keeps a long signature for the implementation, this is done this way to take advantage of any inner optimizations to calculate derivatives inside the procedure.

    Once the model is implemented, the signature can be short like model%residual_helmholtz(n, v, t, ArT2=dArdT2)

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: self

    ArModel
    real(kind=pr), intent(in) :: n(:)

    Moles vector
    real(kind=pr), intent(in) :: v

    Volume [L]
    real(kind=pr), intent(in) :: t

    Temperature [K]
    real(kind=pr), intent(out), optional :: Ar

    Residual Helmoltz energy
    real(kind=pr), intent(out), optional :: ArV

    real(kind=pr), intent(out), optional :: ArT

    real(kind=pr), intent(out), optional :: ArTV

    real(kind=pr), intent(out), optional :: ArV2

    real(kind=pr), intent(out), optional :: ArT2

    real(kind=pr), intent(out), optional :: Arn(size(n))

    real(kind=pr), intent(out), optional :: ArVn(size(n))

    real(kind=pr), intent(out), optional :: ArTn(size(n))

    real(kind=pr), intent(out), optional :: Arn2(size(n),size(n))

procedure, public :: volume

  • public subroutine volume(eos, n, P, T, V, root_type)

    Volume solver routine for residual Helmholtz models.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    real(kind=pr), intent(out) :: V

    Volume [L]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]

procedure, public :: volume_excess

  • private subroutine volume_excess(eos, n, P, T, root_type, Ve)

    Calculate excess volume given pressure and temperature.

    Read more…

    Arguments

    Type IntentOptional Attributes Name
    class(ArModel), intent(in) :: eos

    Model
    real(kind=pr), intent(in) :: n(:)

    Moles number vector
    real(kind=pr), intent(in) :: P

    Pressure [bar]
    real(kind=pr), intent(in) :: T

    Temperature [K]
    character(len=*), intent(in) :: root_type

    Desired root-type to solve. Options are: ["liquid", "vapor", "stable"]
    real(kind=pr), intent(out) :: Ve

    Excess volume [L]