type, public, extends(ArModel) :: CubicEoS

Cubic Equation of State.

Generic Cubic Equation of State as defined by Michelsen and Mollerup with a $\delta_1$ parameter that is not constant, and a $\delta_2$ parameter that depends on it. In the case of a two parameter EoS like PengRobinson the $\delta_1$ is the same for all components so it can be considered as a constant instead of a variable. The expression of the Equation is:

$P = \frac{RT}{V-B} - \frac{D(T_r)}{(V+B\Delta_1)(V+B\Delta_2)}$

Components

Type	Visibility	Attributes		Name
real(kind=pr),	public,	allocatable	::	ac(:)	Attractive critical parameter
class(AlphaFunction),	public,	allocatable	::	alpha	AlphaFunction derived type. Uses the abstract derived type `AlphaFunction` to define the Alpha function that the CubicEoS will use. The Alpha function receives the reduced temperature and returns the values of alpha and its derivatives, named `a`, `dadt` and `dadt2` respectively. Examples Callign the AlphaFunction of a setted up model. `use yaeos, only: CubicEoS, PengRobinson76 type(CubicEoS) :: eos eos = PengRobinson76(tc, pc, w) call eos%alpha%alpha(Tr, a, dadt, dadt2)`
real(kind=pr),	public,	allocatable	::	b(:)	Repulsive parameter
type(Substances),	public		::	components	Substances contained in the module
real(kind=pr),	public,	allocatable	::	del1(:)	$\delta_1$ paramter
real(kind=pr),	public,	allocatable	::	del2(:)	$\delta_2$ paramter
class(CubicMixRule),	public,	allocatable	::	mixrule	CubicMixRule derived type. Uses the abstract derived type `CubicMixRule` to define the mixing rule that the CubicEoS will use. It includes internally three methods to calculate the corresponding parameters for the Cubic EoS: `Dmix`, `Bmix` and `D1mix`. Examples Calculation of the B parameter. `use yaeos, only: CubicEoS, PengRobinson76 type(CubicEoS) :: eos eos = PengRobinson76(tc, pc, w) call eos%mixrule%Bmix(n, eos%b, B, dBi, dBij)` Calculation of the D parameter. use yaeos, only: CubicEoS, PengRobinson76 type(CubicEoS) :: eos eos = PengRobinson76(tc, pc, w) ! The mixing rule takes the `a` parameters of the components so ! they should be calculated externally call eos%alpha%alpha(Tr, a, dadt, dadt2) a = a * eos%ac dadt = dadt * eos%ac / eos%components%Tc dadt = dadt * eos%ac / eos%components%Tc**2 ! Calculate parameter call eos%mixrule%Dmix(n, T, a, dadt, dadt2, D, dDdT, dDdT2, dDi, dDidT, dDij) Calculation of the D1 parameter. `use yaeos, only: CubicEoS, PengRobinson76 type(CubicEoS) :: eos eos = PengRobinson76(tc, pc, w) call eos%mixrule%D1mix(n, eos%del1, D1, dD1i, dD1ij)`
character(len=:),	public,	allocatable	::	name	Name of the model

Type-Bound Procedures

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.

Arguments

Type	Intent		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_vt

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

Calculate residual heat capacity volume constant given V and T.

Arguments

Type	Intent		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	Intent		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_residual_vt

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

Calculate residual enthalpy given volume and temperature.

Arguments

Type	Intent	Optional		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	$\frac{dH^r}}{dV}$
real(kind=pr),	intent(out),	optional	::	HrT	$\frac{dH^r}}{dT}$
real(kind=pr),	intent(out),	optional	::	Hrn(size(n))	$\frac{dH^r}}{dn}$

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.

Arguments

Type	Intent	Optional		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	$\frac{dS^r}}{dV}$
real(kind=pr),	intent(out),	optional	::	SrT	$\frac{dS^r}}{dT}$
real(kind=pr),	intent(out),	optional	::	Srn(size(n))	$\frac{dS^r}}{dn}$

procedure, public :: get_v0 => v0

public function v0(self, n, p, t)

Cubic EoS volume initializer. For a Cubic Equation of State, the covolume calculated with the mixing rule is a good estimate for the initial volume solver on the liquid region.

Arguments

Type	Intent		Name
class(CubicEoS),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)
real(kind=pr),	intent(in)	::	p
real(kind=pr),	intent(in)	::	t

Return Value real(kind=pr)

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.

Arguments

Type	Intent	Optional		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	$\frac{dG^r}}{dV}$
real(kind=pr),	intent(out),	optional	::	GrT	$\frac{dG^r}}{dT}$
real(kind=pr),	intent(out),	optional	::	Grn(size(n))	$\frac{dG^r}}{dn}$

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.

Arguments

Type	Intent	Optional		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	$\frac{dU^r}}{dV}$
real(kind=pr),	intent(out),	optional	::	UrT	$\frac{dU^r}}{dT}$
real(kind=pr),	intent(out),	optional	::	Urn(size(n))	$\frac{dU^r}}{dn}$

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.

Arguments

Type	Intent	Optional		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))	$\ln(\f_i)$ vector
real(kind=pr),	intent(out),	optional	::	dlnfdV(size(n))	$ln(f_i)$ Volume derivative
real(kind=pr),	intent(out),	optional	::	dlnfdT(size(n))	$ln(f_i)$ Temp derivative
real(kind=pr),	intent(out),	optional	::	dlnfdn(size(n),size(n))	$ln(f_i)$ compositional derivative
real(kind=pr),	intent(out),	optional	::	dPdV	$\frac{dP}{dV}$
real(kind=pr),	intent(out),	optional	::	dPdT	$\frac{dP}{dT}$
real(kind=pr),	intent(out),	optional	::	dPdn(:)	$\frac{dP}{dn_i}$

procedure, public :: lnphi_pt

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

Calculate natural logarithm of fugacity given pressure and temperature.

Arguments

Type	Intent	Optional		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))	$\ln(phi)$ 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	$\frac{dP}{dV}$
real(kind=pr),	intent(out),	optional	::	dPdT	$\frac{dP}{dT}$
real(kind=pr),	intent(out),	optional	::	dPdn(size(n))	$\frac{dP}{dn_i}$

procedure, public :: lnphi_vt

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

Calculate natural logarithm of fugacity coefficent.

Arguments

Type	Intent	Optional		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))	$\ln(\phi_i)$ vector
real(kind=pr),	intent(out),	optional	::	dlnPhidP(size(n))	$ln(phi_i)$ Presssure derivative
real(kind=pr),	intent(out),	optional	::	dlnPhidT(size(n))	$ln(phi_i)$ Temp derivative
real(kind=pr),	intent(out),	optional	::	dlnPhidn(size(n),size(n))	$ln(phi_i)$ compositional derivative
real(kind=pr),	intent(out),	optional	::	dPdV	$\frac{dP}{dV}$
real(kind=pr),	intent(out),	optional	::	dPdT	$\frac{dP}{dT}$
real(kind=pr),	intent(out),	optional	::	dPdn(:)	$\frac{dP}{dn_i}$

procedure, public :: pressure

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

Calculate pressure.

Arguments

Type	Intent	Optional		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	$\frac{dP}}{dV}$
real(kind=pr),	intent(out),	optional	::	dPdT	$\frac{dP}}{dT}$
real(kind=pr),	intent(out),	optional	::	dPdn(:)	$\frac{dP}}{dn_i}$

procedure, public :: residual_helmholtz => GenericCubic_Ar

public subroutine GenericCubic_Ar(self, n, v, t, ar, arv, ArT, artv, arv2, ArT2, Arn, ArVn, ArTn, Arn2)

Residual Helmholtz Energy for a generic Cubic Equation of State.

Arguments

Type	Intent	Optional		Name
class(CubicEoS),	intent(in)		::	self
real(kind=pr),	intent(in)		::	n(:)	Number of moles
real(kind=pr),	intent(in)		::	v	Volume [L]
real(kind=pr),	intent(in)		::	t	Temperature [K]
real(kind=pr),	intent(out),	optional	::	ar	Residual Helmholtz
real(kind=pr),	intent(out),	optional	::	arv	$\frac{dAr}{dV}$
real(kind=pr),	intent(out),	optional	::	ArT	$\frac{dAr}{dT}$
real(kind=pr),	intent(out),	optional	::	artv	$\frac{d^2Ar}{dTdV}$
real(kind=pr),	intent(out),	optional	::	arv2	$\frac{d^2Ar}{dV^2}$
real(kind=pr),	intent(out),	optional	::	ArT2	$\frac{d^2Ar}{dT^2}$
real(kind=pr),	intent(out),	optional	::	Arn(size(n))	$\frac{dAr}{dn_i}$
real(kind=pr),	intent(out),	optional	::	ArVn(size(n))	$\frac{d^2Ar}{dVdn_i}$
real(kind=pr),	intent(out),	optional	::	ArTn(size(n))	$\frac{d^2Ar}{dTdn_i}$
real(kind=pr),	intent(out),	optional	::	Arn2(size(n),size(n))	$\frac{d^2Ar}{dn_{ij}}$

procedure, public :: set_delta1

public subroutine set_delta1(self, delta1)

Arguments

Type	Intent	Optional	Attributes		Name
class(CubicEoS)				::	self
real(kind=pr),	intent(in)			::	delta1(:)

procedure, public :: set_mixrule

public subroutine set_mixrule(self, mixrule)

Arguments

Type	Intent	Optional	Attributes		Name
class(CubicEoS),	intent(inout)			::	self
class(CubicMixRule),	intent(in)			::	mixrule

procedure, public :: volume

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

Volume solver optimized for Cubic Equations of State.

Arguments

Type	Intent		Name
class(CubicEoS),	intent(in)	::	eos
real(kind=pr),	intent(in)	::	n(:)
real(kind=pr),	intent(in)	::	P
real(kind=pr),	intent(in)	::	T
real(kind=pr),	intent(out)	::	V
character(len=*),	intent(in)	::	root_type

CubicEoS Derived Type

Contents

Variables

Type-Bound Procedures

type, public, extends(ArModel) :: CubicEoS

Cubic Equation of State.

Components

AlphaFunction derived type.

Examples

Callign the AlphaFunction of a setted up model.

CubicMixRule derived type.

Examples

Calculation of the B parameter.

Calculation of the D parameter.

Calculation of the D1 parameter.

Type-Bound Procedures

procedure, public :: Cp_residual_vt

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

Arguments

procedure, public :: Cv_residual_vt

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

Arguments

procedure, public :: Psat_pure

private function Psat_pure(eos, ncomp, T)

Arguments

Return Value real(kind=pr)

procedure, public :: enthalpy_residual_vt

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

Arguments

procedure, public :: entropy_residual_vt

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

Arguments

procedure, public :: get_v0 => v0

public function v0(self, n, p, t)

Arguments

Return Value real(kind=pr)

procedure, public :: gibbs_residual_vt

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

Arguments

procedure, public :: internal_energy_residual_vt

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

Arguments

procedure, public :: lnfug_vt

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

Arguments

procedure, public :: lnphi_pt

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

Arguments

procedure, public :: lnphi_vt

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

Arguments

procedure, public :: pressure

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

Arguments

procedure, public :: residual_helmholtz => GenericCubic_Ar

public subroutine GenericCubic_Ar(self, n, v, t, ar, arv, ArT, artv, arv2, ArT2, Arn, ArVn, ArTn, Arn2)

Arguments

procedure, public :: set_delta1

public subroutine set_delta1(self, delta1)

Arguments

procedure, public :: set_mixrule

public subroutine set_mixrule(self, mixrule)

Arguments

procedure, public :: volume

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

Arguments