ArModel – yaeos

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 $Ar$ residual_helmholtz and a volume initializer function, that is used to initialize a Newton solver of volume when specifying pressure.

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_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(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	Intent		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_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(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	Intent	Optional		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	$\frac{dAr}{dV}$
real(kind=pr),	intent(out),	optional	::	ArT	$\frac{dAr}{dT}$
real(kind=pr),	intent(out),	optional	::	ArTV	$\frac{d^2Ar}{dTV}$
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))	$\frac{d^2Ar}{dVn_i}$
real(kind=pr),	intent(out),	optional	::	ArTn(size(n))	$\frac{d^2Ar}{dTn_i}$
real(kind=pr),	intent(out),	optional	::	Arn2(size(n),size(n))	$\frac{d^2Ar}{dn_{ij}}$

procedure, public :: volume

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

Volume solver routine for residual Helmholtz models.

Arguments

Type	Intent		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"]`

ArModel Derived Type

Contents

Variables

Type-Bound Procedures

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

Components

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(abs_volume_initializer), public, deferred :: get_v0

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

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(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

Arguments

procedure, public :: volume

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

Arguments