Huron-Vidal (like) mixing rules module

This module contains the mixing rules that are based/similar to the mixing rules defined by Huron-Vidal

Description

Huron-Vidal presented a way to link a $G^E$ model with a Cubic EoS mixing rule. This makes it possible to make good predictions on polar compounds containing mixtures.

Examples

 A basic code example

References

Uses

Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Used by

Help

Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Interfaces

public interface HV_NRTL

public function init_hvnrtl(b, del1, alpha, gji0, gjiT, use_kij, kij) result(mixrule)

Huron-Vidal NRTL mixing rule

This is the Huron-Vidal mixing rule that includes the NRTL model modified by Huron and Vidal.

Description

This is the Huron-Vidal mixing rule that includes the NRTL model modified by Huron and Vidal. It is a mixing rule that allows to use the NRTL model as an excess Gibbs energy model and can. be simplified to the classic Quatratic mixing rules when the parameters are set to: $\alpha_{ji} = 0$

$g_{ii} = -\frac{a_i}{b_i} \lambda$

$g_{ji} = -2\frac{\sqrt{b_i b_j}}{b_i + b_j} \sqrt{g_{ii}g_{jj}} \left(1 - k_{ij})\right)$

Examples

Arguments

Type	Intent		Name
real(kind=pr),	intent(in)	::	b(:)
real(kind=pr),	intent(in)	::	del1(:)
real(kind=pr),	intent(in)	::	alpha(:,:)
real(kind=pr),	intent(in)	::	gji0(:,:)
real(kind=pr),	intent(in)	::	gjiT(:,:)
logical,	intent(in)	::	use_kij(:,:)
real(kind=pr),	intent(in)	::	kij(:,:)

Return Value type(HV_NRTL)

public interface MHV

private function init_mhv(Ge, b, q, lij) result(mixrule)

Arguments

Type	Intent	Optional		Name
class(GeModel),	intent(in)		::	Ge
real(kind=pr),	intent(in)		::	b(:)
real(kind=pr),	intent(in)		::	q
real(kind=pr),	intent(in),	optional	::	lij(:,:)

Return Value type(MHV)

Derived Types

type, public, extends(CubicMixRule) :: HV

Components

Type	Visibility	Attributes		Name		Initial
real(kind=pr),	public,	allocatable	::	bi(:)
real(kind=pr),	public,	allocatable	::	del1(:)
logical,	public		::	dn2	=	.false.	Calculate second order derivatives
class(GeModel),	public,	allocatable	::	ge
logical,	public		::	is_D_ddlc	=	.false.	Mixing rule D parameter dependant on density

Type-Bound Procedures

procedure, public :: Bmix => BmixHV
procedure, public :: D1Mix => D1MixHV
procedure, public :: Dmix => DmixHV

type, public, extends(CubicMixRule) :: HV_NRTL

Huron-Vidal mixing rule including the NRTL model modified by Huron and Vidal.

Components

Type	Visibility	Attributes		Name		Initial
real(kind=pr),	public,	allocatable	::	bi(:)
real(kind=pr),	public,	allocatable	::	del1(:)
logical,	public		::	dn2	=	.false.	Calculate second order derivatives
type(NRTLHV),	public		::	ge
logical,	public		::	is_D_ddlc	=	.false.	Mixing rule D parameter dependant on density
real(kind=pr),	public,	allocatable	::	kij(:,:)
logical,	public,	allocatable	::	use_kij(:,:)

Constructor

public function init_hvnrtl (b, del1, alpha, gji0, gjiT, use_kij, kij)	This is the Huron-Vidal mixing rule that includes the NRTL model modified by Huron and Vidal. Read more…

Type-Bound Procedures

procedure, public :: Bmix => BmixHVNRTL
procedure, public :: D1Mix => D1MixHVNRTL
procedure, public :: Dmix => DmixHVNRTL

type, public, extends(CubicMixRule) :: MHV

Mixing rule at zero-pressure which allows for the inclusion of an excess-gibbs model.

Components

Type	Visibility	Attributes		Name		Initial
logical,	public		::	dn2	=	.false.	Calculate second order derivatives
class(GeModel),	public,	allocatable	::	ge
logical,	public		::	is_D_ddlc	=	.false.	Mixing rule D parameter dependant on density
real(kind=pr),	public,	allocatable	::	l(:,:)
real(kind=pr),	public		::	q
real(kind=pr),	private,	allocatable	::	B
real(kind=pr),	private,	allocatable	::	bi(:)
real(kind=pr),	private,	allocatable	::	dBi(:)
real(kind=pr),	private,	allocatable	::	dBij(:,:)

Constructor

private function init_mhv (Ge, b, q, lij)

Type-Bound Procedures

procedure, public :: Bmix => BmixMHV
procedure, public :: D1Mix => D1MixMHV
procedure, public :: Dmix => DmixMHV

Functions

public function init_hvnrtl(b, del1, alpha, gji0, gjiT, use_kij, kij) result(mixrule)

This is the Huron-Vidal mixing rule that includes the NRTL model modified by Huron and Vidal.

Arguments

Type	Intent		Name
real(kind=pr),	intent(in)	::	b(:)
real(kind=pr),	intent(in)	::	del1(:)
real(kind=pr),	intent(in)	::	alpha(:,:)
real(kind=pr),	intent(in)	::	gji0(:,:)
real(kind=pr),	intent(in)	::	gjiT(:,:)
logical,	intent(in)	::	use_kij(:,:)
real(kind=pr),	intent(in)	::	kij(:,:)

Return Value type(HV_NRTL)

private function init_mhv(Ge, b, q, lij) result(mixrule)

Arguments

Type	Intent	Optional		Name
class(GeModel),	intent(in)		::	Ge
real(kind=pr),	intent(in)		::	b(:)
real(kind=pr),	intent(in)		::	q
real(kind=pr),	intent(in),	optional	::	lij(:,:)

Return Value type(MHV)

Subroutines

public subroutine DmixMHV(self, n, V, T, ai, daidt, daidt2, D, dDdV, dDdT, dDdV2, dDdT2, dDi, dDdTV, dDidV, dDidT, dDij)

Mixing rule at infinite pressure as defined in the book of Michelsen and Møllerup.

Arguments

Type	Intent		Name
class(MHV),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)	Moles vector [mol]
real(kind=pr),	intent(in)	::	V	Volume [L] (unused)
real(kind=pr),	intent(in)	::	T	Temperature [K]
real(kind=pr),	intent(in)	::	ai(:)	Pure components attractive parameters $a_i$
real(kind=pr),	intent(in)	::	daidt(:)	$\frac{da_i}{dT}$
real(kind=pr),	intent(in)	::	daidt2(:)	$\frac{d^2a_i}{dT^2}$
real(kind=pr),	intent(out)	::	D	Mixture attractive parameter $n^2a_{mix}$
real(kind=pr),	intent(out)	::	dDdV	$\frac{dD}{dT}$
real(kind=pr),	intent(out)	::	dDdT	$\frac{dD}{dV}$
real(kind=pr),	intent(out)	::	dDdV2	$\frac{d^2D}{dV^2}$
real(kind=pr),	intent(out)	::	dDdT2	$\frac{d^2D}{dT^2}$
real(kind=pr),	intent(out)	::	dDi(:)	$\frac{dD}{dn_i}$
real(kind=pr),	intent(out)	::	dDdTV	$\frac{d^2D}{dTV$
real(kind=pr),	intent(out)	::	dDidV(:)	$\frac{d^2D}{dVn_i}$
real(kind=pr),	intent(out)	::	dDidT(:)	$\frac{d^2D}{dTn_i}$
real(kind=pr),	intent(out)	::	dDij(:,:)	$\frac{d^2D}{dn_{ij}}$

private subroutine BmixHV(self, n, bi, B, dBi, dBij)

Quadratinc mixing rule for the repulsive parameter.

Arguments

Type	Intent		Name
class(HV),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)
real(kind=pr),	intent(in)	::	bi(:)
real(kind=pr),	intent(out)	::	B
real(kind=pr),	intent(out)	::	dBi(:)
real(kind=pr),	intent(out)	::	dBij(:,:)

private subroutine BmixHVNRTL(self, n, bi, B, dBi, dBij)

Quadratinc mixing rule for the repulsive parameter.

Arguments

Type	Intent		Name
class(HV_NRTL),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)
real(kind=pr),	intent(in)	::	bi(:)
real(kind=pr),	intent(out)	::	B
real(kind=pr),	intent(out)	::	dBi(:)
real(kind=pr),	intent(out)	::	dBij(:,:)

private subroutine BmixMHV(self, n, bi, B, dBi, dBij)

Quadratinc mixing rule for the repulsive parameter, using $b_{ij} = \frac{b_i + b_j}{2} (1 - l_{ij})$ as a combining rule.

Arguments

Type	Intent		Name
class(MHV),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)
real(kind=pr),	intent(in)	::	bi(:)
real(kind=pr),	intent(out)	::	B
real(kind=pr),	intent(out)	::	dBi(:)
real(kind=pr),	intent(out)	::	dBij(:,:)

private subroutine D1MixHV(self, n, d1i, D1, dD1i, dD1ij)

Arguments

Type	Intent		Name
class(HV),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)
real(kind=pr),	intent(in)	::	d1i(:)
real(kind=pr),	intent(out)	::	D1
real(kind=pr),	intent(out)	::	dD1i(:)
real(kind=pr),	intent(out)	::	dD1ij(:,:)

private subroutine D1MixHVNRTL(self, n, d1i, D1, dD1i, dD1ij)

Arguments

Type	Intent		Name
class(HV_NRTL),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)
real(kind=pr),	intent(in)	::	d1i(:)
real(kind=pr),	intent(out)	::	D1
real(kind=pr),	intent(out)	::	dD1i(:)
real(kind=pr),	intent(out)	::	dD1ij(:,:)

private subroutine D1MixMHV(self, n, d1i, D1, dD1i, dD1ij)

Arguments

Type	Intent		Name
class(MHV),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)
real(kind=pr),	intent(in)	::	d1i(:)
real(kind=pr),	intent(out)	::	D1
real(kind=pr),	intent(out)	::	dD1i(:)
real(kind=pr),	intent(out)	::	dD1ij(:,:)

private subroutine DmixHV(self, n, V, T, ai, daidt, daidt2, D, dDdV, dDdT, dDdV2, dDdT2, dDi, dDdTV, dDidV, dDidT, dDij)

Arguments

Type	Intent		Name
class(HV),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)	Moles vector [mol]
real(kind=pr),	intent(in)	::	V	Volume [L] (unused)
real(kind=pr),	intent(in)	::	T	Temperature [K]
real(kind=pr),	intent(in)	::	ai(:)	Pure components attractive parameters $a_i$
real(kind=pr),	intent(in)	::	daidt(:)	$\frac{da_i}{dT}$
real(kind=pr),	intent(in)	::	daidt2(:)	$\frac{d^2a_i}{dT^2}$
real(kind=pr),	intent(out)	::	D	Mixture attractive parameter $n^2a_{mix}$
real(kind=pr),	intent(out)	::	dDdV	$\frac{dD}{dT}$
real(kind=pr),	intent(out)	::	dDdT	$\frac{dD}{dV}$
real(kind=pr),	intent(out)	::	dDdV2	$\frac{d^2D}{dV^2}$
real(kind=pr),	intent(out)	::	dDdT2	$\frac{d^2D}{dT^2}$
real(kind=pr),	intent(out)	::	dDi(:)	$\frac{dD}{dn_i}$
real(kind=pr),	intent(out)	::	dDdTV	$\frac{d^2D}{dTV$
real(kind=pr),	intent(out)	::	dDidV(:)	$\frac{d^2D}{dVn_i}$
real(kind=pr),	intent(out)	::	dDidT(:)	$\frac{d^2D}{dTn_i}$
real(kind=pr),	intent(out)	::	dDij(:,:)	$\frac{d^2D}{dn_{ij}}$

private subroutine DmixHVNRTL(self, n, V, T, ai, daidt, daidt2, D, dDdV, dDdT, dDdV2, dDdT2, dDi, dDdTV, dDidV, dDidT, dDij)

Arguments

Type	Intent		Name
class(HV_NRTL),	intent(in)	::	self
real(kind=pr),	intent(in)	::	n(:)	Moles vector [mol]
real(kind=pr),	intent(in)	::	V	Volume [L] (unused)
real(kind=pr),	intent(in)	::	T	Temperature [K]
real(kind=pr),	intent(in)	::	ai(:)	Pure components attractive parameters $a_i$
real(kind=pr),	intent(in)	::	daidt(:)	$\frac{da_i}{dT}$
real(kind=pr),	intent(in)	::	daidt2(:)	$\frac{d^2a_i}{dT^2}$
real(kind=pr),	intent(out)	::	D	Mixture attractive parameter $n^2a_{mix}$
real(kind=pr),	intent(out)	::	dDdV	$\frac{dD}{dT}$
real(kind=pr),	intent(out)	::	dDdT	$\frac{dD}{dV}$
real(kind=pr),	intent(out)	::	dDdV2	$\frac{d^2D}{dV^2}$
real(kind=pr),	intent(out)	::	dDdT2	$\frac{d^2D}{dT^2}$
real(kind=pr),	intent(out)	::	dDi(:)	$\frac{dD}{dn_i}$
real(kind=pr),	intent(out)	::	dDdTV	$\frac{d^2D}{dTV$
real(kind=pr),	intent(out)	::	dDidV(:)	$\frac{d^2D}{dVn_i}$
real(kind=pr),	intent(out)	::	dDidT(:)	$\frac{d^2D}{dTn_i}$
real(kind=pr),	intent(out)	::	dDij(:,:)	$\frac{d^2D}{dn_{ij}}$

yaeos__models_cubic_mixing_rules_huron_vidal Module

Contents

Interfaces

Derived Types

Functions

Subroutines

Huron-Vidal (like) mixing rules module

Description

Examples

References

Uses

Used by

Interfaces

public interface HV_NRTL

public function init_hvnrtl(b, del1, alpha, gji0, gjiT, use_kij, kij) result(mixrule)

Huron-Vidal NRTL mixing rule

Description

Examples

Arguments

Return Value type(HV_NRTL)

public interface MHV

private function init_mhv(Ge, b, q, lij) result(mixrule)

Arguments

Return Value type(MHV)

Derived Types

type, public, extends(CubicMixRule) :: HV

Components

Type-Bound Procedures

type, public, extends(CubicMixRule) :: HV_NRTL

Components

Constructor

Type-Bound Procedures

type, public, extends(CubicMixRule) :: MHV

Components

Constructor

Type-Bound Procedures

Functions

public function init_hvnrtl(b, del1, alpha, gji0, gjiT, use_kij, kij) result(mixrule)

Arguments

Return Value type(HV_NRTL)

private function init_mhv(Ge, b, q, lij) result(mixrule)

Arguments

Return Value type(MHV)

Subroutines

public subroutine DmixMHV(self, n, V, T, ai, daidt, daidt2, D, dDdV, dDdT, dDdV2, dDdT2, dDi, dDdTV, dDidV, dDidT, dDij)

Arguments

private subroutine BmixHV(self, n, bi, B, dBi, dBij)

Arguments

private subroutine BmixHVNRTL(self, n, bi, B, dBi, dBij)

Arguments

private subroutine BmixMHV(self, n, bi, B, dBi, dBij)

Arguments

private subroutine D1MixHV(self, n, d1i, D1, dD1i, dD1ij)

Arguments

private subroutine D1MixHVNRTL(self, n, d1i, D1, dD1i, dD1ij)

Arguments

private subroutine D1MixMHV(self, n, d1i, D1, dD1i, dD1ij)

Arguments

private subroutine DmixHV(self, n, V, T, ai, daidt, daidt2, D, dDdV, dDdT, dDdV2, dDdT2, dDi, dDdTV, dDidV, dDidT, dDij)

Arguments

private subroutine DmixHVNRTL(self, n, V, T, ai, daidt, daidt2, D, dDdV, dDdT, dDdV2, dDdT2, dDi, dDdTV, dDidV, dDidT, dDij)

Arguments