yaeos__models_ar_cubic_quadratic_mixing

Quadratic Mixing Rules for Cubic EoS.

Uses

Abstract Interfaces

abstract interface

public subroutine get_aij(self, T, ai, daidt, daidt2, aij, daijdt, daijdt2)

Combining rule for the attractive parameter.

From previously calculated attractive parameters calculate the $a_{ij}$ matrix and it’s corresponding derivatives.

Arguments

Type	Intent		Name
class(QMR),	intent(in)	::	self
real(kind=pr),	intent(in)	::	T
real(kind=pr),	intent(in)	::	ai(:)
real(kind=pr),	intent(in)	::	daidt(:)
real(kind=pr),	intent(in)	::	daidt2(:)
real(kind=pr),	intent(out)	::	aij(:,:)
real(kind=pr),	intent(out)	::	daijdt(:,:)
real(kind=pr),	intent(out)	::	daijdt2(:,:)

Derived Types

type, public, extends(CubicMixRule) :: QMR

Quadratic Mixing Rule (QMR) derived type. Classic Van der Waals mixing rules.

Components

Type	Visibility	Attributes		Name		Initial
logical,	public		::	dn2	=	.false.	Calculate second order derivatives
real(kind=pr),	public,	allocatable	::	k(:,:)			Attractive Binary Interatction parameter matrix
real(kind=pr),	public,	allocatable	::	l(:,:)			Repulsive Binary Interatction parameter matrix

Type-Bound Procedures

procedure, public :: Bmix	../../../ Repulsive parameter mixing rule
procedure, public :: D1mix => D1mix_constant
procedure, public :: Dmix	../../../ Attractive parameter mixing rule
procedure, public :: aij => kij_constant	../../../ Default attractive parameter combining rule

type, public, extends(QMR) :: QMRTD

Components

Type	Visibility	Attributes		Name		Initial
real(kind=pr),	public,	allocatable	::	Tref(:,:)
logical,	public		::	dn2	=	.false.	Calculate second order derivatives
real(kind=pr),	public,	allocatable	::	k(:,:)			Attractive Binary Interatction parameter matrix
real(kind=pr),	public,	allocatable	::	k0(:,:)
real(kind=pr),	public,	allocatable	::	l(:,:)			Repulsive Binary Interatction parameter matrix

Type-Bound Procedures

procedure, public :: Bmix	../../../ Repulsive parameter mixing rule
procedure, public :: D1mix => D1mix_constant
procedure, public :: Dmix	../../../ Attractive parameter mixing rule
procedure, public :: aij => kij_exp_tdep

type, public, extends(QMR) :: QMR_RKPR

Components

Type	Visibility	Attributes		Name		Initial
logical,	public		::	dn2	=	.false.	Calculate second order derivatives
real(kind=pr),	public,	allocatable	::	k(:,:)			Attractive Binary Interatction parameter matrix
real(kind=pr),	public,	allocatable	::	l(:,:)			Repulsive Binary Interatction parameter matrix

Type-Bound Procedures

procedure, public :: Bmix	../../../ Repulsive parameter mixing rule
procedure, public :: D1Mix => RKPR_D1mix
procedure, public :: Dmix	../../../ Attractive parameter mixing rule
procedure, public :: aij => kij_constant	../../../ Default attractive parameter combining rule

Subroutines

public subroutine Bmix(self, n, bi, B, dBi, dBij)

Mixture repulsive parameter.

Arguments

Type	Intent		Name
class(QMR),	intent(in)	::	self	Mixing rule object.
real(kind=pr),	intent(in)	::	n(:)	Moles vector.
real(kind=pr),	intent(in)	::	bi(:)	Pure components repulsive parameters.
real(kind=pr),	intent(out)	::	B	Mixture repulsive parameter.
real(kind=pr),	intent(out)	::	dBi(:)	$\frac{dB}{dn_i}$
real(kind=pr),	intent(out)	::	dBij(:,:)	$\frac{d^2B}{dn_{ij}}$

public subroutine D1mix_constant(self, n, d1i, D1, dD1i, dD1ij)

Constant $\delta_1$ parameter.

Arguments

Type	Intent		Name
class(QMR),	intent(in)	::	self	Mixing rule
real(kind=pr),	intent(in)	::	n(:)	Moles vector
real(kind=pr),	intent(in)	::	d1i(:)	$\delta_1$ parameter
real(kind=pr),	intent(out)	::	D1	Mixture’s $\Delta_1$
real(kind=pr),	intent(out)	::	dD1i(:)	$\frac{dDelta_1}{dn_i} = 0$
real(kind=pr),	intent(out)	::	dD1ij(:,:)	$\frac{d^2Delta_1}{dn_{ij}} = 0$

public subroutine Dmix(self, n, T, ai, daidt, daidt2, D, dDdT, dDdT2, dDi, dDidT, dDij)

Attractive parameter mixing rule with quadratic mix.

Arguments

Type	Intent		Name
class(QMR),	intent(in)	::	self	Mixing rule object.
real(kind=pr),	intent(in)	::	n(:)	Moles vector [mol]
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)	::	dDdT	$\frac{dD}{dT}$
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)	::	dDidT(:)	$\frac{d^2D}{dTn_i}$
real(kind=pr),	intent(out)	::	dDij(:,:)	$\frac{d^2D}{dn_{ij}}$

public subroutine RKPR_D1mix(self, n, d1i, D1, dD1i, dD1ij)

RKPR $\delta_1$ parameter mixing rule.

Arguments

Type	Intent		Name
class(QMR_RKPR),	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(:,:)

public subroutine kij_constant(self, T, a, dadt, dadt2, aij, daijdt, daijdt2)

Combining rule that uses constant $k_{ij}$ values.

Arguments

Type	Intent		Name
class(QMR),	intent(in)	::	self
real(kind=pr),	intent(in)	::	T	Temperature [K]
real(kind=pr),	intent(in)	::	a(:)	Pure components attractive parameters (\a_i)
real(kind=pr),	intent(in)	::	dadt(:)	$\frac{da_i}{dT}$
real(kind=pr),	intent(in)	::	dadt2(:)	$\frac{d^2a_i}{dT^2}$
real(kind=pr),	intent(out)	::	aij(:,:)	$a_{ij}$ Matrix
real(kind=pr),	intent(out)	::	daijdt(:,:)	$\frac{da_{ij}{dT}$
real(kind=pr),	intent(out)	::	daijdt2(:,:)	$\frac{d^2a_{ij}{dT^2}$

public subroutine kij_exp_tdep(self, T, a, dadt, dadt2, aij, daijdt, daijdt2)

Combining rule that uses temperature dependant $k_{ij}$ values. With the following expression: $k_{ij}(T) = k_{ij}^0 + k_{ij}^\infty \exp\left(\frac{-T}{T^*}\right)$

Arguments

Type	Intent		Name
class(QMRTD),	intent(in)	::	self
real(kind=pr),	intent(in)	::	T	Temperature [K]
real(kind=pr),	intent(in)	::	a(:)	Pure components attractive parameters (\a_i)
real(kind=pr),	intent(in)	::	dadt(:)	$\frac{da_i}{dT}$
real(kind=pr),	intent(in)	::	dadt2(:)	$\frac{d^2a_i}{dT^2}$
real(kind=pr),	intent(out)	::	aij(:,:)	$a_{ij}$ Matrix
real(kind=pr),	intent(out)	::	daijdt(:,:)	$\frac{da_{ij}{dT}$
real(kind=pr),	intent(out)	::	daijdt2(:,:)	$\frac{d^2a_{ij}{dT^2}$

yaeos__models_ar_cubic_quadratic_mixing Module

Contents

Abstract Interfaces

Derived Types

Subroutines

Uses

Abstract Interfaces

abstract interface

public subroutine get_aij(self, T, ai, daidt, daidt2, aij, daijdt, daijdt2)

Arguments

Derived Types

type, public, extends(CubicMixRule) :: QMR

Components

Type-Bound Procedures

type, public, extends(QMR) :: QMRTD

Components

Type-Bound Procedures

type, public, extends(QMR) :: QMR_RKPR

Components

Type-Bound Procedures

Subroutines

public subroutine Bmix(self, n, bi, B, dBi, dBij)

Arguments

public subroutine D1mix_constant(self, n, d1i, D1, dD1i, dD1ij)

Arguments

public subroutine Dmix(self, n, T, ai, daidt, daidt2, D, dDdT, dDdT2, dDi, dDidT, dDij)

Arguments

public subroutine RKPR_D1mix(self, n, d1i, D1, dD1i, dD1ij)

Arguments

public subroutine kij_constant(self, T, a, dadt, dadt2, aij, daijdt, daijdt2)

Arguments

public subroutine kij_exp_tdep(self, T, a, dadt, dadt2, aij, daijdt, daijdt2)

Arguments