UNIFAC module

Classic liquid-vapor UNIFAC model implementation module.

Description

Classic liquid-vapor UNIFAC model implementation module. The implementation is based on the Thermopack library (SINTEF) implementation.

Examples

 ! Instantiate an UNIFAC model with ethanol-water mix and calculate gammas
 use yaeos, only: pr, Groups, setup_unifac, UNIFAC

 type(UNIFAC) :: model
 type(Groups) :: molecules(2)
 real(pr) :: ln_gammas(2)

 ! Ethanol definition [CH3, CH2, OH]
 molecules(1)%groups_ids = [1, 2, 14] ! Subgroups ids
 molecules(1)%number_of_groups = [1, 1, 1] ! Subgroups occurrences

 ! Water definition [H2O]
 molecules(2)%groups_ids = [16]
 molecules(2)%number_of_groups = [1]

 ! Model setup
 model = setup_unifac(molecules)

 ! Calculate ln_gammas
 call model%ln_activity_coefficient([0.5_pr, 0.5_pr], 298.0_pr, ln_gammas)

 print *, ln_gammas ! result: 0.18534142000449058    0.40331395945417559

References

Dortmund Data Bank Software & Separation Technology
Fredenslund, A., Jones, R. L., & Prausnitz, J. M. (1975). Group‐contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE Journal, 21(6), 1086–1099. https://doi.org/10.1002/aic.690210607
Skjold-Jorgensen, S., Kolbe, B., Gmehling, J., & Rasmussen, P. (1979). Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension. Industrial & Engineering Chemistry Process Design and Development, 18(4), 714–722. https://doi.org/10.1021/i260072a024
Gmehling, J., Rasmussen, P., & Fredenslund, A. (1982). Vapor-liquid equilibriums by UNIFAC group contribution. Revision and extension. 2. Industrial & Engineering Chemistry Process Design and Development, 21(1), 118–127. https://doi.org/10.1021/i200016a021
Macedo, E. A., Weidlich, U., Gmehling, J., & Rasmussen, P. (1983). Vapor-liquid equilibriums by UNIFAC group contribution. Revision and extension. 3. Industrial & Engineering Chemistry Process Design and Development, 22(4), 676–678. https://doi.org/10.1021/i200023a023
Tiegs, D., Rasmussen, P., Gmehling, J., & Fredenslund, A. (1987). Vapor-liquid equilibria by UNIFAC group contribution. 4. Revision and extension. Industrial & Engineering Chemistry Research, 26(1), 159–161. https://doi.org/10.1021/ie00061a030
Hansen, H. K., Rasmussen, P., Fredenslund, A., Schiller, M., & Gmehling, J. (1991). Vapor-liquid equilibria by UNIFAC group contribution. 5. Revision and extension. Industrial & Engineering Chemistry Research, 30 (10), 2352–2355. https://doi.org/10.1021/ie00058a017
Wittig, R., Lohmann, J., & Gmehling, J. (2003). Vapor−Liquid Equilibria by UNIFAC Group Contribution. 6. Revision and Extension. Industrial & Engineering Chemistry Research, 42(1), 183–188. https://doi.org/10.1021/ie020506l
SINTEF - Thermopack

Uses

Derived Types

type, public, extends(GeModel) :: UNIFAC

Classic liquid-vapor UNIFAC model derived type

Components

Type	Visibility	Attributes		Name		Initial
type(Substances),	public		::	components			Substances contained in the module
real(kind=pr),	public		::	d	=	1.0_pr	Model constant d, exponent of the group volume in Flory-Huggins
real(kind=pr),	public,	allocatable	::	group_area(:)			Group areas $Q_k$
real(kind=pr),	public,	allocatable	::	group_volume(:)			Group volumes $R_k$
type(Groups),	public		::	groups_stew			All the groups present in the system
type(Groups),	public,	allocatable	::	molecules(:)			Substances present in the system
integer,	public		::	ngroups			Total number of individual groups in the mixture
integer,	public		::	nmolecules			Total number of molecules in the mixture
class(PsiFunction),	public,	allocatable	::	psi_function			Temperature dependance function of the model
real(kind=pr),	public,	allocatable	::	qk(:)			Area of each group k
real(kind=pr),	public,	allocatable	::	thetas_ij(:,:)			Area fractions of the groups j on molecules i
real(kind=pr),	public,	allocatable	::	vij(:,:)			Ocurrences of each group j on each molecule i
real(kind=pr),	public		::	z	=	10.0_pr	Model constant z

Type-Bound Procedures

procedure, public :: Ge_combinatorial
procedure, public :: Ge_residual
procedure, public :: excess_enthalpy
procedure, public :: excess_entropy
procedure, public :: excess_gibbs
procedure, public :: ln_activity_coefficient

Functions

public function setup_unifac(molecules, parameters)

Instantiate a UNIFAC model

Arguments

Type	Intent	Optional	Attributes		Name
type(Groups),	intent(in)			::	molecules(:)	Molecules (Group type) objects
type(GeGCModelParameters),	intent(in),	optional		::	parameters	UNIFAC parameters

Return Value type(UNIFAC)

public function thetas_i(nm, ng, parameters, stew, molecules) result(thetas_ij)

Calculate the area fraciton of each froup on each molecule.

Arguments

Type	Intent		Name
integer,	intent(in)	::	nm	Number of molecules
integer,	intent(in)	::	ng	Number of groups
type(GeGCModelParameters),	intent(in)	::	parameters	UNIFAC parameters
type(Groups),	intent(in)	::	stew	All the groups present in the system
type(Groups),	intent(in)	::	molecules(:)	Molecules

Return Value real(kind=pr), (nm,ng)

Group j area fraction on molecule i

Subroutines

public subroutine Ge_combinatorial(self, n, T, Ge, dGe_dn, dGe_dn2)

Calculate the UNIFAC combinatorial term of Gibbs excess energy

Arguments

Type	Intent	Optional		Name
class(UNIFAC)			::	self
real(kind=pr),	intent(in)		::	n(self%nmolecules)	Moles vector [mol]
real(kind=pr),	intent(in)		::	T	Temperature [K]
real(kind=pr),	intent(out),	optional	::	Ge	Combinatorial Gibbs excess energy
real(kind=pr),	intent(out),	optional	::	dGe_dn(self%nmolecules)	$\frac{dGe}{dn}$
real(kind=pr),	intent(out),	optional	::	dGe_dn2(self%nmolecules,self%nmolecules)	$\frac{d^2Ge}{dn^2}$

public subroutine Ge_residual(self, n, T, Ge, dGe_dn, dGe_dn2, dGe_dT, dGe_dT2, dGe_dTn)

Evaluate the UNIFAC residual term

Arguments

Type	Intent	Optional		Name
class(UNIFAC)			::	self
real(kind=pr),	intent(in)		::	n(self%nmolecules)	Moles vector
real(kind=pr),	intent(in)		::	T	Temperature [K]
real(kind=pr),	intent(out),	optional	::	Ge	Residual Gibbs excess energy
real(kind=pr),	intent(out),	optional	::	dGe_dn(self%nmolecules)	$\frac{\partial G^{E,R}}{\partial n}$
real(kind=pr),	intent(out),	optional	::	dGe_dn2(self%nmolecules,self%nmolecules)	$\frac{\partial^2 G^{E,R}}{\partial n^2}$
real(kind=pr),	intent(out),	optional	::	dGe_dT	$\frac{\partial G^{E,R}}{\partial T}$
real(kind=pr),	intent(out),	optional	::	dGe_dT2	$\frac{\partial^2 G^{E,R}}{\partial T^2}$
real(kind=pr),	intent(out),	optional	::	dGe_dTn(self%nmolecules)	$\frac{\partial^2 G^{E,R}}{\partial n \partial T}$

public subroutine excess_gibbs(self, n, T, Ge, GeT, GeT2, Gen, GeTn, Gen2)

Calculate the Gibbs excess energy of the UNIFAC model

Arguments

Type	Intent	Optional		Name
class(UNIFAC),	intent(in)		::	self	UNIFAC model
real(kind=pr),	intent(in)		::	n(:)	Moles vector [mol]
real(kind=pr),	intent(in)		::	T	Temperature [K]
real(kind=pr),	intent(out),	optional	::	Ge	Excess Gibbs energy
real(kind=pr),	intent(out),	optional	::	GeT	$\frac{dG^E}{dT}$
real(kind=pr),	intent(out),	optional	::	GeT2	$\frac{d^2G^E}{dT^2}$
real(kind=pr),	intent(out),	optional	::	Gen(size(n))	$\frac{dG^E}{dn}$
real(kind=pr),	intent(out),	optional	::	GeTn(size(n))	$\frac{d^2G^E}{dTdn}$
real(kind=pr),	intent(out),	optional	::	Gen2(size(n),size(n))	$\frac{d^2G^E}{dn^2}$

yaeos__models_ge_group_contribution_unifac Module

Contents

Derived Types

Functions

Subroutines

UNIFAC module

Description

Examples

References

Uses

Derived Types

type, public, extends(GeModel) :: UNIFAC

Components

Type-Bound Procedures

Functions

public function setup_unifac(molecules, parameters)

Arguments

Return Value type(UNIFAC)

public function thetas_i(nm, ng, parameters, stew, molecules) result(thetas_ij)

Arguments

Return Value real(kind=pr), (nm,ng)

Subroutines

public subroutine Ge_combinatorial(self, n, T, Ge, dGe_dn, dGe_dn2)

Arguments

public subroutine Ge_residual(self, n, T, Ge, dGe_dn, dGe_dn2, dGe_dT, dGe_dT2, dGe_dTn)

Arguments

public subroutine excess_gibbs(self, n, T, Ge, GeT, GeT2, Gen, GeTn, Gen2)

Arguments