yaeos__equilibria_boundaries_phase_envelopes_mp_tx

Multiphase Px envelope calculation module.

This module contains the functions to calculate the PT envelope of a mixture with multiple phases.

Uses

Derived Types

type, public :: TXEnvelMP

Multiphase T $alpha$ envelope.

Components

Type	Visibility	Attributes		Name
real(kind=pr),	public,	allocatable	::	Tc(:)	Critical temperatures [K]
real(kind=pr),	public,	allocatable	::	ac(:)	Critical alphas.
real(kind=pr),	public,	allocatable	::	alpha(:)	Array of $alpha$ values for each point in the envelope.
character(len=14),	public,	allocatable	::	kind_w(:)	Kind of the reference phase
character(len=14),	public,	allocatable	::	kinds_x(:)	Kinds of the main phases
type(MPPoint),	public,	allocatable	::	points(:)	Array of converged points.
real(kind=pr),	public,	allocatable	::	z0(:)	Initial mixture composition.
real(kind=pr),	public,	allocatable	::	zi(:)	Second mixture composition.

Type-Bound Procedures

procedure, public, nopass :: get_values_from_X
procedure, public, nopass :: solve_point
procedure, public :: write => write_envelope_TX_MP

type, private :: MPPoint

Multiphase equilibria point.

Components

Type	Visibility	Attributes		Name
real(kind=pr),	public		::	P	Pressure [bar]
real(kind=pr),	public		::	T	Temperature [K]
real(kind=pr),	public		::	beta_w	Fraction of the reference (incipient) phase.
real(kind=pr),	public,	allocatable	::	betas(:)	Fractions of the main phases.
integer,	public		::	iters	Number of iterations needed to converge the point.
character(len=14),	public		::	kind_w	Kind of the reference phase.
character(len=14),	public,	allocatable	::	kinds_x(:)	Kinds of the main phases.
integer,	public		::	nc	Number of components
integer,	public		::	np	Number of phases
integer,	public		::	ns	Number of the specified variable.
real(kind=pr),	public,	allocatable	::	w(:)	Mole fractions of the incipient phase.
real(kind=pr),	public,	allocatable	::	x_l(:,:)	Mole fractions of the main phases.

Functions

public function tx_envelope(model, z0, zi, np, P, kinds_x, kind_w, x_l0, w0, betas0, T0, alpha0, ns0, dS0, beta_w, points)

Calculate the multiphase isobar of a mixture.

Arguments

Type	Intent	Optional		Name
class(ArModel),	intent(in)		::	model	Model to use for the calculations.
real(kind=pr),	intent(in)		::	z0(:)	Initial mixture composition.
real(kind=pr),	intent(in)		::	zi(:)	Second mixture composition.
integer,	intent(in)		::	np	Number of main phases.
real(kind=pr),	intent(in)		::	P	Pressure [bar].
character(len=14),	intent(in)		::	kinds_x(np)	Kinds of the main phases. Can be “liquid”, “vapor”, “stable”
character(len=14),	intent(in)		::	kind_w	Kind of the reference phase. Can be “liquid”, “vapor”, “stable”
real(kind=pr),	intent(in)		::	x_l0(np,size(z0))	Mole fractions matrix of the main phases at the initial point. Each row corresponds to a phase, and each column corresponds to a component.
real(kind=pr),	intent(in)		::	w0(size(z0))	Mole fractions of the incipient/reference phase at the initial point.
real(kind=pr),	intent(in)		::	betas0(np)	Mole fractions of each main phases at the initial point.
real(kind=pr),	intent(in)		::	T0	Initial Temperature [K].
real(kind=pr),	intent(in)		::	alpha0	Initial value of the $alpha$ variable.
integer,	intent(in)		::	ns0	Number of the specified variable. This is the variable that will be used to specify the next point. the first $nc \cdot np$ variables corresponds to the $\ln K_i^l$ of each phase, sorted by phases ([\ln K_1^1, \ln K_2^1, \dots, \ln K_{nc}^1, \dots, \ln K_{nc}^{np}]). The next $np$ variables are the mole fractions of each main phase. The last two variables are the temperature and the $alpha$ variable. Respectively
real(kind=pr),	intent(in)		::	dS0	Step size of the specification for the next point.
real(kind=pr),	intent(in)		::	beta_w	Fraction of the reference (incipient) phase.
integer,	intent(in),	optional	::	points	Number of points to calculate in the envelope. If not specified, the default value is 1000.

Return Value type(TXEnvelMP)

Subroutines

public subroutine tx_F_NP(model, z0, zi, np, P, beta_w, kinds_x, kind_w, X, ns, S, F, df)

Function to solve at each point of a multi-phase envelope.

Arguments

Type	Intent		Name
class(ArModel),	intent(in)	::	model
real(kind=pr),	intent(in)	::	z0(:)
real(kind=pr),	intent(in)	::	zi(:)
integer,	intent(in)	::	np	Number of main phases.
real(kind=pr),	intent(in)	::	P	Pressure [bar]
real(kind=pr),	intent(in)	::	beta_w	Fraction of the reference (incipient) phase.
character(len=14),	intent(in)	::	kinds_x(np)	Kinds of the main phases.
character(len=14),	intent(in)	::	kind_w	Kind of the reference phase.
real(kind=pr),	intent(in)	::	X(:)	Vector of variables.
integer,	intent(in)	::	ns	Number of specification.
real(kind=pr),	intent(in)	::	S	Specification value.
real(kind=pr),	intent(out)	::	F(size(X))	Vector of functions valuated.
real(kind=pr),	intent(out)	::	df(size(X),size(X))	Jacobian matrix.

private subroutine get_values_from_X(X, np, z0, zi, beta_w, x_l, w, betas, T, alpha)

Extract the values of the variables from the vector X.

Arguments

Type	Intent		Name
real(kind=pr),	intent(in)	::	X(:)	Vector of variables.
integer,	intent(in)	::	np	Number of main phases.
real(kind=pr),	intent(in)	::	z0(:)	Initial mixture composition.
real(kind=pr),	intent(in)	::	zi(:)	Second mixture composition.
real(kind=pr),	intent(in)	::	beta_w	Reference phase beta.
real(kind=pr),	intent(out)	::	x_l(np,size(z0))	Mole fractions of the main phases.
real(kind=pr),	intent(out)	::	w(size(z0))	Mole fractions of the incipient phase.
real(kind=pr),	intent(out)	::	betas(np)	Fractions of the main phases.
real(kind=pr),	intent(out)	::	T	Pressure [bar].
real(kind=pr),	intent(out)	::	alpha	$alpha$ .

private subroutine solve_point(model, z0, zi, np, P, beta_w, kinds_x, kind_w, X, ns, S, dXdS, F, df, iters, max_iterations)

Solve a point in the multiphase envelope.

Arguments

Type	Intent		Name
class(ArModel),	intent(in)	::	model	Model to use for the calculations.
real(kind=pr),	intent(in)	::	z0(:)	Initial mixture composition.
real(kind=pr),	intent(in)	::	zi(:)	Second mixture composition.
integer,	intent(in)	::	np	Number of main phases.
real(kind=pr),	intent(in)	::	P	Presure [bar].
real(kind=pr),	intent(in)	::	beta_w	Fraction of the reference (incipient) phase
character(len=14),	intent(in)	::	kinds_x(np)	Kinds of the main phases
character(len=14),	intent(in)	::	kind_w	Kind of the reference phase
real(kind=pr),	intent(inout)	::	X(:)	Vector of variables
integer,	intent(in)	::	ns	Number of specification
real(kind=pr),	intent(in)	::	S	Specification value
real(kind=pr),	intent(in)	::	dXdS(size(X))
real(kind=pr),	intent(out)	::	F(size(X))	Vector of functions valuated
real(kind=pr),	intent(out)	::	df(size(X),size(X))	Jacobian matrix
integer,	intent(out)	::	iters	Number of iterations needed to converge the point.
integer,	intent(in)	::	max_iterations	Maximum number of iterations to solve the point.

private subroutine update_specification(its, nc, np, X, dF, dXdS, ns, dS)

Change the specified variable for the next step.

Arguments

Type	Intent		Name
integer,	intent(in)	::	its	Iterations to solve the current point.
integer,	intent(in)	::	nc	Number of components in the mixture.
integer,	intent(in)	::	np	Number of main phases.
real(kind=pr),	intent(inout)	::	X(:)	Vector of variables.
real(kind=pr),	intent(inout)	::	dF(:,:)	Jacobian matrix.
real(kind=pr),	intent(inout)	::	dXdS(:)	Sensitivity of the variables wrt the specification.
integer,	intent(inout)	::	ns	Number of the specified variable.
real(kind=pr),	intent(inout)	::	dS	Step size of the specification for the next point.

private subroutine write_envelope_TX_MP(env, unit)

Write the multiphase envelope to a file.

Arguments

Type	Intent	Optional	Attributes		Name
class(TXEnvelMP),	intent(in)			::	env	Envelope to write.
integer,	intent(in)			::	unit	Unit to write the envelope to.

yaeos__equilibria_boundaries_phase_envelopes_mp_tx Module

Contents

Derived Types

Functions

Subroutines

Uses

Derived Types

type, public :: TXEnvelMP

Components

Type-Bound Procedures

type, private :: MPPoint

Components

Functions

public function tx_envelope(model, z0, zi, np, P, kinds_x, kind_w, x_l0, w0, betas0, T0, alpha0, ns0, dS0, beta_w, points)

Arguments

Return Value type(TXEnvelMP)

Subroutines

public subroutine tx_F_NP(model, z0, zi, np, P, beta_w, kinds_x, kind_w, X, ns, S, F, df)

Arguments

private subroutine get_values_from_X(X, np, z0, zi, beta_w, x_l, w, betas, T, alpha)

Arguments

private subroutine solve_point(model, z0, zi, np, P, beta_w, kinds_x, kind_w, X, ns, S, dXdS, F, df, iters, max_iterations)

Arguments

private subroutine update_specification(its, nc, np, X, dF, dXdS, ns, dS)

Arguments

private subroutine write_envelope_TX_MP(env, unit)

Arguments