yaeos__equilibria_boundaries_phase_envelopes_mp

Multiphase PT envelope calculation module.

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

Uses

Derived Types

type, public :: PTEnvelMP

Multiphase PT envelope.

Components

Type	Visibility	Attributes		Name		Initial
type(MPPoint),	public,	allocatable	::	points(:)			Array of converged points.

Type-Bound Procedures

procedure, public, nopass :: get_values_from_X
procedure, public, nopass :: solve_point
procedure, public :: write => write_envelope_PT_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.
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 pt_envelope(model, z, np, x_l0, w0, betas0, P0, T0, ns0, dS0, beta_w, points, max_pressure)

Calculation of a multiphase PT envelope.

Arguments

Type	Intent	Optional		Name
class(ArModel),	intent(in)		::	model
real(kind=pr),	intent(in)		::	z(:)	Mixture global composition.
integer,	intent(in)		::	np	Number of main phases.
real(kind=pr),	intent(in)		::	x_l0(np,size(z))	Initial guess for the mole fractions of each phase. arranged as an array of size `(np, nc)`, where nc is the number of components and `np` the number of main phases. Each row correspond to the composition of each main phaase.
real(kind=pr),	intent(in)		::	w0(size(z))	Initial guess for the mole fractions of the reference/incipient phase.
real(kind=pr),	intent(in)		::	betas0(np)	Initial guess for the fractions of the main phases. arranged as an array of size `(np)`, where `np` is the number of main phases.
real(kind=pr),	intent(in)		::	P0	Initial guess for the pressure [bar].
real(kind=pr),	intent(in)		::	T0	Initial guess for the temperature [K].
integer,	intent(in)		::	ns0	Number of the specified variable. The variable to be specified. This is the variable that will be used to calculate the first point of the envelope. The variable can be any of the variables in the vector X, but it is recommended to use the temperature or pressure. The variables are aranged as follows: Read more…
real(kind=pr),	intent(in)		::	dS0	Step size of the specification for the next point. This is the step size that will be used to calculate the next point. Inside the algorithm this value is modified to adapt the step size to facilitate the convergence of each point.
real(kind=pr),	intent(in)		::	beta_w	Fraction of the reference (incipient) phase.
integer,	intent(in),	optional	::	points	Number of points to calculate.
real(kind=pr),	intent(in),	optional	::	max_pressure	Maximum pressure [bar] to calculate. If the pressure of the point is greater than this value, the calculation is stopped. This is useful to avoid calculating envelopes that go to infinite values of pressure.

Return Value type(PTEnvelMP)

Subroutines

public subroutine pt_F_NP(model, z, np, beta_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	Model to use.
real(kind=pr),	intent(in)	::	z(:)	Mixture global composition.
integer,	intent(in)	::	np	Number of main phases.
real(kind=pr),	intent(in)	::	beta_w	Fraction of the reference (incipient) 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 detect_critical(nc, np, X, dXdS, ns, dS, S)

Detect if the system is close to a critical point.

Arguments

Type	Intent		Name
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)	::	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.
real(kind=pr),	intent(inout)	::	S	Specification value.

private subroutine get_values_from_X(X, np, z, x_l, w, betas, P, T)

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)	::	z(:)	Mixture composition.
real(kind=pr),	intent(out)	::	x_l(np,size(z))	Mole fractions of the main phases.
real(kind=pr),	intent(out)	::	w(size(z))	Mole fractions of the incipient phase.
real(kind=pr),	intent(out)	::	betas(np)	Fractions of the main phases.
real(kind=pr),	intent(out)	::	P	Pressure [bar].
real(kind=pr),	intent(out)	::	T	Temperature [K].

private subroutine solve_point(model, z, np, beta_w, X, ns, S, dXdS, F, df, iters, max_iterations)

Arguments

Type	Intent		Name
class(ArModel),	intent(in)	::	model	Model to use.
real(kind=pr),	intent(in)	::	z(:)	Mixture global composition.
integer,	intent(in)	::	np	Number of main phases
real(kind=pr),	intent(in)	::	beta_w	Fraction of the reference (incipient) 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 to solve the current 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_PT_MP(env, unit)

Arguments

Type	Intent	Optional	Attributes		Name
class(PTEnvelMP),	intent(in)			::	env
integer,	intent(in)			::	unit

yaeos__equilibria_boundaries_phase_envelopes_mp Module

Contents

Derived Types

Functions

Subroutines

Uses

Derived Types

type, public :: PTEnvelMP

Components

Type-Bound Procedures

type, private :: MPPoint

Components

Functions

public function pt_envelope(model, z, np, x_l0, w0, betas0, P0, T0, ns0, dS0, beta_w, points, max_pressure)

Arguments

Return Value type(PTEnvelMP)

Subroutines

public subroutine pt_F_NP(model, z, np, beta_w, X, ns, S, F, df)

Arguments

private subroutine detect_critical(nc, np, X, dXdS, ns, dS, S)

Arguments

private subroutine get_values_from_X(X, np, z, x_l, w, betas, P, T)

Arguments

private subroutine solve_point(model, z, np, beta_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_PT_MP(env, unit)

Arguments