yaeos__equilibria_boundaries_phase_envelopes_mp Module

Multiphase PT envelope calculation module.

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


Uses

  • module~~yaeos__equilibria_boundaries_phase_envelopes_mp~~UsesGraph module~yaeos__equilibria_boundaries_phase_envelopes_mp yaeos__equilibria_boundaries_phase_envelopes_mp module~yaeos__constants yaeos__constants module~yaeos__equilibria_boundaries_phase_envelopes_mp->module~yaeos__constants module~yaeos__equilibria_boundaries_auxiliar yaeos__equilibria_boundaries_auxiliar module~yaeos__equilibria_boundaries_phase_envelopes_mp->module~yaeos__equilibria_boundaries_auxiliar module~yaeos__equilibria_equilibrium_state yaeos__equilibria_equilibrium_state module~yaeos__equilibria_boundaries_phase_envelopes_mp->module~yaeos__equilibria_equilibrium_state module~yaeos__math yaeos__math module~yaeos__equilibria_boundaries_phase_envelopes_mp->module~yaeos__math module~yaeos__models_ar yaeos__models_ar module~yaeos__equilibria_boundaries_phase_envelopes_mp->module~yaeos__models_ar iso_fortran_env iso_fortran_env module~yaeos__constants->iso_fortran_env module~yaeos__equilibria_boundaries_auxiliar->module~yaeos__constants module~yaeos__equilibria_boundaries_auxiliar->module~yaeos__math module~yaeos__equilibria_equilibrium_state->module~yaeos__constants module~yaeos__math->module~yaeos__constants module~yaeos__math_continuation yaeos__math_continuation module~yaeos__math->module~yaeos__math_continuation module~yaeos__math_linalg yaeos__math_linalg module~yaeos__math->module~yaeos__math_linalg module~yaeos__models_ar->module~yaeos__constants module~yaeos__models_base yaeos__models_base module~yaeos__models_ar->module~yaeos__models_base module~yaeos__math_continuation->module~yaeos__constants module~yaeos__math_continuation->module~yaeos__math_linalg module~yaeos__math_linalg->module~yaeos__constants module~yaeos__substance yaeos__substance module~yaeos__models_base->module~yaeos__substance module~yaeos__substance->module~yaeos__constants

Used by

  • module~~yaeos__equilibria_boundaries_phase_envelopes_mp~~UsedByGraph module~yaeos__equilibria_boundaries_phase_envelopes_mp yaeos__equilibria_boundaries_phase_envelopes_mp module~yaeos__equilibria yaeos__equilibria module~yaeos__equilibria->module~yaeos__equilibria_boundaries_phase_envelopes_mp module~yaeos__equilibria_boundaries_phase_envelopes_pt yaeos__equilibria_boundaries_phase_envelopes_pt module~yaeos__equilibria->module~yaeos__equilibria_boundaries_phase_envelopes_pt module~yaeos__equilibria_boundaries_phase_envelopes_pt->module~yaeos__equilibria_boundaries_phase_envelopes_mp module~yaeos yaeos module~yaeos->module~yaeos__equilibria

Variables

Type Visibility Attributes Name Initial
type(NearCritical), private :: near_critical_state

Singleton to follow the near critical status.

Derived Types

type, public ::  PTEnvelMP

Multiphase PT envelope.

Components

Type Visibility Attributes Name Initial
real(kind=pr), public, allocatable :: Pc(:)

Critical pressures.
real(kind=pr), public, allocatable :: Tc(:)

Critical temperatures.
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 Initial
real(kind=pr), public :: P

Pressure [bar]
real(kind=pr), public :: S

Specified variable value.
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.
real(kind=pr), public :: dS

Step size of the specification to reach this point.
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.

type, private ::  NearCritical

Near critical point information.

Components

Type Visibility Attributes Name Initial
logical, public :: entering = .false.

Entering a critical region. This attribute is used to ensure that the correct indexes are used since they should not be updated while inside the region, just on the first point.
integer, public :: i

Index of the component with the max

integer, public :: j

Index of the component with the minimum

integer, public :: l

Index of the phase that is becoming critical with the reference phase.
logical, public :: near_critical = .false.

If we are satisfying the condition of being near a critical point.

Functions

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

Calculation of a multiphase PT envelope.

Read more…

Arguments

Type IntentOptional Attributes Name
class(ArModel), intent(in) :: model
real(kind=pr), intent(in) :: z(:)

Mixture global composition.
integer, intent(in) :: np

Number of main phases.
character(len=14), intent(in) :: kinds_x(np)

Kind of the main phases.
character(len=14), intent(in) :: kind_w

Kind of the reference phase.
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.
logical, intent(in), optional :: allow_negative_betas

Do not stop calculating when there are negative values of beta.

Return Value type(PTEnvelMP)


Subroutines

public subroutine pt_F_NP(model, z, np, beta_w, kinds_x, kind_w, X, ns, S, F, df, Vl, Vw)

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

Arguments

Type IntentOptional Attributes 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.
character(len=14), intent(in) :: kinds_x(np)

Kind 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.
real(kind=pr), intent(out) :: Vl(np)
real(kind=pr), intent(out) :: Vw

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

Extract the values of the variables from the vector X.

Read more…

Arguments

Type IntentOptional Attributes 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(in) :: beta_w

Fraction of the reference phase.
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, kinds_x, kind_w, X, ns, S, dXdS, F, df, Vl, Vw, iters, max_iterations)

Arguments

Type IntentOptional Attributes 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
character(len=14), intent(in) :: kinds_x(np)

Kind 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
real(kind=pr), intent(out) :: Vl(np)

Main phases volumes
real(kind=pr), intent(out) :: Vw

Reference phase volume
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, S, dS, near_crit, l_nc, i_nc, j_nc, Vl, Vw)

Change the specified variable for the next step.

Read more…

Arguments

Type IntentOptional Attributes 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) :: S

Specified value.
real(kind=pr), intent(inout) :: dS

Step size of the specification for the next point.
logical, intent(out) :: near_crit

If true, the point is near a critical point.
integer, intent(out) :: l_nc

Index of the phase near a critical point.
integer, intent(out) :: i_nc

Index of the component with the maximum lnK if near a critical point.
integer, intent(out) :: j_nc

Index of the component with the minimum lnK if near a critical point.
real(kind=pr), intent(in) :: Vl(:)

Molar volumes of the main phases [L/mol].
real(kind=pr), intent(in) :: Vw

Molar volume of the reference phase [L/mol].

private subroutine write_envelope_PT_MP(env, unit)

Arguments

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