yaeos__equilibria_boundaries_phase_envelopes_mp_px Module

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 ::  PXEnvelMP

Multiphase PX envelope.

Components

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

Molar relation between two mixtures.
type(MPPoint), public, allocatable :: points(:)

Array of converged points.
real(kind=pr), public, allocatable :: z0(:)

Original mixture mole fractions.
real(kind=pr), public, allocatable :: zi(:)

Other mixture mole fractions

Type-Bound Procedures

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

type, private ::  MPPoint

Multiphase equilibria point.

Components

Type Visibility Attributes Name Initial
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 px_envelope(model, z0, zi, np, T, x_l0, w0, betas0, P0, alpha0, ns0, dS0, beta_w, points)

Calculation of a multiphase Px envelope.

Read more…

Arguments

Type IntentOptional Attributes Name
class(ArModel), intent(in) :: model

Model to use.
real(kind=pr), intent(in) :: z0(:)

Original fluid composition.
real(kind=pr), intent(in) :: zi(:)

Other fluid compostion.
integer, intent(in) :: np

Number of phases, without including the reference phaes
real(kind=pr), intent(in) :: T

Temperature [K]
real(kind=pr), intent(in) :: x_l0(np,size(z0))

Initial guess for composition of phases.
real(kind=pr), intent(in) :: w0(size(z0))

Initial guess for composition of reference phase.
real(kind=pr), intent(in) :: betas0(np)

Mole fractions of each phase. Excluding the reference phase.
real(kind=pr), intent(in) :: P0

Initial guess for pressure [bar]
real(kind=pr), intent(in) :: alpha0

Initial guess for relation between two fluids

integer, intent(in) :: ns0

First specified variable.

Read more…
real(kind=pr), intent(in) :: dS0

First step to extrapolate for next point calculation. After that It will use an adaptive algorithm.
real(kind=pr), intent(in) :: beta_w

Fraction of the reference (incipient) phase.
integer, intent(in), optional :: points

Maximum number of points to calculate.

Return Value type(PXEnvelMP)


Subroutines

public subroutine px_F_NP(model, z0, zi, np, T, beta_w, X, ns, S, F, df)

System of equations to solve a multiphase-point at constant temperature.

Read more…

Arguments

Type IntentOptional Attributes Name
class(ArModel), intent(in) :: model

Model to use.
real(kind=pr), intent(in) :: z0(:)

First mixture composition.
real(kind=pr), intent(in) :: zi(:)

Second mixture composition.
integer, intent(in) :: np

Number of main phases.
real(kind=pr), intent(in) :: T

Temperature [K].
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.

Read more…

Arguments

Type IntentOptional Attributes 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, z0, zi, beta_w, x_l, w, betas, P, alpha)

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) :: 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) :: P

Pressure [bar].
real(kind=pr), intent(out) :: alpha

.

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

Solve the system of equations for a multiphase point.

Read more…

Arguments

Type IntentOptional Attributes Name
class(ArModel), intent(in) :: model

Model to use.
real(kind=pr), intent(in) :: z0(:)

First mixture composition.
real(kind=pr), intent(in) :: zi(:)

Second mixture composition.
integer, intent(in) :: np

Number of main phases
real(kind=pr), intent(in) :: T

Temperature [K]
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))

Sensitivity of the variables wrt the specification
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.

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) :: dS

Step size of the specification for the next point.

private subroutine write_envelope_PX_MP(env, unit)

Arguments

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