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Radial Flow Models

Radial flow models are available for the LRM, LRMP and GRM. The configurations specified here complement the description for the respective model, i.e. please additionally refer to Lumped Rate Model Without Pores or Lumped rate model with pores or General Rate Model, respectively. If input variables are described in both files, then only the description provided here applies for radial flow models.

The unit type input must be specified with the prefix \(\texttt{RADIAL_}\) followed by the respective transport model name. In this document, we specify the unit type as the radial GRM, but the LRM and LRMP are also available and the changes to input variables are the same for all three models.

Group /input/model/unit_XXX - UNIT_TYPE - RADIAL_GENERAL_RATE_MODEL

For information on model equations, refer to Lumped rate model without pores (LRM) or Lumped rate model with pores (LRMP) or General rate model (GRM), respectively.

UNIT_TYPE

Specifies the type of unit operation model

Type: string

Range: \(\texttt{RADIAL_GENERAL_RATE_MODEL}\)

Length: 1

COL_DISPERSION

Radial dispersion coefficient

Unit: \(\mathrm{m}_{\mathrm{IV}}^{2}\,\mathrm{s}^{-1}\)

Type: double

Range: \(\geq 0\)

Length: see \(\texttt{COL_DISPERSION_MULTIPLEX}\)

In addition to the multiplex specification (e.g. component dependency, see General rate model (GRM)), the dispersion coefficient for radial flow model usually depends on other parameters. Parameter dependencies are described here Parameter Dependencies.

COL_RADIUS_INNER

Inner column radius

Unit: \(\mathrm{m}\)

Type: double

Range: \(> 0\)

Length: 1

COL_RADIUS_OUTER

Outer column radius

Unit: \(\mathrm{m}\)

Type: double

Range: \(> 0\)

Length: 1

CROSS_SECTION_AREA

Is not explicitly specified. Both the inner and outer cross section areas are implicitly given by the volumetric flow rates and either the velocity coefficient or column length

COL_LENGTH

Column length/height (optional if \(\texttt{VELOCITY_COEFF}\) is present, see Section Specification of flow rate / velocity and direction)

Unit: \(\mathrm{m}\)

Type: double

Range: \(> 0\)

Length: 1

VELOCITY_COEFF

Interstitial velocity coefficient of the mobile phase (optional \(\texttt{COL_LENGTH}\) is present, see Section Specification of flow rate / velocity and direction). This input replaces the VELOCITY field, which is used for axial flow models. The distinction is made to emphasize that radial flow models do not incorporate a global velocity but a variable velocity field that depends on the spatial position, for details see Section Radial flow GRM.

Unit: \(\mathrm{m}\,\mathrm{s}^{-1}\)

Type: double

Range: \(\mathbb{R}\)

Length: \(1 / \texttt{NSEC}\)

Group /input/model/unit_XXX/discretization - UNIT_TYPE - RADIAL_GENERAL_RATE_MODEL

NCOL

Number of radial column discretization points

Type: int

Range: \(\geq 1\)

Length: 1

Currently, there is only a first order FV spatial discretization available. Higher order spatial discretizations are planned for the future. Accordingly, the following specifications can be left out for radial flow models.

RECONSTRUCTION

Type of reconstruction method for fluxes

Type: string

Range: \(\texttt{NONE}\)

Length: 1

Parameters specified under flux_restruction_methods can also be ignored.