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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 or lumped_rate_model_with_pores or general_rate_model, 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 reconstruction methods can also be ignored.