**
You're reading the documentation for a development version.
For the latest released version, please have a look at v4.4.0.
**

# Lumped Rate Model Without Pores¶

## Group /input/model/unit_XXX - UNIT_TYPE = LUMPED_RATE_MODEL_WITHOUT_PORES¶

For information on model equations, refer to Lumped rate model without pores (LRM).

`UNIT_TYPE`

Specifies the type of unit operation model

Type:string

Range:\(\texttt{LUMPED_RATE_MODEL_WITHOUT_PORES}\)

Length:1

`NCOMP`

Number of chemical components in the chromatographic medium

Type:int

Range:\(\geq 1\)

Length:1

`ADSORPTION_MODEL`

Specifies the type of binding model

Type:string

Range:See Section Binding models

Length:1

`NBOUND`

Number of bound states for each component

Type:int

Range:\(\geq 0\)

Length:\(\texttt{NCOMP}\)

`REACTION_MODEL`

Specifies the type of reaction model of the combined bulk and particle volume. The model is configured in the subgroup \(\texttt{reaction}\).

Type:string

Range:See Section Reaction models

Length:1

`INIT_C`

Initial concentrations for each component in the bulk mobile phase

Unit:\(\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\)

Type:double

Range:\(\geq 0\)

Length:\(\texttt{NCOMP}\)

`INIT_Q`

Initial concentrations for each bound state of each component in the bead solid phase in component-major ordering

Unit:\(\mathrm{mol}\,\mathrm{m}_{\mathrm{SP}}^{-3}\)

Type:double

Range:\(\geq 0\)

Length:\(\texttt{NTOTALBND}\)

`INIT_STATE`

Full state vector for initialization (optional, \(\texttt{INIT_C}\) and \(\texttt{INIT_Q}\) will be ignored; if length is \(2\texttt{NDOF}\), then the second half is used for time derivatives)

Unit:\(various\)

Type:double

Range:\(\mathbb{R}\)

Length:\(\texttt{NDOF} / 2\texttt{NDOF}\)

`COL_DISPERSION`

Axial dispersion coefficient

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

Type:double

Range:\(\geq 0\)

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

`COL_DISPERSION_MULTIPLEX`

Multiplexing mode of \(\texttt{COL_DISPERSION}\). Determines whether \(\texttt{COL_DISPERSION}\) is treated as component- and/or section-independent. This field is optional. When left out, multiplexing behavior is inferred from the length of \(\texttt{COL_DISPERSION}\). Valid modes are:

Component-independent, section-independent; length of \(\texttt{COL_DISPERSION}\) is \(1\)

Component-dependent, section-independent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NCOMP}\)

Component-independent, section-dependent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NSEC}\)

Component-dependent, section-dependent; length of \(\texttt{COL_DISPERSION}\) is \(\texttt{NCOMP} \cdot \texttt{NSEC}\); ordering is section-major

Type:int

Range:\(\{0, \dots, 3 \}\)

Length:1

`COL_LENGTH`

Column length

Unit:\(\mathrm{m}\)

Type:double

Range:\(> 0\)

Length:1

`TOTAL_POROSITY`

Total porosity

Type:double

Range:\([0,1]\)

Length:1

`VELOCITY`

Interstitial velocity of the mobile phase (optional if \(\texttt{CROSS_SECTION_AREA}\) is present, see Section Specification of flow rate / velocity and direction)

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

Type:double

Range:\(\mathbb{R}\)

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

`CROSS_SECTION_AREA`

Cross section area of the column (optional if \(\texttt{VELOCITY}\) is present, see Section Specification of flow rate / velocity and direction)

Unit:\(\mathrm{m}^{2}\)

Type:double

Range:\(>0\)

Length:1

## Group /input/model/unit_XXX/discretization - UNIT_TYPE = LUMPED_RATE_MODEL_WITHOUT_PORES¶

`USE_ANALYTIC_JACOBIAN`

Determines whether analytically computed Jacobian matrix (faster) is used (value is 1) instead of Jacobians generated by algorithmic differentiation (slower, value is 0)

Type:int

Range:\(\{0, 1\}\)

Length:1

## Spatial discretization - Numerical Methods¶

CADET offers two spatial discretization methods: Finite Volumes (FV) and Discontinuous Galerkin (DG). Only the input fields for the chosen method need to be specified. While both methods approximate the same solution to the same underlying model, they may differ in terms of computational performance. Generally, FV is more performant for solutions with steep gradients or discontinuities, while DG excels for rather smooth solutions. We note that DG is only faster in the sense that less spatial discrete points are required to achieve the same accuracy as FV. For the same number of discrete points, DG will be slower, but more accurate. For further information on the choice of discretization methods and their parameters, see Spatial discretization methods.

`SPATIAL_METHOD`

Spatial discretization method. Optional, defaults to \(\texttt{FV}\)

Type:string

Range:\(\{\texttt{FV}, \texttt{DG}\}\)

Length:1

## Finite Volumes (Default)¶

`NCOL`

Number of axial column discretization points

Type:int

Range:\(\geq 1\)

Length:1

`RECONSTRUCTION`

Type of reconstruction method for fluxes only (only needs to be specified for FV)

Type:string

Range:\(\texttt{WENO}\)

Length:1

For further discretization parameters, see also Flux reconstruction methods (FV specific)), and Nonlinear solver for consistent initialization.

## Discontinuous Galerkin¶

`POLYDEG`

DG polynomial degree. Optional, defaults to 4 and \(N_d \in \{3, 4, 5\}\) is recommended. The total number of axial discrete points is given by (

`POLYDEG`

+ 1 ) *`NELEM`

Type:int

Range:\(\geq 1\)

Length:1

`NELEM`

Number of axial column discretization DG cellselements. The total number of axial discrete points is given by (

`POLYDEG`

+ 1 ) *`NELEM`

Type:int

Range:\(\geq 1\)

Length:1

`NCOL`

Number of axial discrete points. Optional and ignored if

`NELEM`

is defined. Otherwise, used to calculate`NELEM`

= \(\lfloor\)`NCOL`

/ (`POLYDEG`

+ 1 ) \(\rfloor\)

Type:int

Range:\(\geq 1\)

Length:1

`EXACT_INTEGRATION`

Specifies the DG integration variant. Optional, defaults to 0

Type:int

Range:\(\{0, 1\}\)

Length:1For further discretization parameters, see also Nonlinear solver for consistent initialization.