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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:

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

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

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

  4. 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). Each method has it’s own set of input fields. While both methods approximate the same solution to the same underlying model, they may differ in terms of computational performance. With our currently implemented variants of FV and DG, FV perform better for solutions with steep gradients or discontinuities, while DG can be much faster for rather smooth solutions. For the same number of discrete points, DG will generally be slower but often 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: 1

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