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Frustum Flow Column 1D

Group /input/model/unit_XXX - UNIT_TYPE - FRUSTUM_COLUMN_MODEL_1D

UNIT_TYPE

Specifies the type of unit operation model

Type: string

Range: \(\texttt{FRUSTUM_COLUMN_MODEL_1D}\)

Length: 1

NCOMP

Number of chemical components in the chromatographic medium

Type: int

Range: \(\geq 1\)

Length: 1

COL_RADIUS_INNER

Smaller column radius

Unit: \(\mathrm{m}\)

Type: double

Range: \(> 0\)

Length: 1

COL_RADIUS_OUTER

Larger column radius

Unit: \(\mathrm{m}\)

Type: double

Range: \(> 0\)

Length: 1

COL_LENGTH

Column/bed length. NOT optional for the frustum model.

Unit: \(\mathrm{m}\)

Type: double

Range: \(> 0\)

Length: 1

COL_POROSITY

Column porosity

Type: double

Range: \((0,1]\)

Length: 1

NPARTYPE

Number of particle types.

Type: int

Range: \(\geq 1\)

Length: 1

PAR_TYPE_VOLFRAC

Volume fractions of the particle types. The volume fractions can be set for all axial cells together or for each individual axial cell. For each cell, the volume fractions have to sum to \(1\). In case of a spatially inhomogeneous setting, the data is expected in cell-major ordering and the \(\texttt{SENS_SECTION}\) field is used for indexing the axial cell when specifying parameter sensitivities. This field is optional in case of only one particle type.

Type: double

Range: \([0,1]\)

Length: \(\texttt{NPARTYPE} / \texttt{NCOL} \cdot \texttt{NPARTYPE}\)

VELOCITY_COEFF

Used only to indicate flow direction, which is taken from the sign. Positive sign corresponds to flow from the smaller COL_RADIUS_INNER to the larger COL_RADIUS_OUTER column radius

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

Type: double

Range: \(\mathbb{R}\)

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

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

REACTION_MODEL_BULK

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

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_STATE

Full state vector for initialization (optional, \(\texttt{INIT_C}\), \(\texttt{INIT_CP}\), and \(\texttt{INIT_CS}\) will be ignored; if length is \(2\texttt{NDOF}\), then the second half is used for time derivatives). The ordering of the state vector is defined in Unit Operation state vector ordering.

Unit: \(various\)

Type: double

Range: \(\mathbb{R}\)

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

Group /input/model/unit_XXX/particle_type_XXX

Each particle type is specified in another subgroup particle_type_XXX, see Particle Model.

Group /input/model/unit_XXX/discretization - UNIT_TYPE - FRUSTUM_COLUMN_MODEL_1D

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 a 1st order upwind FV method for frustum flow chromatography

SPATIAL_METHOD

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

Type: string

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

Length: 1

NCELLS

Number of axial column discretization points, i.e. FV cells

Type: int

Range: \(\geq 1\)

Length: 1

The following FV discretization parameters are only required if particles are present:

GS_TYPE

Type of Gram-Schmidt orthogonalization, see IDAS guide Section 4.5.7.3, p. 41f. A value of \(0\) enables classical Gram-Schmidt, a value of 1 uses modified Gram-Schmidt.

Type: int

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

Length: 1

MAX_KRYLOV

Defines the size of the Krylov subspace in the iterative linear GMRES solver (0: \(\texttt{MAX_KRYLOV} = \texttt{NCOL} \cdot \texttt{NCOMP} \cdot \texttt{NPARTYPE}\))

Type: int

Range: \(\{0, \dots, \texttt{NCOL} \cdot \texttt{NCOMP} \cdot \texttt{NPARTYPE} \}\)

Length: 1

MAX_RESTARTS

Maximum number of restarts in the GMRES algorithm. If lack of memory is not an issue, better use a larger Krylov space than restarts.

Type: int

Range: \(\geq 0\)

Length: 1

SCHUR_SAFETY

Schur safety factor; Influences the tradeoff between linear iterations and nonlinear error control; see IDAS guide Section~2.1 and 5.

Type: double

Range: \(\geq 0\)

Length: 1

When using the FV method, we generally recommend specifying USE_MODIFIED_NEWTON = 0 in Group /solver/time_integrator, i.e. to use the full Newton method to solve the linear system within the time integrator. For further information on discretization parameters, see also Flux reconstruction methods (FV specific)), and Nonlinear solver for consistent initialization.