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Radial Flow Column 1D¶
Group /input/model/unit_XXX - UNIT_TYPE - RADIAL_COLUMN_MODEL_1D¶
UNIT_TYPE
Specifies the type of unit operation model
Type: string
Range: \(\texttt{RADIAL_COLUMN_MODEL_1D}\)
Length: 1
NCOMP
Number of chemical components in the chromatographic medium
Type: int
Range: \(\geq 1\)
Length: 1
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
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
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
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
VELOCITYfield, 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. Specifically, the velocity coefficient here is defined as \(\frac{Q}{2 \pi L \varepsilon_c}\), for details see Section Radial flow GRM.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:
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
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)
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 - RADIAL_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 radial 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.