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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:
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). 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 calculateNELEM
= \(\lfloor\)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.