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Particle Model

Group /input/model/unit_XXX/particle_type_XXX

PAR_POROSITY

Particle porosity of all particle types or for each particle type

Type: double

Range: \((0,1]\)

Length: 1

PAR_RADIUS

Particle radius of all particle types or for each particle type

Unit: \(\mathrm{m}\)

Type: double

Range: \(>0\)

Length: 1

PAR_CORERADIUS

Particle core radius of all particle types or for each particle type (optional, defaults to \(\mathrm{0}\)) Is only applied when \(\texttt{HAS_PORE_DIFFUSION} == 1\).

Unit: \(\mathrm{m}\)

Type: double

Range: \([0, \texttt{PAR_RADIUS})\)

Length: 1

PORE_ACCESSIBILITY

Pore accessibility factor of each component in each particle type (optional, defaults to \(1\)). Note: Should not be used in combination with any binding model!

Type: double

Range: \((0, 1]\)

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

PORE_ACCESSIBILITY_MULTIPLEX

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

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

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

Type: int

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

Length: 1

HAS_FILM_DIFFUSION

Specifies whether transport into the particles is limited by film diffusion kinetics.

Type: int

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

Length: 1

FILM_DIFFUSION

Film diffusion coefficients for each component of each particle type, required if \(\texttt{HAS_FILM_DIFFUSION} == 1\), otherwise ignored.

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

Type: double

Range: \(\geq 0\)

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

FILM_DIFFUSION_MULTIPLEX

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

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

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

Type: int

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

Length: 1

HAS_PORE_DIFFUSION

Specifies whether radial transport within the particle pores is limited by pore diffusion kinetics.

Type: int

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

Length: 1

PORE_DIFFUSION

Effective particle diffusion coefficients of each component in each particle type, required if \(\texttt{HAS_PORE_DIFFUSION} == 1\), otherwise ignored.

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

Type: double

Range: \(> 0\)

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

PORE_DIFFUSION_MULTIPLEX

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

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

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

Type: int

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

Length: 1

HAS_SURFACE_DIFFUSION

Specifies whether radial transport within the particle is supported but limited by surface diffusion kinetics.

Type: int

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

Length: 1

SURFACE_DIFFUSION

Particle surface diffusion coefficients of each bound state of each component in each particle type. Ooptional, defaults to all 0 \(\mathrm{m}_{\mathrm{SP}}^{2}\,\mathrm{s}^{-1}\), required if \(\texttt{HAS_SURFACE_DIFFUSION} == 1\), otherwise ignored.

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

Type: double

Range: \(\geq 0\)

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

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

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

  2. Component-dependent, section-dependent; length of \(\texttt{SURFACE_DIFFUSION}\) is \(\texttt{NBOUND} \cdot \texttt{NSEC}\); ordering is section-major

Type: int

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

Length: 1

PAR_GEOM

Specifies the particle geometry for all or each particle type. Valid values are \(\texttt{SPHERE}\), \(\texttt{CYLINDER}\), \(\texttt{SLAB}\). Optional, defaults to \(\texttt{SPHERE}\). Is only applied when \(\texttt{HAS_PORE_DIFFUSION} == 1\).

Type: string

Range: \(\{\texttt{SPHERE}, \texttt{CYLINDER}, \texttt{SLAB} \}\)

Length: 1

ADSORPTION_MODEL

Specifies the type of binding model of each particle type (or of all particle types if length is \(1\))

Type: string

Range: Binding models

Length: 1

NBOUND

Number of bound states for each component in each particle type in type-major ordering

Type: int

Range: \(\geq 0\)

Length: \(\texttt{NCOMP}\)

REACTION_MODEL

Specifies the type of reaction model of each particle type (or of all particle types if length is \(1\)). The model is configured in the subgroup \(\texttt{reaction_particle}\), or \(\texttt{reaction_particle_XXX}\) in case of disabled multiplexing.

Type: string

Range: See Section Reaction models

Length: 1

INIT_CP

Initial concentrations for each component in the bead liquid phase (optional, \(\texttt{INIT_C}\) is used if left out). The length of this field can be \(\texttt{NCOMP}\) (same values for each particle type) or \(\texttt{NPARTYPE} \cdot \texttt{NCOMP}\) Values for each particle type can only be given when \(\texttt{ADSORPTION_MODEL_MULTIPLEX}\) is \(0\). The ordering is type-major.

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

Type: double

Range: \(\geq 0\)

Length: \(\texttt{NCOMP}\)

INIT_CS

Initial concentrations for each bound state of each component in the bead solid phase. If \(\texttt{ADSORPTION_MODEL_MULTIPLEX}\) is \(0\), values for each particle type are required in type-component-major ordering (length is \(\texttt{NTOTALBND}\)). If \(\texttt{ADSORPTION_MODEL_MULTIPLEX}\) is \(1\), values for one particle type are required in component-major ordering (length is \(\sum_{i = 0}^{\texttt{NCOMP} - 1} \texttt{NBND}_i\)).

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

Type: double

Range: \(\geq 0\)

\{PARAM_NAME\}_PARTYPE_DEPENDENT

Only required for parameter sensitivities of the respective parameter, defaults to 1. Specifies whether or not a parameter is the same across particle types or ‘dependent’ on the particle type. In the first case, the parameter sensitivity should be computed jointly across particle types, by specifying this field as 0. Can be specified for any of the above parameters except NCOMP and NBOUND. For more information on parameter sensitivities, see Spatial discretization methods.

Type: int

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

Length: 1

Group /input/model/unit_XXX/particle_type_XXX/discretization

PAR_DISC_TYPE

Specifies the discretization scheme inside the particles for all or each particle type. Valid values are \(\texttt{EQUIDISTANT}\), \(\texttt{EQUIVOLUME}\), and \(\texttt{USER_DEFINED}\).

Type: string

Length: 1

PAR_DISC_VECTOR

Node coordinates for the cell boundaries (ignored if \(\texttt{PAR_DISC_TYPE} \neq \texttt{USER_DEFINED}\)). The coordinates are relative and have to include the endpoints \(0\) and \(1\). They are later linearly mapped to the true radial range \([r_{c,j}, r_{p,j}]\). The coordinates for each particle type are appended to one long vector in type-major ordering.

Type: double

Range: \([0,1]\)

Length: \(\texttt{NPAR}_ + 1\)

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 Parameter Sensitivities.

SPATIAL_METHOD

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

Type: string

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

Length: 1

Discontinuous Galerkin

PAR_POLYDEG

DG particle (radial) polynomial degree. Optional, defaults to 3. The total number of particle (radial) discrete points is given by (PARPOLYDEG + 1 ) * PAR_NELEM.

Type: int

Range: \(\geq 1\)

Length: 1

PAR_NELEM

Number of particle (radial) discretization DG elements for each particle type. For the particle discretization, it is usually most performant to fix PAR_NELEM = 1 and to increase the polynomial degree for more accuracy.

Type: int

Range: \(\geq 1\)

Length: 1

PAR_GSM

Specifies whether Galerkin spectral method should be used (as opposed to discontinuous variant, DGSEM), optional, defaults to 1 if PAR_NELEM == 1. Always recommended.

Type: int

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

Length: 1

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

Finite Volumes

NCELLS

Number of particle (radial) discretization points for each particle type

Type: int

Range: \(\geq 1\)

Length: 1

FV_BOUNDARY_ORDER

Order of accuracy of outer particle boundary condition. Optional, defaults to \(2\).

Type: int

Range: \(\{ 1,2 \}\)

Length: 1

OPTIMIZE_PAR_BANDWIDTH

Only available if both particle and bulk spatial methods are all FV Determines whether the surface diffusion parameters \(\texttt{SURFACE_DIFFUSION}\) are fixed if the parameters are zero. If the parameters are fixed to zero (\(\texttt{FIX_ZERO_SURFACE_DIFFUSION} = 1\), \(\texttt{SURFACE_DIFFUSION} = 0\)), the parameters must not become non-zero during this or subsequent simulation runs. The internal data structures are optimized for a more efficient simulation. This field is optional and defaults to \(0\) (optimization disabled in favor of flexibility).

Type: int

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

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