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# General Rate Model¶

## Group /input/model/unit_XXX - UNIT_TYPE - GENERAL_RATE_MODEL¶

UNIT_TYPE

Specifies the type of unit operation model

 Type: string Range: $$\texttt{GENERAL_RATE_MODEL}$$ 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 of each particle type (or of all particle types if length is $$1$$)

 Type: string Range: Binding models Length: $$1 / \texttt{NPARTYPE}$$

ADSORPTION_MODEL_MULTIPLEX

Multiplexing mode of $$\texttt{ADSORPTION_MODEL}$$. If set to $$0$$, each particle type has a different binding model and the length of $$\texttt{ADSORPTION_MODEL}$$ is $$\texttt{NPARTYPE}$$. If set to $$1$$, all particle types share the same binding model and the length of $$\texttt{ADSORPTION_MODEL}$$ is $$1$$. This field is optional and inferred from the length of $$\texttt{ADSORPTION_MODEL}$$ if left out.

 Type: int Range: $$\{0, 1\}$$ 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

REACTION_MODEL_PARTICLES

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: $$1 / \texttt{NPARTYPE}$$

REACTION_MODEL_PARTICLES_MULTIPLEX

Multiplexing mode of $$\texttt{REACTION_MODEL_PARTICLES}$$. If set to $$0$$, each particle type has a different reaction model and the length of $$\texttt{REACTION_MODEL_PARTICLES}$$ is $$\texttt{NPARTYPE}$$. If set to $$1$$, all particle types share the same reaction model and the length of $$\texttt{REACTION_MODEL_PARTICLES}$$ is $$1$$. This field is optional and inferred from the length of $$\texttt{REACTION_MODEL_PARTICLES}$$ if left out.

 Type: int Range: $$\{0, 1\}$$ 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_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: $$\texttt{NCOMP} / \texttt{NPARTYPE} \cdot \texttt{NCOMP}$$

INIT_Q

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: $$\geq 0$$

INIT_STATE

Full state vector for initialization (optional, $$\texttt{INIT_C}$$, $$\texttt{INIT_CP}$$, 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

COL_POROSITY

Column porosity

 Type: double Range: $$(0,1]$$ Length: 1

FILM_DIFFUSION

Film diffusion coefficients for each component of each particle type

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, type-independent, section-independent; length of $$\texttt{FILM_DIFFUSION}$$ is $$\texttt{NCOMP}$$

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

3. Component-dependent, type-dependent, section-independent; length of $$\texttt{FILM_DIFFUSION}$$ is $$\texttt{NCOMP} \cdot \texttt{NPARTYPE}$$; ordering is type-major

4. Component-dependent, type-dependent, section-dependent; length of $$\texttt{FILM_DIFFUSION}$$ is $$\texttt{NCOMP} \cdot \texttt{NPARTYPE} \cdot \texttt{NSEC}$$; ordering is section-type-major

 Type: int Range: $$\{0, \dots, 3 \}$$ Length: 1

PAR_POROSITY

Particle porosity of all particle types or for each particle type

 Type: double Range: $$(0,1]$$ Length: $$1 / \texttt{NPARTYPE}$$

PAR_RADIUS

Particle radius of all particle types or for each particle type

Unit: $$\mathrm{m}$$

 Type: double Range: $$>0$$ Length: $$1 / \texttt{NPARTYPE}$$

PAR_CORERADIUS

Particle core radius of all particle types or for each particle type (optional, defaults to $$\mathrm{m}$$)

Unit: $$\mathrm{m}$$

 Type: double Range: $$[0, \texttt{PAR_RADIUS})$$ Length: $$1 / \texttt{NPARTYPE}$$

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, type-independent, section-independent; length of $$\texttt{PORE_ACCESSIBILITY}$$ is $$\texttt{NCOMP}$$

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

3. Component-dependent, type-dependent, section-independent; length of $$\texttt{PORE_ACCESSIBILITY}$$ is $$\texttt{NCOMP} \cdot \texttt{NPARTYPE}$$; ordering is type-major

4. Component-dependent, type-dependent, section-dependent; length of $$\texttt{PORE_ACCESSIBILITY}$$ is $$\texttt{NCOMP} \cdot \texttt{NPARTYPE} \cdot \texttt{NSEC}$$; ordering is section-type-major

 Type: int Range: $$\{0, \dots, 3 \}$$ Length: 1

PAR_DIFFUSION

Effective particle diffusion coefficients of each component in each particle type

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

 Type: double Range: $$\geq 0$$ Length: see $$\texttt{PAR_DIFFUSION_MULTIPLEX}$$

PAR_DIFFUSION_MULTIPLEX

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

1. Component-dependent, type-independent, section-independent; length of $$\texttt{PAR_DIFFUSION}$$ is $$\texttt{NCOMP}$$

2. Component-dependent, type-independent, section-dependent; length of $$\texttt{PAR_DIFFUSION}$$ is $$\texttt{NCOMP} \cdot \texttt{NSEC}$$; ordering is section-major

3. Component-dependent, type-dependent, section-independent; length of $$\texttt{PAR_DIFFUSION}$$ is $$\texttt{NCOMP} \cdot \texttt{NPARTYPE}$$; ordering is type-major

4. Component-dependent, type-dependent, section-dependent; length of $$\texttt{PAR_DIFFUSION}$$ is $$\texttt{NCOMP} \cdot \texttt{NPARTYPE} \cdot \texttt{NSEC}$$; ordering is section-type-major

 Type: int Range: $$\{0, \dots, 3 \}$$ Length: 1

PAR_SURFDIFFUSION

Particle surface diffusion coefficients of each bound state of each component in each particle type (optional, defaults to all 0 $$\mathrm{m}_{\mathrm{SP}}^{2}\,\mathrm{s}^{-1}$$)

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

 Type: double Range: $$\geq 0$$ Length: see $$\texttt{PAR_SURFDIFFUSION_MULTIPLEX}$$

PAR_SURFDIFFUSION_MULTIPLEX

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

1. Component-dependent, type-independent, section-independent; length of $$\texttt{PAR_SURFDIFFUSION}$$ is $$\texttt{NBND}$$; ordering is component-major

2. Component-dependent, type-independent, section-dependent; length of $$\texttt{PAR_SURFDIFFUSION}$$ is $$\texttt{NBND} \cdot \texttt{NSEC}$$; ordering is section-component-major

3. Component-dependent, type-dependent, section-independent; length of $$\texttt{PAR_SURFDIFFUSION}$$ is $$\texttt{NTOTALBND}$$; ordering is type-component-major

4. Component-dependent, type-dependent, section-dependent; length of $$\texttt{PAR_SURFDIFFUSION}$$ is $$\texttt{NTOTALBND} \cdot \texttt{NSEC}$$; ordering is section-type-component-major

 Type: int Range: $$\{0, \dots, 3 \}$$ 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

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: $$\texttt{NPARTYPE} / \texttt{NCOL} \cdot \texttt{NPARTYPE}$$

## Group /input/model/unit_XXX/discretization - UNIT_TYPE - GENERAL_RATE_MODEL¶

NCOL

Number of axial column discretization cells

 Type: int Range: $$\geq 1$$ Length: 1

NPARTYPE

Number of particle types. Optional, inferred from the length of $$\texttt{NPAR}$$ or $$\texttt{NBOUND}$$ if left out.

 Type: int Range: $$\geq 1$$ Length: 1

NPAR

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

 Type: int Range: $$\geq 1$$ Length: $$1$$ / $$\texttt{NPARTYPE}$$

NBOUND

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

 Type: int Range: $$\geq 0$$ Length: $$\texttt{NCOMP}$$ / $$\texttt{NPARTYPE} \cdot \texttt{NCOMP}$$

PAR_GEOM

Specifies the particle geometry for all or each particle type. Valid values are $$\texttt{SPHERE}$$, $$\texttt{CYLINDER}$$, $$\texttt{SLAB}$$. Optional, defaults to $$\texttt{SPHERE}$$.

 Type: string Length: $$1$$ / $$\texttt{NPARTYPE}$$

PAR_DISC_TYPE

Specifies the discretization scheme inside the particles for all or each particle type. Valid values are $$\texttt{EQUIDISTANT_PAR}$$, $$\texttt{EQUIVOLUME_PAR}$$, and $$\texttt{USER_DEFINED_PAR}$$.

 Type: string Length: $$1$$ / $$\texttt{NPARTYPE}$$

PAR_DISC_VECTOR

Node coordinates for the cell boundaries (ignored if $$\texttt{PAR_DISC_TYPE} \neq \texttt{USER_DEFINED_PAR}$$). 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: $$\sum_i (\texttt{NPAR}_i + 1)$$

PAR_BOUNDARY_ORDER

Order of accuracy of outer particle boundary condition. Optional, defaults to $$2$$.

 Type: int Range: $$\{ 1,2 \}$$ Length: 1

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

RECONSTRUCTION

Type of reconstruction method for fluxes

 Type: string Range: $$\texttt{WENO}$$ Length: 1

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

FIX_ZERO_SURFACE_DIFFUSION

Determines whether the surface diffusion parameters $$\texttt{PAR_SURFDIFFUSION}$$ are fixed if the parameters are zero. If the parameters are fixed to zero ($$\texttt{FIX_ZERO_SURFACE_DIFFUSION} = 1$$, $$\texttt{PAR_SURFDIFFUSION} = 0$$), 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

For further discretization parameters, see also Flux reconstruction methods, and Nonlinear solver for consistent initialization.