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Parameter Dependencies¶
A description on parameter dependencies from a modeling perspective is provided under Parameter Dependencies.
Parameter-Parameter Dependencies¶
Group /input/model/unit_XXX¶
COL_DISPERSION_DEP
Parameter dependence of column dispersion on the interstitial velocity. Available for all 1D units and both the FV and DG discretization. For the DG discretization,
DISPERSION_SPATIAL_DEPENDENCE_POLYDEGmust additionally be set (see below).
Type: string
Range: \(\texttt{POWER_LAW}, \texttt{VAN_DEEMTER}\)
Length: 1
DISPERSION_SPATIAL_DEPENDENCE_POLYDEG
Quadrature polynomial degree used to evaluate the position-dependent (velocity-dependent) dispersion integral when
COL_DISPERSION_DEPis set together with DG bulk discretization. Required in that case only; ignored for FV.
Type: int
Range: \(\geq 0\)
Length: 1
Group /input/model/unit_XXX/particle_type_YYY¶
FILM_DIFFUSION_DEP
Parameter dependence of film diffusion on the interstitial velocity. Available For all 1D unit operations and both the FV and DG discretizations. For the DG discretization there might be a loss of accuracy since the current implementation only supports a pointwise/”mass-lumped” evaluation.
Type: string
Range: \(\texttt{POWER_LAW}, \texttt{VAN_DEEMTER}\)
Length: 1
Correlations¶
Different types of parameter correlations can be applied.
The following correlations can be used for all parameter-parameter dependencies, but we specify the required input fields only for COL_DISPERSION_DEP, for the sake of conciseness.
Power Law
Here, \(p_{dep}\) is the dependent parameter and \(p_{on}\) is the parameter it depends on.
COL_DISPERSION_DEP_BASE
Base \(b\) of the power law parameter dependence. Optional, defaults to \(1.0\)
Type: double
Range: \(\mathbb{R}\)
Length: 1
COL_DISPERSION_DEP_EXPONENT
Exponent \(x\) of the power law parameter dependence
Type: double
Range: \(\mathbb{R}\)
Length: 1
COL_DISPERSION_DEP_ABS
Specifies whether or not the absolute value should be computed. Optional, defaults to \(1\)
Type: int
Range: \(\{0, 1\}\)
Length: 1
Van Deemter
The van Deemter parameter dependence reproduces the classical van Deemter plate-height correlation \(H(v) = A + B / |v| + C\, |v|\) and applies it to a dispersion-type parameter via the standard equilibrium-dispersive-model relation \(D_\mathrm{ax}(v) = H(v)\, v / 2\). Concretely,
Here, \(p_{dep}\) is the dependent parameter (e.g. COL_DISPERSION) and \(p_{on}\) is the parameter it depends on (e.g. the local interstitial velocity).
Using this dependence with the associated base parameter left at its default (dimensionless placeholder \(1\)) directly evaluates \(D_\mathrm{ax}(v) = H(v)\, v / 2\) for a local, velocity-dependent plate height \(H(v)\).
Unlike POWER_LAW, the absolute value of \(p_{on}\) is always taken (there is no _ABS flag).
COL_DISPERSION_DEP_A
Coefficient \(A\) (eddy diffusion / flow-independent term) of the van Deemter parameter dependence
Type: double
Range: \(\mathbb{R}\)
Length: 1
COL_DISPERSION_DEP_B
Coefficient \(B\) (longitudinal molecular diffusion term) of the van Deemter parameter dependence
Type: double
Range: \(\mathbb{R}\)
Length: 1
COL_DISPERSION_DEP_C
Coefficient \(C\) (mass transfer resistance term) of the van Deemter parameter dependence
Type: double
Range: \(\mathbb{R}\)
Length: 1
Parameter-State Dependencies¶
Currently, the dependence of surface diffusion on the particle liquid salt component is the only available parameter-state dependence and is only implemented for the arrow-head optimzed (see FV_ARROW_HEAD_OPTIMIZATION) GRM unit.
Group /input/model/unit_XXX/particle_type_YYY¶
SURFACE_DIFFUSION_DEP
Parameter dependence of \(\texttt{SURFACE_DIFFUSION}\) on the particle liquid salt component (i.e. component with index 0). Valid dependencies are:
\(\texttt{NONE}\) Original parameter is used unmodified.
\(\texttt{LIQUID_SALT_EXPONENTIAL}\) Original parameter is modified by exponential law of liquid phase salt concentration.
\(\texttt{LIQUID_SALT_POWER}\) Original parameter is modified by power law of liquid phase salt concentration.
\(\texttt{LIQUID_SALT_COLLOIDAL_AFFINITY}\) Original parameter is modified by colloidal binding affinity based on liquid phase salt concentration.
Optional: If left out, no parameter dependence is assumed and the original surface diffusion coefficients are used unmodified.
Type: string
Length: \(1 / \texttt{NPARTYPE}\)
SURFACE_DIFFUSION_EXPFACTOR
Factor \(\texttt{p1}\) in exponential law particle surface diffusion relation \(D_{s, i, m} = \tilde{D}_{s, i, m} p_{1, i, m} exp \left(p_{2, i, m} c_{0}^{p} \right)\), where \(\tilde{D}_{s, i, m}\) is the original surface diffusion coefficient. Only required if \(\texttt{SURFACE_DIFFUSION_DEP}\) is \(\texttt{LIQUID_SALT_EXPONENTIAL}\).
Type: double
Range: \(\geq 0\)
Length: \(\texttt{NBOUND}\)
SURFACE_DIFFUSION_EXPFACTOR\(D_{s, i, m} = \tilde{D}_{s, i, m} \left[ p_{4, i, m} \left( k_{i, m} \left( c_{0}^{p} \right) \right)^{p_{5, i, m}} p_{6, i, m} exp \left( p_{7, i, m} k_{i, m} \left( c_{0}^{p} \right) \right) \right]\) where \(\tilde{D}_{s, i, m}\) is the original surface diffusion coefficient and \(k_{i, m} \left( c_{0}^{p} \right) = p_{1, i, m}\left( c_{0}^{p} \right)^{p_{2, i, m}} + p_{3, i, m}\). Only required if \(\texttt{SURFACE_DIFFUSION_DEP}\) is \(\texttt{LIQUID_SALT_COLLOIDAL_AFFINITY}\).
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NBOUND}\)
SURFACE_DIFFUSION_EXPARGMULT
Factor \(\texttt{p2}\) in exponential law particle surface diffusion relation \(D_{s, i, m} = \tilde{D}_{s, i, m} p_{1, i, m} exp \left(p_{2, i, m} c_{0}^{p} \right)\) where \(\tilde{D}_{s, i, m}\) is the original surface diffusion coefficient. Only required if \(\texttt{SURFACE_DIFFUSION_DEP}\) is \(\texttt{LIQUID_SALT_EXPONENTIAL}\).
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NBOUND}\)
SURFACE_DIFFUSION_POWFACTOR
Factor \(\texttt{p1}\) in power law particle surface diffusion relation \(D_{s, i, m} = \tilde{D}_{s, i, m} p_{1, i, m} \left( c_{0}^{p} \right)^{p_{2, i, m}}\) where \(\tilde{D}_{s, i, m}\) is the original surface diffusion coefficient. Only required if \(\texttt{SURFACE_DIFFUSION_DEP}\) is \(\texttt{LIQUID_SALT_POWER}\).
Type: double
Range: \(\geq 0\)
Length: \(\texttt{NBOUND}\)
SURFACE_DIFFUSION_POWEXP
Fjactor \(\texttt{p2}\) in power law particle surface diffusion relation \(D_{s, i, m} = \tilde{D}_{s, i, m} p_{1, i, m} \left( c_{0}^{p} \right)^{p_{2, i, m}}\) where \(\tilde{D}_{s, i, m}\) is the original surface diffusion coefficient. Only required if \(\texttt{SURFACE_DIFFUSION_DEP}\) is \(\texttt{LIQUID_SALT_POWER}\).
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NBOUND}\)
SURFACE_DIFFUSION_LOGKEQFACTOR
Factor \(\texttt{p1}\) in colloidal affinity law particle surface diffusion relation \(D_{s, i, m} = \tilde{D}_{s, i, m} \left[ p_{4, i, m} \left( k_{i, m} \left( c_{0}^{p} \right) \right)^{p_{5, i, m}} p_{6, i, m} exp \left( p_{7, i, m} k_{i, m} \left( c_{0}^{p} \right) \right) \right]\) where \(\tilde{D}_{s, i, m}\) is the original surface diffusion coefficient and \(k_{i, m} \left( c_{0}^{p} \right) = p_{1, i, m}\left( c_{0}^{p} \right)^{p_{2, i, m}} + p_{3, i, m}\). Only required if \(\texttt{SURFACE_DIFFUSION_DEP}\) is \(\texttt{LIQUID_SALT_COLLOIDAL_AFFINITY}\).
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NBOUND}\)
SURFACE_DIFFUSION_LOGKEQEXP
Factor \(\texttt{p2}\) in colloidal affinity law particle surface diffusion relation \(D_{s, i, m} = \tilde{D}_{s, i, m} \left[ p_{4, i, m} \left( k_{i, m} \left( c_{0}^{p} \right) \right)^{p_{5, i, m}} p_{6, i, m} exp \left( p_{7, i, m} k_{i, m} \left( c_{0}^{p} \right) \right) \right]\) where \(\tilde{D}_{s, i, m}\) is the original surface diffusion coefficient and \(k_{i, m} \left( c_{0}^{p} \right) = p_{1, i, m}\left( c_{0}^{p} \right)^{p_{2, i, m}} + p_{3, i, m}\). Only required if \(\texttt{SURFACE_DIFFUSION_DEP}\) is \(\texttt{LIQUID_SALT_COLLOIDAL_AFFINITY}\).
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NBOUND}\)
SURFACE_DIFFUSION_LOGKEQCONST
Factor \(\texttt{p3}\) in colloidal affinity law particle surface diffusion relation \(D_{s, i, m} = \tilde{D}_{s, i, m} \left[ p_{4, i, m} \left( k_{i, m} \left( c_{0}^{p} \right) \right)^{p_{5, i, m}} p_{6, i, m} exp \left( p_{7, i, m} k_{i, m} \left( c_{0}^{p} \right) \right) \right]\) where \(\tilde{D}_{s, i, m}\) is the original surface diffusion coefficient and \(k_{i, m} \left( c_{0}^{p} \right) = p_{1, i, m}\left( c_{0}^{p} \right)^{p_{2, i, m}} + p_{3, i, m}\). Only required if \(\texttt{SURFACE_DIFFUSION_DEP}\) is \(\texttt{LIQUID_SALT_COLLOIDAL_AFFINITY}\).
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NBOUND}\)
Dependence on external functions¶
Dependence on external functions is currently only implemented for binding model parameters, as detailed in Dependence on external function.