.. _parameter_dependencies_config: Parameter Dependencies ====================== A description on parameter dependencies from a modeling perspective is provided under :ref:`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_POLYDEG`` must additionally be set (see below). ================ =========================================================== ============= **Type:** string **Range:** :math:`\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_DEP`` is set together with DG bulk discretization. Required in that case only; ignored for FV. ============= ========================= ============= **Type:** int **Range:** :math:`\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:** :math:`\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** .. math:: \begin{aligned} p_{dep} &= p_{dep} \cdot b \ |p_{on}^x| \end{aligned} Here, :math:`p_{dep}` is the dependent parameter and :math:`p_{on}` is the parameter it depends on. ``COL_DISPERSION_DEP_BASE`` Base :math:`b` of the power law parameter dependence. Optional, defaults to :math:`1.0` ================ ============================= ============= **Type:** double **Range:** :math:`\mathbb{R}` **Length:** 1 ================ ============================= ============= ``COL_DISPERSION_DEP_EXPONENT`` Exponent :math:`x` of the power law parameter dependence ================ ============================= ============= **Type:** double **Range:** :math:`\mathbb{R}` **Length:** 1 ================ ============================= ============= ``COL_DISPERSION_DEP_ABS`` Specifies whether or not the absolute value should be computed. Optional, defaults to :math:`1` ============= =========================== ============= **Type:** int **Range:** :math:`\{0, 1\}` **Length:** 1 ============= =========================== ============= **Van Deemter** The van Deemter parameter dependence reproduces the classical van Deemter plate-height correlation :math:`H(v) = A + B / |v| + C\, |v|` and applies it to a dispersion-type parameter via the standard equilibrium-dispersive-model relation :math:`D_\mathrm{ax}(v) = H(v)\, v / 2`. Concretely, .. math:: \begin{aligned} p_{dep} &= p_{dep} \cdot \left( A\, |p_{on}| + B + C\, p_{on}^2 \right) / 2 \end{aligned} Here, :math:`p_{dep}` is the dependent parameter (e.g. ``COL_DISPERSION``) and :math:`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 :math:`1`) directly evaluates :math:`D_\mathrm{ax}(v) = H(v)\, v / 2` for a local, velocity-dependent plate height :math:`H(v)`. Unlike ``POWER_LAW``, the absolute value of :math:`p_{on}` is always taken (there is no ``_ABS`` flag). ``COL_DISPERSION_DEP_A`` Coefficient :math:`A` (eddy diffusion / flow-independent term) of the van Deemter parameter dependence ================ ============================= ============= **Type:** double **Range:** :math:`\mathbb{R}` **Length:** 1 ================ ============================= ============= ``COL_DISPERSION_DEP_B`` Coefficient :math:`B` (longitudinal molecular diffusion term) of the van Deemter parameter dependence ================ ============================= ============= **Type:** double **Range:** :math:`\mathbb{R}` **Length:** 1 ================ ============================= ============= ``COL_DISPERSION_DEP_C`` Coefficient :math:`C` (mass transfer resistance term) of the van Deemter parameter dependence ================ ============================= ============= **Type:** double **Range:** :math:`\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 :math:`\texttt{SURFACE_DIFFUSION}` on the particle liquid salt component (i.e. component with index 0). Valid dependencies are: - :math:`\texttt{NONE}` Original parameter is used unmodified. - :math:`\texttt{LIQUID_SALT_EXPONENTIAL}` Original parameter is modified by exponential law of liquid phase salt concentration. - :math:`\texttt{LIQUID_SALT_POWER}` Original parameter is modified by power law of liquid phase salt concentration. - :math:`\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:** :math:`1 / \texttt{NPARTYPE}` ================ ========================================= ``SURFACE_DIFFUSION_EXPFACTOR`` Factor :math:`\texttt{p1}` in exponential law particle surface diffusion relation :math:`D_{s, i, m} = \tilde{D}_{s, i, m} p_{1, i, m} exp \left(p_{2, i, m} c_{0}^{p} \right)`, where :math:`\tilde{D}_{s, i, m}` is the original surface diffusion coefficient. Only required if :math:`\texttt{SURFACE_DIFFUSION_DEP}` is :math:`\texttt{LIQUID_SALT_EXPONENTIAL}`. ================ ========================= =================================== **Type:** double **Range:** :math:`\geq 0` **Length:** :math:`\texttt{NBOUND}` ================ ========================= =================================== ``SURFACE_DIFFUSION_EXPFACTOR`` :math:`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 :math:`\tilde{D}_{s, i, m}` is the original surface diffusion coefficient and :math:`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 :math:`\texttt{SURFACE_DIFFUSION_DEP}` is :math:`\texttt{LIQUID_SALT_COLLOIDAL_AFFINITY}`. ================ ============================= =================================== **Type:** double **Range:** :math:`\mathbb{R}` **Length:** :math:`\texttt{NBOUND}` ================ ============================= =================================== ``SURFACE_DIFFUSION_EXPARGMULT`` Factor :math:`\texttt{p2}` in exponential law particle surface diffusion relation :math:`D_{s, i, m} = \tilde{D}_{s, i, m} p_{1, i, m} exp \left(p_{2, i, m} c_{0}^{p} \right)` where :math:`\tilde{D}_{s, i, m}` is the original surface diffusion coefficient. Only required if :math:`\texttt{SURFACE_DIFFUSION_DEP}` is :math:`\texttt{LIQUID_SALT_EXPONENTIAL}`. ================ ============================= =================================== **Type:** double **Range:** :math:`\mathbb{R}` **Length:** :math:`\texttt{NBOUND}` ================ ============================= =================================== ``SURFACE_DIFFUSION_POWFACTOR`` Factor :math:`\texttt{p1}` in power law particle surface diffusion relation :math:`D_{s, i, m} = \tilde{D}_{s, i, m} p_{1, i, m} \left( c_{0}^{p} \right)^{p_{2, i, m}}` where :math:`\tilde{D}_{s, i, m}` is the original surface diffusion coefficient. Only required if :math:`\texttt{SURFACE_DIFFUSION_DEP}` is :math:`\texttt{LIQUID_SALT_POWER}`. ================ ========================= =================================== **Type:** double **Range:** :math:`\geq 0` **Length:** :math:`\texttt{NBOUND}` ================ ========================= =================================== ``SURFACE_DIFFUSION_POWEXP`` Fjactor :math:`\texttt{p2}` in power law particle surface diffusion relation :math:`D_{s, i, m} = \tilde{D}_{s, i, m} p_{1, i, m} \left( c_{0}^{p} \right)^{p_{2, i, m}}` where :math:`\tilde{D}_{s, i, m}` is the original surface diffusion coefficient. Only required if :math:`\texttt{SURFACE_DIFFUSION_DEP}` is :math:`\texttt{LIQUID_SALT_POWER}`. ================ ============================= =================================== **Type:** double **Range:** :math:`\mathbb{R}` **Length:** :math:`\texttt{NBOUND}` ================ ============================= =================================== ``SURFACE_DIFFUSION_LOGKEQFACTOR`` Factor :math:`\texttt{p1}` in colloidal affinity law particle surface diffusion relation :math:`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 :math:`\tilde{D}_{s, i, m}` is the original surface diffusion coefficient and :math:`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 :math:`\texttt{SURFACE_DIFFUSION_DEP}` is :math:`\texttt{LIQUID_SALT_COLLOIDAL_AFFINITY}`. ================ ============================= =================================== **Type:** double **Range:** :math:`\mathbb{R}` **Length:** :math:`\texttt{NBOUND}` ================ ============================= =================================== ``SURFACE_DIFFUSION_LOGKEQEXP`` Factor :math:`\texttt{p2}` in colloidal affinity law particle surface diffusion relation :math:`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 :math:`\tilde{D}_{s, i, m}` is the original surface diffusion coefficient and :math:`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 :math:`\texttt{SURFACE_DIFFUSION_DEP}` is :math:`\texttt{LIQUID_SALT_COLLOIDAL_AFFINITY}`. ================ ============================= =================================== **Type:** double **Range:** :math:`\mathbb{R}` **Length:** :math:`\texttt{NBOUND}` ================ ============================= =================================== ``SURFACE_DIFFUSION_LOGKEQCONST`` Factor :math:`\texttt{p3}` in colloidal affinity law particle surface diffusion relation :math:`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 :math:`\tilde{D}_{s, i, m}` is the original surface diffusion coefficient and :math:`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 :math:`\texttt{SURFACE_DIFFUSION_DEP}` is :math:`\texttt{LIQUID_SALT_COLLOIDAL_AFFINITY}`. ================ ============================= =================================== **Type:** double **Range:** :math:`\mathbb{R}` **Length:** :math:`\texttt{NBOUND}` ================ ============================= =================================== Dependence on external functions ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Dependence on external functions is currently only implemented for binding model parameters, as detailed in :ref:`dependence-on-external-function_bind`.