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# Reaction models¶

## Externally dependent reaction models¶

Some reaction models have a variant that can use external sources as specified /input/model/external/ (also see Section Dependence on external function). For the sake of brevity, only the standard variant of those reaction models is specified below. In order to obtain the format for the externally dependent variant, first replace the reaction model name XXX by EXT_XXX. Each parameter $$p$$ (except for stoichiometric and exponent matrices) depends on a (possibly distinct) external source in a polynomial way:

\begin{aligned} p(T) &= p_{\texttt{TTT}} T^3 + p_{\texttt{TT}} T^2 + p_{\texttt{T}} T + p. \end{aligned}

Thus, a parameter XXX_YYY of the standard reaction model variant is replaced by the four parameters EXT_XXX_YYY, EXT_XXX_YYY_T, EXT_XXX_YYY_TT, and EXT_XXX_YYY_TTT. Since each parameter can depend on a different external source, the dataset EXTFUN (not listed in the standard variants below) should contain a vector of 0-based integer indices of the external source of each parameter. The ordering of the parameters in EXTFUN is given by the ordering in the standard variant. However, if only one index is passed in EXTFUN, this external source is used for all parameters.

Note that parameter sensitivities with respect to column radius, column length, particle core radius, and particle radius may be wrong when using externally dependent reaction models. This is caused by not taking into account the derivative of the external profile with respect to column position.

## Multiple particle types¶

The group that contains the parameters of a reaction model in unit operation with index XXX reads /input/model/unit_XXX/reaction_particle. This is valid for models with a single particle type. If a model has multiple particle types, it may have a different reaction model in each type. The parameters are then placed in the group /input/model/unit_XXX/reaction_particle_YYY instead, where YYY denotes the index of the particle type.

Note that, in any case, /input/model/unit_XXX/reaction_particle_000 contains the parameters of the first (and possibly sole) particle type. This group also takes precedence over a possibly existing /input/model/unit_XXX/adsorption_particle group.

## Group /input/model/unit_XXX/reaction - REACTION_MODEL = MASS_ACTION_LAW¶

MAL_KFWD_BULK

Forward rate constants for bulk volume reactions (available for external functions)

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

MAL_KBWD_BULK

Backward rate constants for bulk volume reactions (available for external functions)

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

MAL_KFWD_LIQUID

Forward rate constants for particle liquid phase reactions (available for external functions)

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

MAL_KBWD_LIQUID

Backward rate constants for particle liquid phase reactions (available for external functions)

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

MAL_KFWD_SOLID

Forward rate constants for particle solid phase reactions (available for external functions)

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

MAL_KBWD_SOLID

Backward rate constants for particle solid phase reactions (available for external functions)

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

MAL_STOICHIOMETRY_BULK

Stoichiometric matrix of bulk volume reactions as $$\texttt{NCOMP} \times \texttt{NREACT}$$ matrix in row-major storage

 Type: double Length: $$\texttt{NCOMP} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_BULK_FWD

Forward exponent matrix of bulk volume reactions as $$\texttt{NCOMP} \times \texttt{NREACT}$$ matrix in row-major storage (optional, calculated from $$\texttt{MAL_STOICHIOMETRY_BULK}$$ by default)

 Type: double Length: $$\texttt{NCOMP} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_BULK_BWD

Backward exponent matrix of bulk volume reactions as $$\texttt{NCOMP} \times \texttt{NREACT}$$ matrix in row-major storage (optional, calculated from $$\texttt{MAL_STOICHIOMETRY_BULK}$$ by default)

 Type: double Length: $$\texttt{NCOMP} \cdot \texttt{NREACT}$$

MAL_STOICHIOMETRY_LIQUID

Stoichiometric matrix of particle liquid phase reactions as $$\texttt{NCOMP} \times \texttt{NREACT}$$ matrix in row-major storage

 Type: double Length: $$\texttt{NCOMP} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_LIQUID_FWD

Forward exponent matrix of particle liquid phase reactions as $$\texttt{NCOMP} \times \texttt{NREACT}$$ matrix in row-major storage (optional, calculated from $$\texttt{MAL_STOICHIOMETRY_LIQUID}$$ by default)

 Type: double Length: $$\texttt{NCOMP} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_LIQUID_BWD

Backward exponent matrix of particle liquid phase reactions as $$\texttt{NCOMP} \times \texttt{NREACT}$$ matrix in row-major storage (optional, calculated from $$\texttt{MAL_STOICHIOMETRY_LIQUID}$$ by default)

 Type: double Length: $$\texttt{NCOMP} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_LIQUID_FWD_MODSOLID

Forward solid phase modifier exponent matrix of particle liquid phase reactions as $$\texttt{NTOTALBND} \times \texttt{NREACT}$$ matrix in row-major storage (optional, defaults to all 0)

 Type: double Length: $$\texttt{NTOTALBND} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_LIQUID_BWD_MODSOLID

Backward solid phase modifier exponent matrix of particle liquid phase reactions as $$\texttt{NTOTALBND} \times \texttt{NREACT}$$ matrix in row-major storage (optional, defaults to all 0)

 Type: double Length: $$\texttt{NTOTALBND} \cdot \texttt{NREACT}$$

MAL_STOICHIOMETRY_SOLID

Stoichiometric matrix of particle solid phase reactions as $$\texttt{NTOTALBND} \times \texttt{NREACT}$$ matrix in row-major storage

 Type: double Length: $$\texttt{NTOTALBND} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_SOLID_FWD

Forward exponent matrix of particle solid phase reactions as $$\texttt{NTOTALBND} \times \texttt{NREACT}$$ matrix in row-major storage (optional, calculated from $$\texttt{MAL_STOICHIOMETRY_SOLID}$$ by default)

 Type: double Length: $$\texttt{NTOTALBND} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_SOLID_BWD

Backward exponent matrix of particle solid phase reactions as $$\texttt{NTOTALBND} \times \texttt{NREACT}$$ matrix in row-major storage (optional, calculated from $$\texttt{MAL_STOICHIOMETRY_SOLID}$$ by default)

 Type: double Length: $$\texttt{NTOTALBND} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_SOLID_FWD_MODLIQUID

Forward liquid phase modifier exponent matrix of particle solid phase reactions as $$\texttt{NCOMP} \times \texttt{NREACT}$$ matrix in row-major storage (optional, defaults to all 0)

 Type: double Length: $$\texttt{NCOMP} \cdot \texttt{NREACT}$$

MAL_EXPONENTS_SOLID_BWD_MODLIQUID

Backward liquid phase modifier exponent matrix of particle solid phase reactions as $$\texttt{NCOMP} \times \texttt{NREACT}$$ matrix in row-major storage (optional, defaults to all 0)

 Type: double Length: $$\texttt{NCOMP} \cdot \texttt{NREACT}$$