# 4.13.3.4. Example: Compound DEM reaction¶

CO combustion:

$\text{CO}(g) + 0.5\text{O}_2 (g) → \text{CO}_2 (g)$

CO2 gasification:

$\text{C}(s) + \text{CO}_2 (g) → 2\text{CO}(g)$

Char combustion:

$\text{C}(s) + 0.5\text{O}_2 (g) → \text{CO}(g)$

Notes:

• Gas phase species names and aliases are defined on the same line.

• Heats of reaction for all reactions are calculated automatically.

• A TFM reaction block is used for the gas phase homogeneous reaction.

• A DEM reaction block is used for gas/solids reactions.

• Reaction constructs are given in one line.

! Gas phase species data
NMAX_g = 3
Species_g(1) = "O2"
Species_Alias_g(1) = "O2"
Species_g(2) = "CO"
Species_Alias_g(2) = "CO"
Species_g(3) = "CO2"
Species_Alias_g(3) = "CO2"
! DES solids phase species data
NMAX_s(1) = 2
Species_s(1,1) = "C(GR) REF ELEMENT"
Species_s(1,2) = "Coal Ash"
Species_Alias_s(1,1) = "C"
Species_Alias_s(1,2) = "Ash"
! Homogeneous gas phase reactions
@(RXNS)
CO_Combustion { chem_eq = "CO + 0.5O2 --> CO2" }
@(END)
! DES Reaction block
@(DES_RXNS)
CO2_Gasification { chem_eq = "2.0C + O2 --> 2CO" }
Char_Combustion { chem_eq = "C + CO2 --> 2CO" }
@(DES_END)


• Coal Ash is not a species included in the thermochemical database and would require that its properties be given in the data file (see Section 8.14 Thermochemical properties).

• One-line reaction constructs are only possible when the heat of reaction is automatically calculated (i.e., the chemical equation is the only input parameter).

## 4.13.3.4.1. Reaction Rates¶

Define chemical reaction rates in user defined function (UDF) files.

• A reaction rate should be given in either usr_rates.f or usr_rates_des.f for each reaction listed in the data file.

• All TFM gas and solids phase reactions as well as homogeneous gas phase reactions for DEM simulations are to be included in usr_rates.f. Reaction rates defined in usr_rates.f must have units of reacted moles per time per volume (i.e., moles/sec/cm3 for CGS units and kmoles/sec/m3 for SI units).

• All discrete phase heterogeneous (particle/gas) reactions are to be included in usr_rates_des.f located in the des subfolder. Reaction rates defined in usr_rates_des.f must have units of reacted moles per time (i.e., moles/sec for CGS units and kmoles/sec for SI units).

Note

Formation and consumption rates are automatically calculated for each species from the reaction rate and chemical equation.

The rate in terms of reacted moles is related to the rates of formation and consumption through the stoichiometric coefficients. For example, consider the homogeneous gas phase reaction of methane combustion:

$\text{CH}_4 + 2\text{O}_2 → \text{CO}_2 + 2\text{H}_2 O$

The rate in terms of reacted moles is related to the rates of formation and consumption as

$\begin{split}rate &= \frac{-r_{CH_4}}{1} (\frac{kmol_{CH_4} / (s \cdot m^3)}{mol_{CH_4}}) = \frac{-r_{O_2}}{2} (\frac{kmol_{O_2} / (s \cdot m^3)}{mol_{O_2}}) \\ &= \frac{r_{CO_2}}{1} (\frac{kmol_{CO_2} / (s \cdot m^3)}{mol_{CO_2}}) = \frac{r_{H_{2}O}}{2} (\frac{kmol_{H_{2}O} / (s \cdot m^3)}{mol_{H_{2}O}})\end{split}$

where $$-r_{CH_4}$$ and $$-r_{O_2}$$ are the rates of consumption of methane and oxygen, and $$r_{CO_2}$$ and $$r_{H_{2}O}$$ are the rates of formation of carbon dioxide and water vapor, respectively.

Each reaction rate is assigned to the variable RATES(rxn_name), where rxn_name is the reaction identifier used in the reaction construct. To minimize input errors when specifying reaction rates, species aliases (SPECIES_ALIAS) defined in the data file should be used in lieu of the associated species index.

For example, if oxygen is defined as gas phase species 2 with an alias of O2, (e.g., SPECIES_ALIAS_g(2)="O2"), when accessing gas phase species data for oxygen (e.g., molecular weight; MW_g), “O2” should be used and not the integer index 2, (e.g, MW_g(O2)).