[Kummi]

Hello Foamers,
My topic of research is to build a 1D mathematical model for simulating the coal pyrolysis in OpenFOAM. I have adopted the pyrolysis 1D solver based on FireFOAM in OpenFOAM-2.1.1. This 1D model supports basic data of the coke oven conditions as input and solves the heat transfer equation for both solid and gas phase by describing the reaction kinetics using the Arrhenius equation. For the initial case, the Arrhenius reaction rate for the simple reaction "Coal = H2O + CO2 + CH4 + Char" has to be calculated using the formula below,

dm/dt = ∑(i=1 to N)[Ai*e(-E/RT) (Mi-mi)] --> (1)

The above Arrhenius relation for volatile gas release (from coal) is described in terms of mass fraction of all volatile chemical species (mi), where Mi, Ai, E, R and T are the final yields, frequency factor, activation energy, gas constant and coal temperature, respectively.

But, in openFOAM, the calculation for the Solid Arrhenius reaction rate described in $FOAM_SRC/thermophysicalModels/solid/reaction/reactionRate/ solidArrheniusReactionRate/solidArrheniusReactionRateI.H as

ak *= exp(-Ta_/T)
which can be formulated as, A*exp(-E/RT) → (2).

I am not sure whether the expression in solidArrheniusReactionRateI.H [Equ. (2)] really goes well and same as above Equ .(1). Because the terms dm/dt and (Mi-mi) are clearly missing explicitly.

On the whole, can someone explain me whether the solid Arrhenius reaction rates mentioned in Equs. (1) and (2) are relatively the same or not? If no, kindly assist me to solve this problem.

[Kummi]

Following the above message,

In addition,
I have looked into the code (OpenFOAM 2.1.1) and it seems that the source of pyrolysis modeling is built-in reactingOneDim.C file [~regionModels/pyrolysisModels/reactingOneDim.C], which solves continuity, species and energy equations. In the energy equation, the source terms are implemented with chemistrySh (total heat release rate), phiQr (radiative flux) and phiGas (total gas mass flux released due to pyrolysis). The phiGas was calculated based on reaction rate of pyrolysis gaseous species [RRg] and sensible enthalpy [gasHs], correlated with ODESolidChemistryModel.H file [$FOAM_SRC//thermophysicalModels/solidChemistryModel/ODESolidChemistryModel]. Based on it, the irreversible Solid Arrhenius Reaction is solved by the solid chemistry model in “chemistryProperties” file as shown in the attachment.

As per my insight view, it looks like that the reaction rate of species are calculated in ODESolidChemistryModel.H and called back in source file reactingOneDim.C to predict the phiGas (total gas mass flux released due to pyrolysis).
However, the involvement of mass fraction of species is not explicitly mentioned in the Arrhenius equation as stated above – which makes me quite confused and think whether my approach is right or wrong.

Certain tips or word of advice will be more helpful. Thank you !!!