The conditional methodology, which has been proven very successful in modelling of turbulent reactive flows, is extended to simulate reactive flows through porous media. Conditional models take into account variations in gas species concentrations between pores and inter-pore locations allowing for a more accurate (as compared to unconditional models) and consistent treatment of heterogeneous reactions. Different versions of conditional models have been formulated [1-4]. Some of the models were specifically designed for consistent modelling of multi-cascade processes of reactive transport in complex porous media. One of the conditional models, PDCMC, was formulated for and applied to simulation of CH4 replacement by CO2 in coal and demonstrated a good agreement with the experimental data [3].
While conditional models represent effective tools for evaluation of reactive transport in porous media, the problem of determining the model coefficients is not fully resolved within the conditional methods. A general approach, which allows us to derive analytical expressions for the transport coefficients in porous media (both conditional and unconditional), is suggested to resolve this problem [5]. This approach combines two classical approaches -- the effective medium approximation and the macroscopic continuum model analogous to the Fokker-Planck equation -- into single, general and powerful methodology, which can deal with irregular porous media while taking into account percolation effects. There is no need for excessive detail or computational effort. A brief overview of conditional methods developed for reacting flows in porous media is given in [6]
Propagation and stability of curved flames in porous combustible media have been studied in the context of Underground Coal Gasification (UCG,[7]). A theory for reverse flame propagation, which explains a number of experimentally observed phenomena, has been suggested [8]. The theory demonstrates that only near-stoichiometric flames are stable and relates the formation of a channel in the reverse combustion linking to this stability condition. The developed approach also involved a comparison of different regimes of both co-current and counter-current combustion [9] and for the elaboration of the optimal regimes [10].
In addition, stability of the evaporation front in porous media is studied in [11] and the theory that describes two possible regimes for flame propagation (upstream and downstream) in a channel with combustible walls has also been introduced and shown to qualitatively agree with experiments [12].