| We develop a number of models for a variety of Filtration Combustion (FC) processes, including forward and reverse combustion. The models are based on a Pore-Network (PN) representation of the porous medium. Numerical schemes are developed to solve the highly-coupled differential equations describing conservation laws in the pore-space and the solid matrix. A novel moving-coordinate method based on front-tracking is also developed to model long-time behavior.; Simulations of 2-D forward FC show that the heterogeneity of the porous medium has significant effects, depending on the values of parameters, such as mass diffusivity, thermal conductivity and injection velocity. The effects depend on the length scales for diffusion, heat conduction and pore-size correlation. Heat losses lead to multiple steady states in agreement with recent findings. Simulation of FC in a layered system shows that the coupling of front propagation in the layers depends on the permeability ratio. Such information is useful for assessing the effect of heterogeneity on methods for oil recovery. The effect of the density of the in-situ fuel was investigated by using a percolation-like model in a gasless system and determining the percolation threshold in the fraction of pores containing fuel for sustained propagation. This was analyzed as a function of parameters, such as thermal conductivity.; Simulations of reverse FC in both 2-D and 3-D networks showed the formation of fingering patterns, in general agreement with experiments in Hele-Shaw cells. The influence of two characteristic length scales was analyzed. While consistent with previous results, more complex interactions were also observed. Numerical examples on 3-D reverse FC are reported. The similarity between the fingering patterns to those using Diffusion-Limited-Aggregation (DLA) led us to simpler and accurate stochastic models for pattern description.; To upscale the results to the continuum scale, we proposed two hybrid methods, in which continuum models are used on either side of the reactive front region, and are coupled to each other through a PN model, resolving the frontal region. The validation and efficiency of the models were checked with several numerical examples. Advantages and shortcomings were discussed. |
