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In this study, the conditional moment closure approach, which is proven to be very useful for modelling of reactions in turbulent flows, is extended to characterise adsorbing, desorbing or reacting flows in porous media. A complete specification of the porous distance conditioned moment closure model, which is formulated in terms of single-conditioned expectations, is presented. The closure of the model equations is obtained assuming the diffusion approximation for fluxes of the reactive species. The model simulates complex multi-cascade processes of convective and diffusive transport of species between pores in a continuous and consistent manner and is a generalisation of dual (or triple) porosity concept. The model addresses the major difficulty of describing transport, entrapment and sorption processes in porous media with fractal properties, where distant transport occurs in the largest pores or fractures, while the adsorbing or desorbing surface is mainly allocated in small pores. The model is able to simulate various regimes of methane replacement by CO 2 in a coal sample, which makes it useful for optimising the design and parameters of enhanced coal bed methane recovery operations. It is demonstrated that the power-low decrease in downstream methane concentration, which has been observed experimentally, can be accurately reproduced by the model.

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