Nonlocal models of flow in multi-scale porous and fractured media

Abstract : The thesis concerns the models of flow in multiscale fractured media which prove the memory effect at each scale. The analyzed process in these media is self-similar. The necessary and sufficient condition of self-similarity has been proposed so that it is possible to analyze the behavior of media for any number of scales. We analyzed the diffusion equation at each scale and applied the asymptotic homogenization method with the objective to construct the macroscopic model averaged over all scales of heterogeneity. A system of closed recurrent equations for the effective exchange kernels was obtained. The procedure of analytico-numerical solution of this system was developed. We showed a convergence of the results obtained for various numbers of scales to a stable limit behavior. The limit problem for the effective kernels from the recurrent equations obtained for a relatively large number of scales. In addition we analyzed the flow in a single fracture and circular channel immersed in porous reservoir at various Reynolds numbers. The Navier-Stokes equations was solved by the method of two-scale asymptotic method with the objective to obtain the flow equation averaged over the fracture aperture in the presence of inflow through the limits and irregular geometry of walls.
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Mojdeh Rasoulzadeh. Nonlocal models of flow in multi-scale porous and fractured media. Other [cond-mat.other]. Institut National Polytechnique de Lorraine, 2011. English. ⟨NNT : 2011INPL025N⟩. ⟨tel-01749533⟩

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