This thesis aims at numerically simulating gas flows in porous matrices with micro-sized pores. We study the influence of hydrodynamic slip phenomena that appear when the characteristic dimension of micro pores is characterized by Knudsen numbers between Kn = 0.01 and Kn = 0.1.The thesis consists of five chapters followed by a conclusion in which we present some perspectives for further studies. Chapter I is the preliminary work of thesis that turned into complementary approaches. The principle of periodic homogenization methods is first exposed. We present then two methods in the Fourier space: the stress approach and the strain approach. The extension of these methods for solving flows governed by the Stokes equation is described in what follows. Applications to flows through networks of cylinders, subjected to no slip or slip condition, are then discussed. Two techniques for modeling transport phenomena in porous media saturated by a mono-component fluid are presented in the second chapter. The first is based on the method of asymptotic expansions, also known as homogenization method, based on the concept of separation of scales. It is explained that the process consists of three steps: local description, localization and macroscopic description. The second technique is based on the method of averaging at the level of a representative elementary volume (REV). The starting point of this method is based on the equations of Continuum Mechanics and theorems giving the averaged expressions of all operators involved in a transport equation. We show that it extends easily to gas flows in micro porous media. After a short presentation of the commercial software used, we present the spatial convergence studies carried out and we compare our solutions with the results of the literature in Chapter III. Various geometries are considered (plane to 3D geometries made of cubes or spheres), but these comparisons are limited to isothermal flows. The effect of slip on the permeability in micro porous media is discussed in Chapter IV. The resulting formalism of the periodic homogenization structures is used for numerical simulation of isothermal gas in various geometries of increasing complexity. The permeabilities are determined by calculating the spatial averages of velocity fields, solutions of the Stokes equations. The values obtained by imposing no slip conditions are compared with first order slip conditions. We discuss the relative increase in permeability due to slip according to the geometry of the pores. In Chapter V, we present the solutions for anisothermal flows and we study the effect of slip on the effective conductivity in 2D and 3D microporous media. In this chapter, we solve the Navier-Stokes and energy equations by imposing symmetry conditions in one or two directions. The intrinsic mean velocity and temperature fields are calculated from these local solutions. We consider cases where the local thermal equilibrium condition can be considered as satisfied and other corresponding to a non-local thermal equilibrium (NLTE). We determine the dispersion conductivity based on the Péclet number and show the influence of velocity slip on longitudinal and transverse components for various porosities and slip lengths. In NLTE cases, the macroscopic fluid-to-solid heat transfer coefficient is also calculated
