Direct elaboration processes of composite materials, such as LCM, involve transient two-phase flows within multi-scale fibrous media. Based on stabilised finite element simulations of such flows at the fibre scale, statistical descriptions of the impregnation in randomly generated representative volume elements are proposed. For modelling resin infusion at the preform scale, homogenised properties are identified in both saturated and transient regimes, with assessment of the influence of boundary conditions and flow regimes on the flow dynamics in both fully and partially saturated regimes. An explicit stochastic permeability is first proposed for stationary regimes. Then, capillary pressures and local saturation dynamics are identified for transient two-phase flows with surface tension effects. Eventually, identification of the length-scales at play which have never been established so far leads to draw some limits on the validity of homogenization process, depending on both geometry and physics.