Direct elaboration processes of composite materials, such as LCM processes, induce transient two-phase flows within multi-scale fibrous media. Based on stabilized finite element simulations of such flows at the fibre scale, statistical descriptions of the responses of randomly generated representative volume elements are proposed. For modelling resin infusion at the preform scale, upscaled properties are identified through data science analyses. With this objective of homogenization, this work addresses in particular the influence of boundary conditions, the resultant of capillary effects, and 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.