Modeling and simulation of two-phase flows in a porous random media is a highly challenging task due the non-linearity of the wetting process, the time and space scales at stake and the very large spatial variability and anisotropy of the intrinsic permeability. In the particular case of an injection problem being statistically invariant for any rotation around the axis of the well a coupled 3D/rotation-invariant probabilistic model is proposed following the methodology introduced in [1] and [2]. The idea of a variational coupling between a probabilistic local model and a deterministic or probabilistic model is developed here in the context of a coupling along a surface and not over a volume. 3D/2D coupling is also considered. The implementation in a general purpose Finite Element Code is then addressed and illustrated in the context of Risk assessment of geological storage of carbon dioxide.