  We consider immiscible and incompressible two-phase flow in porous media
under steady-state conditions using a dynamic pore network model. We focus on
the fluctuations in a Representative Elementary Area (REA), with the aim to
demonstrate that the statistical distributions of the volumetric flow rate and
the saturation within the REA become independent of the size of the entire
model when the model is large enough. This independence is a necessary
condition for developing a local statistical theory for the flow, which in turn
opens for the possibility to formulate a description at scales large enough for
the typical pore size to be negligible using differential equations.
