Parameterizations of immiscible two-phase flow in porous media

A fundamental variable characterizing immiscible two-phase flow in porous media is the wetting saturation, which ratio between pore volume filled with fluid and total volume. More generally, this comes from a specific choice of coordinates on some underlying space, domain variables that can be used to express volumetric rate. The mathematical structure allows for introduction other containing same information, but are more convenient theoretical point view. We introduce along these lines polar where angle plays role similar saturation. derive relations new based Euler homogeneity theorem. formulate coordinate-free fashion using differential forms. Finally, we discuss interpret co-moving velocity terms representation.