Non-Darcy two-phase flow in fractured rocks

The paper recalls the main cases in which the two-phase flow in fractured and porous rocks does not follow the classical extension of Darcy’s law to multiphase flow. In particular, here are highlighted some applications in the field of hydrogeology and of hydrocarbon reservoir engineering. Apart from the case (typical also of single-phase flow) of “high-velocity” flow, where inertial forces cannot be neglected with respect to viscous ones, the paper analyzes the typical cases of two-phase flow, where the interactions between the two phases, both in motion (coupling effect), can influence the flow behavior. It is also recalled that Darcy’s law does not hold in case of two-phase dispersed flow. Generally, it is pointed out that both natural porous media and fractured rocks may have very different features of the porous network. Natural porous media range from cemented sandstones to unconsolidated sand or loose gravel, with large variation of the geometry and interconnection of the porous network. Fractured rocks are characterized by a matrix (occasionally porous and permeable, depending on lithological types) intersected by a network of fractures whose opening can range between a few microns to several centimeters or more. In both cases, the dimensions of the flow channels may be very different, and hence the ratios among the forces driving the fluid flow (i.e., viscous, gravitational, inertial and capillary forces). It would therefore be of practical interest to study the laws of fluid flow in the above cases not based on the geological distinction between porous media and fractured rocks, but on the values of the ratio between viscous, gravitational, inertial and capillary forces driving fluid flow inside the porous or fractured network. Finally, it is pointed out that, notwithstanding the apparent differences between porous and fractured media, the study of fluid flow behavior inside both media can be performed with the same physical approach.