Shock–like structure of phase-change flow in porous media

Shock-like features of phase-change flows in porous media are explained, based on the generalized Darcy model. The flow field consists of two-phase zones of parabolic/hyperbolic type as well as adjacent or imbedded single-phase zones of either parabolic (superheated, compressible vapour) or elliptic (subcooled, incompressible liquid) type. Within the two-phase zones or at the two-phase/single-phase interfaces, there may be steep gradients in saturation and temperature approaching shock-like behaviour when the dissipative effects of capillarity and heat-conduction are negligible. Illustrative of these shocked, multizone flow-structures are the transient condensing flows in porous media, for which a self-similar, shock-preserving (Rankine–Hugoniot) analysis is presented.

Experiments on Transient Condensing Flow through a Porous Medium

A cold, initially-dry column of sand receives a sudden inflow of dry saturated Freon vapor (CCl3F) from a high-pressure high-temperature reservoir. Condensation occurs as the hot vapor penetrates into the cold sand, resulting in a co-current liquid/vapor flow. The axial distribution of condensate is wave-like with a (Buckley/Leverett-type) saturation-jump on the leading edge. Temperature and pressure profiles are in good agreement with a simple integral analysis which includes the essential features of the process: vapor-phase mass transfer, fluid/solid energy transfer by condensation, and liquid-phase flooding of the pore volume. The reported ensemble of experiments confirms the theoretical model over a broad range of saturation (from nearly dry to liquid-full) and over a broad range of Reynolds number (from Darcy flow to inertia-dominated flow). The considered problem is exemplary of the phase-change flows which occur in a number of geologic applications: containment of underground nuclear tests, steam stimulation of oil fields, geothermal energy, and in situ combustion processes.