Transition to instability of the interface in geothermal systems

High-temperature geothermal reservoir in porous media is under consideration, consisting of two high-permeability layers, which are separated by a low-permeability stratum. The thermodynamic conditions are assumed to imply that the upper and lower high-permeability layers are filled in by water and by vapour, respectively. In these circumstances the low-permeability stratum possesses the phase transition interface, separating domains occupied by water and vapour. The stable stationary regimes of vertical phase flow between water and vapour layers in the low-permeability stratum may exist. Stability of such regimes where the heavier fluid is located over the lighter one is supported by a heat transfer, caused by a temperature gradient in the Earth's interior. We give the classification of the possible types of transition to instability of the vertical flows in such a system under the condition of smallness of the advective heat transfer in comparison with the conductive one. It is found that in the non-degenerate case there exist three different scenarios of the onset of instability of the stationary vertical phase transition flows. Two of them are accompanied by the bifurcations of the destabilizing vertical flow, leading to appearance of horizontally non-homogeneous regimes with non-constant shape of the interface. The bifurcations correspond to the simple resonance and 1:1-resonance, which typically arise in reversible systems.