Nonuniqueness and stability of the water boiling surface in a geothermal reservoir

Abstract

The stability of the boiling surface of water at rest in high-temperature rock, when the domain of ​​water is located above the domain of vapor is investigated. It is shown that the solution is not unique and there are two positions of the interface. As the parameters change, the solutions approach each other and the solutions seases to exist. The normal mode method was used to study the stability of the positions of the interface. A dispersion equation was obtained, which was studied numerically and analytically. It is shown that the transition to instability occurs with a decrease in pressure in the vapor region or an increase in pressure in the water region. Bifurcation diagrams are presented, illustrating the merging and nonexistence of solutions, and parts of the branches corresponding to stable and unstable flow regimes are highlighted.