Brinkman’s Filtration Law and the Stability of the Water-Over-Vapor Systems in Geothermal Reservoirs

The problem of the stability of a layer of water above a layer of vapor separated by a phase transition surface in high-temperature rocks is considered. A mathematical model of the flow with a generalized Brinkman filtration equation is proposed. Dynamic conditions on the interface are derived. The stability of the flow was studied by the method of normal modes. A dispersion equation was obtained, which was investigated analytically and numerically. A criterion for the stability of the flow is found and the characteristic linear size of the most unstable disturbance is determined. The comparison of the obtained results is carried out with the results of the study of stability in the Darcy approximation.