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 cease 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.
Similar content being viewed by others
REFERENCES
Grant, M. and Bixley, P.F., Geothermal Reservoir Engineering, London: Acad. Press, 2011.
White, D.E., Muffler, L.J.P., and Truesdell, A.H., Vapor-dominated hydrothermal systems compared with hot water systems, Econ. Geol., 1971, vol. 66, pp. 75–97.
Grant, M.A., Geothermal reservoir modeling, Geothermics, 1983, vol. 12, pp. 251–263.
Schubert, G. and Straus, J.M., Gravitational stability of water over steam in vapor-dominated geothermal system, J. Geophys. Res., 1980, vol. 85, no. B11, pp. 6505–6512.
Tsypkin, G.G. and Il’ichev, A.T., Gravitational stability of the water-vapor phase transition interface in geothermal systems, Transp. Porous Media, 2004, vol. 55, pp. 183–199.
Khan, Z.H. and Pritchard, D., Liquid-vapour fronts in porous media: multiplicity and stability of front positions, Int. J. Heat Mass Transfer, 2013, vol. 61, pp. 1–17.
Tsypkin, G.G. and Calore, C., Role of capillary forces in vapour extraction from low permeability, water saturated geothermal reservoir, Geothermics, 2003, vol. 32, pp. 219–237.
Li, K. and Horne, R.N., Systematic study of steam-water capillary pressure, Geothermics, 2007, vol. 36, pp. 558–574.
Li, K. and Horne, R.N., Estimation of wettability in gas-liquid-rock systems, Geothermics, 2008, vol. 37, pp. 429–443.
Tsypkin, G.G. and Shargatov, V.A., Influence of capillary pressure gradient on connectivity of flow through a porous medium, Int. J. Heat Mass Transfer, 2018, vol. 127, pp. 1053–1063.
Saffman, P.G. and Taylor, G., The penetration of a fluid into a porous medium or hele-shaw cell con1taining a more viscous liquid, Proc. R. Soc. London, Ser. A, 1958, vol. 245, pp. 312–329.
Soboleva, E.B., Instability problems and density-driven convection in saturated porous media linking to hydrogeology: a review, Fluids, 2023, vol. 36, no. 8, p. 28.
Funding
This work was supported by the Russian Science Foundation, project no. 21-11-00126.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Rights and permissions
About this article
Cite this article
Tsypkin, G.G. Nonuniqueness and Stability of the Water Boiling Surface in a Geothermal reservoir. Fluid Dyn 58, 919–926 (2023). https://doi.org/10.1134/S0015462823601250
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462823601250