Email this article Nonuniqueness and stability of the water boiling surface in a geothermal reservoir
- Authors: Tsypkin G.G.1
-
Affiliations:
- Institute for Problems in Mechanics of the Russian Academy of Sciences
- Issue: No 5 (2023)
- Pages: 95-102
- Section: Articles
- URL: https://journals.rcsi.science/1024-7084/article/view/135103
- DOI: https://doi.org/10.31857/S1024708423600355
- EDN: https://elibrary.ru/FZUXAM
- ID: 135103
Cite item
Open Access
Access granted
Subscription Access
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.
About the authors
G. G. Tsypkin
Institute for Problems in Mechanics of the Russian Academy of Sciences
Author for correspondence.
Email: tsypkin@ipmnet.ru
Moscow, Russia
References
- Grant M., Bixley P.F. Geothermal reservoir engineering. London: Acad. Press, 2011. 378 p.
- White D.E., Muffler L.J.P., Truesdell A.H. Vapor-dominated hydrothermal systems compared with hot water systems // Econ. Geol. 1971. V. 66. P. 75–97.
- Grant M.A. Geothermal reservoir modeling // Geothermics. 1983. V. 12. P. 251–263.
- Schubert G., Straus J.M. Gravitational stability of water over steam in vapor-dominated geothermal system // J. Geophys. Res. 1980. V. 85. № B11. P. 6505–6512.
- Tsypkin G.G., Il’ichev A.T. Gravitational stability of the water-vapor phase transition interface in geothermal systems // TiPM. 2004. V. 55. P. 183–199.
- Khan Z.H., Pritchard D. Liquid–vapour fronts in porous media: Multiplicity and stability of front positions // Int. J. Heat Mass Transfer. 2013. V. 61. P. 1–17.
- Tsypkin G.G., Calore C. Role of capillary forces in vapour extraction from low permeability, water saturated geothermal reservoir // Geothermics. 2003. V. 32. P. 219–237.
- Li K., Horne R.N. Systematic study of steam–water capillary pressure // Geothermics. 2007. V. 36. P. 558–574.
- Li K., Horne R.N. Estimation of wettability in gas-liquid-rock systems // Geothermics. 2008. V. 37. P. 429–443.
- Tsypkin G.G., Shargatov V.A. Influence of capillary pressure gradient on connectivity of flow through a porous medium // Int. J. Heat Mass Transfer. 2018. V. 127. P. 1053–1063.
- Saffman P.G., Taylor G. The penetration of a fluid into a porous medium or Hele-Shaw cell con1taining a more viscous liquid // Proc. R. Soc. Lond. A 1958. V. 245. P. 312–329.
- Soboleva E.B. Instability Problems and Density-Driven Convection in Saturated Porous Media Linking to Hydrogeology: A Review // Fluids. 2023. V. 36. № 8. 28 p.
Supplementary files
