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

G. G. Tsypkin; Цыпкин Г. Г.

doi:10.31857/S1024708423600355

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

Authors: Tsypkin G.G.¹
Affiliations:
1. 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

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Abstract
About the authors
References
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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.

Keywords

geothermal reservoir, boiling surface, capillary pressure, nonuniqueness, stability

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.