- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Evolution of a gas current injected into a curved axisymmetric porous channel

Peter Castellucci*

Radha Boya

Lin Ma

Igor L. Chernyavsky and Oliver E. Jensen

  • *Contact author: peter.castellucci@manchester.ac.uk
PDF

Phys. Rev. Fluids 11, 103801 – Published 21 October, 2026

DOI: https://doi.org/10.1103/dffm-sv4s

Abstract

We investigate gas injection into axisymmetric water-saturated porous channels with Gaussian and parabolic profiles as idealized models of underground gas storage in dome-shaped anticlines. Exploiting the slenderness of each channel, we derive an evolution equation for the gas-liquid interface using a composite asymptotic approximation that accommodates large channel slopes and has a simplified small-slope form describing spreading in weakly curved channels. In the high gas-mobility limit, in contrast with flat planar channels, buoyancy influences the dynamics through different mechanisms in each geometry. For gas injected steadily into a Gaussian channel, buoyancy can continually affect the flow due to the attenuation of the gas velocity caused by axisymmetry. In parabolic channels, the increasing channel slope ensures that buoyancy eventually influences the flow at a timescale depending on injection rate and fluid properties. Asymptotic analysis of the parabolic-channel flow reveals five temporal regimes, each with multiple spatial regions and a distinct spreading rate, reflecting the evolving spatiotemporal competition between injection and buoyancy. Initially, a thin film of gas spreads along the upper boundary; the channel slope and elongation of the film then generate a hydrostatic pressure gradient, which strengthens until buoyancy arrests the upper contact line and thickens the film. Beneath the film, liquid then drains until the interface flattens under buoyancy. Analytical solutions of reduced-order models capture interface evolution and contact-line motion through each regime and are validated against full numerical simulations. These results have implications for subsurface hydrogen and CO2 storage, where a horizontal interface that advances vertically enhances both safety and storage efficiency.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. R. Kushnir, A. Ullmann, and A. Dayan, Thermodynamic models for the temperature and pressure variations within adiabatic caverns of compressed air energy storage plants, J. Energy Resour. Technol. 134, 021901 (2012).
  2. P. Dudfield and A. Woods, On the periodic injection of fluid into, and its extraction from, a porous medium for seasonal heat storage, J. Fluid Mech. 707, 467 (2012).
  3. D. Zivar, S. Kumar, and J. Foroozesh, Underground hydrogen storage: A comprehensive review, Int. J. Hydr. Energy 46, 23436 (2021).
  4. R. Kushnir, A. Ullmann, and A. Dayan, Thermodynamic and hydrodynamic response of compressed air energy storage reservoirs: A review, Rev. Chem. Engng 28, 123 (2012).
  5. N. S. Muhammed, B. Haq, D. Al Shehri, A. Al-Ahmed, M. M. Rahman, and E. Zaman, A review on underground hydrogen storage: Insight into geological sites, influencing factors and future outlook, Energy Rep. 8, 461 (2022).
  6. N. Heinemann, M. Booth, R. Haszeldine, M. Wilkinson, J. Scafidi, and K. Edlmann, Hydrogen storage in porous geological formations–onshore play opportunities in the Midland Valley (Scotland, UK), Int. J. Hydr. Energy 43, 20861 (2018).
  7. Z. Zheng and H. A. Stone, The influence of boundaries on gravity currents and thin films: Drainage, confinement, convergence, and deformation effects, Annu. Rev. Fluid Mech. 54, 27 (2022).
  8. H. E. Huppert and A. W. Woods, Gravity-driven flows in porous layers, J. Fluid Mech. 292, 55 (1995).
  9. S. S. Pegler, H. E. Huppert, and J. A. Neufeld, Fluid injection into a confined porous layer, J. Fluid Mech. 745, 592 (2014).
  10. Z. Zheng, B. Guo, I. C. Christov, M. A. Celia, and H. A. Stone, Flow regimes for fluid injection into a confined porous medium, J. Fluid Mech. 767, 881 (2015).
  11. J. M. Nordbotten and M. A. Celia, Similarity solutions for fluid injection into confined aquifers, J. Fluid Mech. 561, 307 (2006).
  12. B. Guo, Z. Zheng, M. A. Celia, and H. A. Stone, Axisymmetric flows from fluid injection into a confined porous medium, Phys. Fluids 28, 022107 (2016).
  13. Z. Zheng and J. A. Neufeld, Self-similar dynamics of two-phase flows injected into a confined porous layer, J. Fluid Mech. 877, 882 (2019).
  14. S. M. Farahani, L. Chiapponi, S. Longo, and V. Di Federico, Darcy–Forchheimer gravity currents in porous media, J. Fluid Mech. 1000, A89 (2024).
  15. P. Castellucci, R. Boya, L. Ma, I. L. Chernyavsky, and O. E. Jensen, Dynamics of a compressible gas injected into a confined porous layer, J. Fluid Mech. 1029, A28 (2026).
  16. M. L. Szulczewski and R. Juanes, The evolution of miscible gravity currents in horizontal porous layers, J. Fluid Mech. 719, 82 (2013).
  17. C. W. MacMinn, M. L. Szulczewski, and R. Juanes, CO2 migration in saline aquifers. Part 1. Capillary trapping under slope and groundwater flow, J. Fluid Mech. 662, 329 (2010).
  18. C. W. MacMinn, M. L. Szulczewski, and R. Juanes, CO2 migration in saline aquifers. Part 2. Capillary and solubility trapping, J. Fluid Mech. 688, 321 (2011).
  19. I. Gunn and A. W. Woods, On the flow of buoyant fluid injected into a confined, inclined aquifer, J. Fluid Mech. 672, 109 (2011).
  20. S. S. Pegler, H. E. Huppert, and J. A. Neufeld, Topographic controls on gravity currents in porous media, J. Fluid Mech. 734, 317 (2013).
  21. X. Di, Y. Huang, M. Quintard, and H. E. Huppert, Low-dimensional modelling of viscous fluids in porous media over curvilinear surfaces, J. Fluid Mech. 1016, A16 (2025).
  22. B. Hagemann, M. Rasoulzadeh, M. Panfilov, L. Ganzer, and V. Reitenbach, Mathematical modeling of unstable transport in underground hydrogen storage, Environ. Earth Sci. 73, 6891 (2015).
  23. P. K. Mortimer, N. Mingotti, and A. W. Woods, A dynamic model of storage in layered anticlines, J. Fluid Mech. 979, A39 (2024).
  24. G. M. Homsy, Viscous fingering in porous media, Annu. Rev. Fluid Mech. 19, 271 (1987).
  25. S. Lyle, H. E. Huppert, M. Hallworth, M. Bickle, and A. Chadwick, Axisymmetric gravity currents in a porous medium, J. Fluid Mech. 543, 293 (2005).
  26. M. Bickle, A. Chadwick, H. E. Huppert, M. Hallworth, and S. Lyle, Modelling carbon dioxide accumulation at Sleipner: Implications for underground carbon storage, Earth Planet. Sci. Lett. 255, 164 (2007).
  27. S. Harati, S. Rezaei Gomari, F. Gasanzade, S. Bauer, T. Pak, and C. Orr, Underground hydrogen storage to balance seasonal variations in energy demand: Impact of well configuration on storage performance in deep saline aquifers, Int. J. Hydr. Energy 48, 26894 (2023).
  28. M. Saeed and P. Jadhawar, Optimizing underground hydrogen storage in aquifers: The impact of cushion gas type, Int. J. Hydr. Energy 52, 1537 (2024).
  29. D. Sun, Z. Chu, W. Chen, P. Feng, and J. Zhang, Comparison of the characteristics of compressed air energy storage in dome-shaped and horizontal aquifers based on the Pittsfield aquifer field test, Appl. Energy 348, 121465 (2023).
  30. R. Zhang and G. Zhao, A comprehensive review of compressed air energy storage technologies: Current status and future trends, J. Renew. Sustain. Energy 17, 022702 (2025).
  31. P. G. Saffman and G. I. Taylor, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. R. Soc. Lond. A 245, 312 (1958).
  32. E. M. Hinton and A. Jyoti, Buoyancy segregation suppresses viscous fingering in horizontal displacements in a porous layer, J. Fluid Mech. 946, A48 (2022).
  33. M. Javaheri, J. Abedi, and H. Hassanzadeh, Linear stability analysis of double-diffusive convection in porous media, with application to geological storage of CO2, Transp. Porous Med. 84, 441 (2010).
  34. P. Castellucci, Matlab code used to generate data in Castellucci et al. (2026) “Evolution of a gas current injected into a curved axisymmetric porous channel,” Figshare, 2026, https://doi.org/10.6084/m9.figshare.32064996.

Outline

Information

Phys. Rev. Fluids 11, 103801– Published 21 October, 2026
  • Received 21 April 2026
  • Accepted 26 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation