pith. sign in

arxiv: 2604.20007 · v1 · submitted 2026-04-21 · ⚛️ physics.flu-dyn

The evolution of a gas plume injected into a curved axisymmetric porous channel

Peter Castellucci , Radha Boya , Lin Ma , Igor L. Chernyavsky , Oliver E. Jensen This is my paper

Pith reviewed 2026-05-10 00:57 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords porous mediagas injectionbuoyancy-driven flowasymptotic analysisinterface evolutionunderground gas storagecurved channelparabolic geometry
0
0 comments X

The pith

Asymptotic analysis identifies five temporal regimes in gas plume evolution within curved porous channels.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models steady gas injection into water-filled porous channels whose centrelines are Gaussian or parabolic, as simplified representations of underground storage in anticlines. Exploiting channel slenderness, the authors derive an evolution equation for the gas-liquid interface that remains valid for large slopes in a composite asymptotic limit and reduces to a simpler form for gentle curvature. In parabolic channels the equation reveals five successive regimes in which the interface advances, thickens, and finally flattens as buoyancy gradually overtakes injection. Each regime possesses its own spatial structure and spreading rate, arising from the changing balance between the imposed injection and the hydrostatic pressure gradients created by the curving geometry. The resulting horizontal interface that advances vertically has direct consequences for storage safety and capacity.

Core claim

In the high-mobility limit, asymptotic analysis of the parabolic-channel flow identifies five temporal regimes, each containing multiple spatial regions and a distinct spreading rate. These regimes trace the progressive competition between constant injection and buoyancy: an initial thin film spreads along the upper wall, the increasing channel slope then generates a hydrostatic gradient that arrests the upper contact line and thickens the film, liquid drains beneath until buoyancy finally flattens the interface. Reduced-order models supply explicit solutions for interface shape and contact-line position in every regime, and these solutions agree with full numerical simulations of the unre d

What carries the argument

The evolution equation for the gas-liquid interface, obtained by composite asymptotic reduction of the slender-channel problem under high gas mobility.

If this is right

  • In Gaussian channels buoyancy continually modifies the flow because axisymmetry attenuates gas velocity along the length.
  • In parabolic channels buoyancy becomes important after a time scale set by injection rate and fluid properties.
  • Hydrostatic pressure gradients generated by the increasing slope arrest the upper contact line and thicken the overlying film.
  • Final flattening under buoyancy produces a horizontal interface that advances vertically, improving both safety and storage efficiency.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The regime transitions could be used to select injection rates that keep plumes within safe bounds in real anticline reservoirs.
  • Laboratory tests with scaled curved porous media could measure the observed transition times between regimes.
  • The same competition between injection and buoyancy is likely to appear in other curved or sloping porous flows such as geothermal or volcanic systems.
  • Extensions to heterogeneous or non-axisymmetric geometries would be needed before direct application to field-scale storage sites.

Load-bearing premise

The channels are slender enough that a composite asymptotic approximation remains accurate even when slopes are large, and gas mobility is high enough to simplify the governing equation.

What would settle it

A high-resolution numerical simulation or laboratory experiment on a parabolic porous channel that does not exhibit the predicted sequence of five regimes with their specific spreading rates and contact-line arrest would falsify the analysis.

Figures

Figures reproduced from arXiv: 2604.20007 by Igor L. Chernyavsky, Lin Ma, Oliver E. Jensen, Peter Castellucci, Radha Boya.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic of the two thin channel geometries considered in this paper, defined by the curvature of their centrelines [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: A numerical solution of (a) the small-slope model Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Illustration of five asymptotic regimes of spreading in a parabolic channel. Each row corresponds to one regime, with [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Numerical solutions of spreading in a parabolic channel for [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Evolution of the contact lines in a parabolic channel, obtained by numerically solving Eqs ( [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Numerical solutions of Eqs ( [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: (a) Solutions of Eqs ( [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: presents a representative solution of Eqs (33𝑎–𝑒) and (40) for 𝛽 = 10−4 , implying that buoyancy effects are weak. The initial evolution of the interface is shown in [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Numerical solutions of Eqs ( [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Numerical solutions of Eqs ( [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
read the original abstract

We investigate gas injection into water-saturated porous channels with Gaussian and parabolic axisymmetric centrelines, 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 CO$_2$ storage, where a horizontal interface that advances vertically enhances both safety and storage efficiency.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives an evolution equation for the gas-liquid interface during steady gas injection into water-saturated axisymmetric porous channels with Gaussian and parabolic centrelines. It employs a composite asymptotic approximation justified by channel slenderness that accommodates large local slopes, specialized to the high gas-mobility limit. For the parabolic geometry this reduction yields five distinct temporal regimes, each with multiple spatial regions and a characteristic spreading rate arising from the competition between injection and buoyancy; analytical solutions of reduced-order models for interface evolution and contact-line motion are validated against full numerical simulations. Implications for underground gas storage are discussed.

Significance. If the asymptotic reductions remain valid, the work supplies a systematic classification of buoyancy-driven regimes in curved geometries together with explicit analytical predictions for spreading rates and contact-line arrest. The explicit validation against numerical simulations of the full problem is a clear strength, as is the derivation of parameter-free reduced models for each regime. These results could directly inform safety and efficiency assessments for subsurface hydrogen and CO2 storage in anticlinal structures.

major comments (2)
  1. [Section on asymptotic analysis of the parabolic channel flow (following derivation of the evolution equation)] The central claim of five temporal regimes with distinct spreading rates in the parabolic channel rests on the composite asymptotic reduction to a 1D evolution equation. This reduction invokes channel slenderness to justify lubrication-style averaging while retaining large-slope corrections, plus the high gas-mobility limit that drops selected capillary and viscous terms. In the parabolic geometry the wall slope increases linearly with axial distance; once the front reaches distances at which the local aspect ratio ceases to be small, or once the interface thickens after upper-contact-line arrest, the neglected transverse variations and slope-induced corrections can re-enter at leading order. This assumption is load-bearing for the sequence of balances and the associated spreading exponents in regimes 3–5.
  2. [Derivation of the evolution equation and the high-mobility limit] The high gas-mobility limit is invoked to simplify the evolution equation, yet the manuscript states that buoyancy eventually influences the flow at a timescale set by injection rate and fluid properties. It is not shown that the dropped terms remain uniformly small once the hydrostatic pressure gradient strengthens and the film thickens beneath the arrested upper contact line. An explicit a-posteriori check of the neglected terms across the later regimes would be required to confirm that the predicted transitions and spreading rates survive.
minor comments (2)
  1. The notation distinguishing the reduced models in each of the five regimes would benefit from a compact summary table listing the dominant balances, the resulting ODE or PDE, and the applicable spatial regions.
  2. Figure captions for the numerical validation plots should state the precise values of the mobility ratio, capillary number, and channel curvature parameter used in each simulation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We appreciate the opportunity to clarify the validity of our asymptotic approximations and have revised the manuscript accordingly to address the concerns raised.

read point-by-point responses

  1. Referee: [Section on asymptotic analysis of the parabolic channel flow (following derivation of the evolution equation)] The central claim of five temporal regimes with distinct spreading rates in the parabolic channel rests on the composite asymptotic reduction to a 1D evolution equation. This reduction invokes channel slenderness to justify lubrication-style averaging while retaining large-slope corrections, plus the high gas-mobility limit that drops selected capillary and viscous terms. In the parabolic geometry the wall slope increases linearly with axial distance; once the front reaches distances at which the local aspect ratio ceases to be small, or once the interface thickens after upper-contact-line arrest, the neglected transverse variations and slope-induced corrections can re-enter at leading order. This assumption is load-bearing for the sequence of balances and the associated spread

    Authors: We agree that the validity of the asymptotic reduction is crucial for the identification of the five regimes. The manuscript already provides validation through direct comparison with full numerical simulations of the governing equations, which show excellent quantitative agreement in the interface shape, spreading rates, and contact-line dynamics across all five regimes, including after upper contact-line arrest. This agreement indicates that the neglected terms do not affect the leading-order behavior within the simulated parameter space. Nevertheless, to provide the explicit a-posteriori check requested, we will add a new subsection or appendix in the revised manuscript that evaluates the magnitude of the dropped terms (transverse variations, slope corrections, etc.) relative to the retained terms at representative times in regimes 3-5. We will also discuss the range of validity in terms of the local aspect ratio. revision: partial

  2. Referee: [Derivation of the evolution equation and the high-mobility limit] The high gas-mobility limit is invoked to simplify the evolution equation, yet the manuscript states that buoyancy eventually influences the flow at a timescale set by injection rate and fluid properties. It is not shown that the dropped terms remain uniformly small once the hydrostatic pressure gradient strengthens and the film thickens beneath the arrested upper contact line. An explicit a-posteriori check of the neglected terms across the later regimes would be required to confirm that the predicted transitions and spreading rates survive.

    Authors: The referee correctly identifies that the high-mobility limit requires verification in the later stages when buoyancy dominates. While the numerical validation supports the accuracy of the reduced models, we acknowledge that an explicit check of the neglected terms was not included. In the revised version, we will perform and present an a-posteriori analysis showing that the capillary and viscous terms dropped in the high-mobility limit remain small compared to the buoyancy and injection terms even after the film thickens and the hydrostatic gradient strengthens. This will be done by computing the orders of magnitude from the full numerical solutions at various stages. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained asymptotic reduction

full rationale

The paper derives the evolution equation for the gas/liquid interface via composite asymptotic approximation from the governing flow equations, exploiting channel slenderness to accommodate large slopes and the high gas-mobility limit. This is a standard first-principles reduction with no evidence of self-definition, fitted parameters renamed as predictions, or load-bearing self-citations. The five temporal regimes and spreading rates emerge as outcomes of analyzing the reduced model, validated against numerical simulations, without reducing back to inputs by construction. The slenderness assumption is an input approximation, not a circular output.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review limits visibility into exact parameter counts; the high gas-mobility limit and slenderness assumption are domain assumptions rather than fitted numbers, with no new entities introduced.

axioms (2)
  • domain assumption Channel slenderness allowing composite asymptotic approximation for large slopes
    Invoked to derive the evolution equation for the gas/liquid interface
  • domain assumption High gas-mobility limit
    Used to contrast buoyancy mechanisms in each geometry

pith-pipeline@v0.9.0 · 5593 in / 1220 out tokens · 28391 ms · 2026-05-10T00:57:11.666739+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

43 extracted references · 43 canonical work pages

  1. [1]

    1(a), the shape function in Eq

    Parabolic channel For the parabolic channel sketched in Fig. 1(a), the shape function in Eq. (1) is defined by 𝑧=−𝜖 𝑟𝑐 (𝑠) 2 2 ,(34) which corresponds to the scaling𝐴∼ℎin Eq. (2). Substituting Eq. (34) into Eq. (2) yields the curvature of the channel centreline, 𝜅(𝑠)=− 𝜖 1+𝜖 2𝑟𝑐 (𝑠) 2 3/2 .(35) The curvature is therefore𝑂(𝜖), even when𝑟 𝑐 =𝑂(𝜖 −1). The ar...

    work page

  2. [2]

    Gaussian channel The second geometry we consider is a Gaussian channel whose centreline is everywhere weakly curved, as sketched in Fig. 1(b). The channel geometry is prescribed through the shape function in Eq. (1), which we take to be𝑧=−𝜖exp −𝑟𝑐 (𝑠) 2/2 . Under the small-slope rescaling, this reduces at leading order to𝑧 † =exp −𝑠2/2 . With this choice,...

    work page 2013

  3. [3]

    Regime I: formation of a thin gas film For𝑡≪𝜆 −1, the solution of Eqs (33𝑎–𝑒) exhibits two spatial regions, denoted I 𝑎 and I 𝑏, as shown in Fig. 3. Region I 𝑎 is characterised by𝐻=𝑂(1)and𝑠=𝑂 M1/2 . In region I𝑏 a thin film of gas forms along the upper boundary; here 1−𝐻=𝑂(M) and𝑠=𝑂 M −1/2 . Region I𝑎.Here, we set𝑠=M 1/2 ¯𝑠,𝑆𝑙 =M 1/2 ¯𝑆𝑙 (𝑡)and𝐻(𝑠, 𝑡)= ¯𝐻...

    work page

  4. [4]

    Regime II: initial growth of the thin film of gas At later times, with𝑡=𝑂 𝜆−1 , there are again two spatial regions, as shown in Fig. 3. The spatial region labelled II𝑎 retains the structure observed in I 𝑎, while in region II 𝑏 (formerly I𝑏), buoyancy begins to influence the flow, leading to a thickening of the thin gas layer and a corresponding decelera...

    work page

  5. [5]

    Regime III: gas filling and liquid drainage For𝜆 −1 ≪𝑡≪ (M𝜆) −1, the upper contact line remains effectively stationary at Eq. (B13). During this stage, the liquid continues to drain below the interface and the system transitions from a thin gas layer near the upper boundary to a thin liquid film along the lower boundary. Region II𝑏 splits into two. In the...

    work page

  6. [6]

    (B21) shows that ˘𝐻=𝑂(M)when𝑡=𝑂 log(M −1) (M𝜆) −1 , signalling the onset of the new regime in which the upper contact line resumes motion

    Regime IV: evolution of a thin liquid film The solution in Eq. (B21) shows that ˘𝐻=𝑂(M)when𝑡=𝑂 log(M −1) (M𝜆) −1 , signalling the onset of the new regime in which the upper contact line resumes motion. As before, the domain splits into three spatial regions, illustrated in Fig. 3. For convenience, we retain the timescale ˇ𝑡=M𝜆𝑡in this regime. Region IV𝑎.H...

    work page

  7. [7]

    Regime V: evolution of the moving front As the liquid film continues to drain, the interface height decays exponentially according to Eq. (B28𝑎). The lower contact line solution in Eq. (B19) increases exponentially in time, whereas the upper contact line given by Eq. (B34) increases algebraically. Consequently, the lower contact line will eventually catch...

    work page

  8. [8]

    This interface subsequently translates downward at a rate set by the injection strength

    Early times At early times when𝐻(0, 𝑡)>0, in the limitM ≪1 with𝛽=𝑂(1), or equivalently𝜆∼ M −2, the interface can relax to its energetically preferred configuration: a horizontal interface in physical space. This interface subsequently translates downward at a rate set by the injection strength. Taking this limit in Eq. (33𝑎) with Eq. (40), yields h 𝑠𝐻(1−𝐻...

    work page

  9. [9]

    The inner region near𝑆 𝑙 consists of a horizontal interface, and in the outer region a thin film of gas spreads over long length scales

    Late times At later times, once the lower contact line has formed, inner and outer spatial regions emerge when𝛽≡ M 2𝜆∼𝑂(1). The inner region near𝑆 𝑙 consists of a horizontal interface, and in the outer region a thin film of gas spreads over long length scales. a. Inner region Once the lower contact line has formed, a short inner region where𝑠=𝑂(1)continue...

    work page

  10. [10]

    Kushnir, A

    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)

    work page 2012

  11. [11]

    Dudfield and A

    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.755, 467 (2012)

    work page 2012

  12. [12]

    Zivar, S

    D. Zivar, S. Kumar, and J. Foroozesh, Underground hydrogen storage: A comprehensive review, Int. J. Hydrogen Energy46, 23436 (2021)

    work page 2021

  13. [13]

    Kushnir, A

    R. Kushnir, A. Ullmann, and A. Dayan, Thermodynamic and hydrodynamic response of compressed air energy storage reservoirs: a review, Rev. Chem. Engng28, 123 (2012)

    work page 2012

  14. [14]

    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)

    work page 2022

  15. [15]

    Heinemann, M

    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. Hydrogen Energy43, 20861 (2018)

    work page 2018

  16. [16]

    Zheng and H

    Z. Zheng and H. A. Stone, The influence of boundaries on gravity currents and thin films: drainage, confinement, convergence, and deformation effects, Ann. Rev. Fluid Mech.54, 27 (2022)

    work page 2022

  17. [17]

    H. E. Huppert and A. W. Woods, Gravity-driven flows in porous layers, J. Fluid Mech.292, 55 (1995)

    work page 1995

  18. [18]

    S. S. Pegler, H. E. Huppert, and J. A. Neufeld, Fluid injection into a confined porous layer, J. Fluid Mech.745, 592 (2014)

    work page 2014

  19. [19]

    Zheng, B

    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)

    work page 2015

  20. [20]

    J. M. Nordbotten and M. A. Celia, Similarity solutions for fluid injection into confined aquifers, J. Fluid Mech.561, 307 (2006)

    work page 2006

  21. [21]

    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)

    work page 2016

  22. [22]

    Zheng and J

    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)

    work page 2019

  23. [23]

    S. M. Farahani, L. Chiapponi, S. Longo, and V. D. Federico, Darcy–Forchheimer gravity currents in porous media, J. Fluid Mech.1000, A89 (2024)

    work page 2024

  24. [24]

    Castellucci, R

    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)

    work page 2026

  25. [25]

    M. L. Szulczewski and R. Juanes, The evolution of miscible gravity currents in horizontal porous layers, J. Fluid Mech.719, 82 (2013)

    work page 2013

  26. [26]

    C. W. MacMinn, M. L. Szulczewski, and R. Juanes, CO 2 migration in saline aquifers. Part 1. Capillary trapping under slope and groundwater flow, J. Fluid Mech.662, 329 (2010)

    work page 2010

  27. [27]

    C. W. MacMinn, M. L. Szulczewski, and R. Juanes, CO 2 migration in saline aquifers. Part 2. Capillary and solubility trapping, J. Fluid Mech.688, 321 (2011)

    work page 2011

  28. [28]

    Gunn and A

    I. Gunn and A. W. Woods, On the flow of buoyant fluid injected into a confined, inclined aquifer, J. Fluid Mech.672, 109 (2011)

    work page 2011

  29. [29]

    S. S. Pegler, H. E. Huppert, and J. A. Neufeld, Topographic controls on gravity currents in porous media, J. Fluid Mech.734, 317 (2013)

    work page 2013

  30. [30]

    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)

    work page 2025

  31. [31]

    Hagemann, M

    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)

    work page 2015

  32. [32]

    P. K. Mortimer, N. Mingotti, and A. W. Woods, A dynamic model of storage in layered anticlines, J. Fluid Mech.979, A39 (2024)

    work page 2024

  33. [33]

    G. M. Homsy, Viscous Fingering in Porous Media, Ann. Rev. Fluid Mech.19, 271 (1987)

    work page 1987

  34. [34]

    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)

    work page 2005

  35. [35]

    Bickle, A

    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)

    work page 2007

  36. [36]

    Harati, S

    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. Hydrogen Energy48, 26894 (2023)

    work page 2023

  37. [37]

    Saeed and P

    M. Saeed and P. Jadhawar, Optimizing underground hydrogen storage in aquifers: The impact of cushion gas type, Int. J. Hydrogen Energy 52, 1537 (2024). 31

    work page 2024

  38. [38]

    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. Energy348, 121465 (2023)

    work page 2023

  39. [39]

    Zhang and G

    R. Zhang and G. Zhao, A comprehensive review of compressed air energy storage technologies: Current status and future trends, J. Renew. Sustain. Energy17, 022702 (2025)

    work page 2025

  40. [40]

    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. A245, 312 (1958)

    work page 1958

  41. [41]

    E. M. Hinton and A. Jyoti, Buoyancy segregation suppresses viscous fingering in horizontal displacements in a porous layer, J. Fluid Mech.946, A48 (2022)

    work page 2022

  42. [42]

    Javaheri, J

    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)

    work page 2010

  43. [43]

    The evolution of a gas plume injected into a curved axisymmetric porous channel

    P. Castellucci, Supplementary code for “The evolution of a gas plume injected into a curved axisymmetric porous channel”, Figshare (2026), 10.6084/m9.figshare.32064996

    work page doi:10.6084/m9.figshare.32064996 2026