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REVIEW 2 major objections 6 minor 48 references

Gas injection and leakage in layered aquifers

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read CO2 injected into layered aquifers can build enough capillary pressure to leak through thin seals without a fault or fracture conduit, and this may explain the stratified leakage at Sleipner.

desk verdict A well-derived upscaled model showing that water-film relative permeability can control seal leakage, but the Sleipner claim is an end-member scenario that needs better parameter constraints. read the letter →

arxiv 1908.08137 v1 pith:AFXVIUBU submitted 2019-08-21 physics.flu-dyn physics.geo-ph

Luke T. Jenkins , Martino Foschi , Christopher W. MacMinn This is my paper · ORCID
classification physics.flu-dynphysics.geo-ph PACS 47.56.+r
keywords CO2storagelayeredaquiferscapillaryentrypressuregravitycurrentrelativepermeabilityofwateringasregionSleipnerdistributedleakagedissipation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Using a vertically integrated two-phase gravity-current model, this paper argues that the capillary pressure capable of driving CO2 through a thin sealing layer is not controlled by buoyancy alone: it depends strongly on whether the gas plume blocks vertical water flow. When water can flow freely through the gas region, the capillary pressure at the base of the seal is just the buoyant overpressure, which is far too small to breach typical seals. When the water relative permeability inside the gas region is small, the water column is hydraulically disconnected and the capillary pressure becomes larger by more than two orders of magnitude in the reference case. Applying this to the Sleipner site, the model finds the capillary pressure can reach about 3.2 MPa, enough to invade mudstone seals with entry pressures around 0.5-5 MPa. This suggests that the distributed CO2 leakage observed at Sleipner could occur through the pore space of the seals without any focused conduit.

What carries the argument

The machinery is the dimensionless ratio $\Lambda^s_w h_n/k^\star_{rw}$, which compares the vertical resistance to water flow through the gas-saturated region with that through the seal. It controls the hydraulic connectivity of the water column across the plume: when the ratio is small the capillary pressure follows the buoyant-overpressure limit, and when it is large the water pressure is disconnected and the capillary pressure is instead set by the water pressure in the aquifer above. The model also couples the layers through a smoothed capillary entry threshold for gas flow across seals, with dimensionless groups $\Lambda^s_w$, $M^s_z$, and $\tilde{p}^E_c$ governing the strength and extent of leakage.

What would settle it

Measure the relative permeability of water in CO2-brine systems at residual water saturation under reservoir conditions, for example with core floods at $s_{wr}\approx0.2$: if $k^\star_{rw}$ is of order $10^{-2}$ or larger, then $\Lambda^s_w h_n/k^\star_{rw}\ll 1$ in the Sleipner scenario, the capillary pressure falls to the roughly 11 kPa buoyant-overpressure value, and the predicted distributed leakage across the mudstone seals does not occur.

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Extended reading notes

Core claim

The paper's central claim is that distributed gas leakage in layered aquifers can be switched on, or dramatically amplified, by a single material property: the relative permeability of water inside the gas plume, $k^\star_{rw}$. In the conventional limit where $k^\star_{rw}$ is large, the water pressure remains nearly hydrostatic across the plume and the capillary pressure on the underside of the seal equals the buoyant overpressure $(\rho_w-\rho_g)gh_n$; at the reference parameter set this is about 11 kPa. If $k^\star_{rw}$ is small enough that $\Lambda^s_w h_n/k^\star_{rw}\gg 1$, the plume blocks vertical water flow, the water pressure is set by the overlying aquifer, and the capillary pressure rises to about 3.2 MPa. The latter exceeds the estimated entry pressure of the intermediate mudstone seals at Sleipner, so the authors conclude that CO2 may be able to leak across those seals by distributed flow even with no fault or fracture conduit.

Load-bearing premise

The load-bearing premise is that water is nearly immobile inside the CO2 plume ($k^\star_{rw}$ very small); the paper says the value is very poorly constrained and likely small, but no direct measurement is given, and if water can flow through the plume easily the capillary pressure reverts to the buoyant-overpressure limit and the Sleipner conclusion fails.

Editorial extensions

If this is right

  • If $k^\star_{rw}$ is small, the maximum capillary pressure beneath a seal can exceed the buoyant overpressure by two to three orders of magnitude, making gas leakage possible where a buoyancy-only estimate would rule it out.
  • Decreasing $k^\star_{rw}$ by one to two orders of magnitude can initiate gas leakage or substantially increase the leaked mass, so uncertainty in this parameter translates directly into uncertainty in storage security.
  • At Sleipner parameter values, the disconnected-water limit gives a capillary pressure near 3.2 MPa, exceeding entry-pressure estimates of 0.5-5 MPa and implying that distributed leakage across the intermediate mudstone seals is plausible without a focused conduit.
  • The amount of gas that leaks grows roughly linearly with the seal-to-aquifer conductance ratio $\Lambda^s_w$ and the seal gas-to-water mobility ratio $M^s_z$ when leakage is weak, and this growth saturates once leakage itself modifies the pressure field.
  • Distributed gas leakage can also alter plume geometry, narrowing the plume in the injection aquifer by up to about 25 percent relative to pressure dissipation alone.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If this mechanism operates, seismic images showing multiple stratified CO2 plumes at Sleipner may be reinterpreted as evidence of distributed seal breakthrough rather than hidden faults; a testable check is whether the predicted leakage onset matches the timing of plume appearance in each layer.
  • The same ratio-based mechanism should apply to other buoyant gases stored underground, such as methane or hydrogen, and to hydrocarbon migration, so containment assessments for any layered storage system should include water-relative-permeability effects in the gas-saturated zone.
  • Because $k^\star_{rw}$ depends on the conductivity and connectivity of residual water films, direct core-flood measurements of CO2-brine relative permeability at representative saturations could calibrate the model and narrow the factor-of-300 uncertainty in predicted capillary pressure.
  • If film connectivity changes with geochemistry over time, for example through drying or mineral reactions near the injection well, leakage risk could evolve during a storage project, a coupling the present model does not include.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This paper extends the vertically integrated two-phase model of Jenkins et al. (2019) to include vertical gas leakage across thin seals with a capillary entry threshold. The authors derive coupled PDEs for water and gas in layered aquifers, coupled through vertical water fluxes and through gas fluxes controlled by a smoothed step function of capillary pressure. They analyze a two-aquifer reference case and show that the maximum capillary pressure at the base of the seal is extremely sensitive to the relative permeability of water in the gas region, k*_rw. Two limiting approximations are derived: buoyant overpressure (Eq. 46) and hydraulically disconnected water column (Eq. 47). They then apply the model to Sleipner and argue that if k*_rw is small, capillary pressures may reach ~3.2 MPa and invade interbedded mudstone seals without a focused conduit.

Significance. If the model and its Sleipner interpretation hold, the paper provides a physically plausible mechanism for distributed CO2 leakage across thin intermediate seals, which would challenge the widespread inference of a focused conduit at Sleipner. The derivation is internally consistent, and the two limiting closures (Eqs. 46 and 47) are tested against the full numerical model in Figs. 2 and 3. The paper also gives a clear, falsifiable prediction: the leakage fraction should be strongly controlled by k*_rw. Its main limitation is that the field-scale conclusion is conditioned on a parameter, k*_rw, that the authors admit is very poorly constrained, and the model closures have not been validated against higher-fidelity simulations or experimental data.

major comments (2)
  1. [Section IV, Eq. (47), Fig. 3] The Sleipner estimate pc ≈ 3.2 MPa is computed in the k*_rw ≈ 0 end-member. The high-capillary limit in Eq. (47) requires k*_rw << Λ_s_w h_n, which with the reference values (Λ_s_w = 10^-4 and h_n ~ O(1)) means k*_rw << 10^-4. The paper provides no measurement, core-flood data, pore-network calculation, or field calibration to support values below this threshold. If k*_rw is near the high end of plausibility, say 10^-2, Fig. 3 shows that the maximum capillary pressure drops by two to three orders of magnitude, returning to the buoyant-overpressure limit of Eq. (46), which would not exceed the ~2 MPa seal entry pressure. The statement in the Abstract and Section IV that CO2 at Sleipner 'may be able to leak across the intermediate seals in the absence of a focused conduit' is therefore a conditional scenario rather than a robust prediction; the required constraint on k*_rw should be stated explicitly and the conclusions reframed accordingly.
  2. [Section II.A, Eqs. (5), (10), (15)] The vertical-flux ansatz (piecewise-linear q_w,z and vertically uniform q_g,z) and the assumption that leaked gas appears instantaneously in the overlying aquifer are central to the model, but they are not validated against full 2D two-phase simulations or laboratory experiments. Since the paper uses the model to make quantitative leakage predictions (e.g., M2_g fractions in Figs. 4–9), a comparison with a high-resolution numerical model for a few representative parameter sets would materially strengthen the central claims. At present, the predictive accuracy of the upscaled closure is an assumption rather than a demonstrated property.
minor comments (6)
  1. [Section II.D/E] The dimensionless notation is inconsistent: Eq. (34) defines tilde quantities, but the tildes are dropped immediately afterward, and some source terms in Eqs. (36)–(37) still appear with tildes. Please make the notation uniform throughout.
  2. [Section III.B] The sentence 'M 1 g (t = 1) = 2−M 1 g (t = 1)< 2' appears to contain an indexing error; the second term should presumably refer to M 2 g (t = 1).
  3. [Section IV] The text 'see §33' when referring to the characteristic pressure should refer to the appropriate section or equation (§II.D or Eq. (33)).
  4. [Section II.B.2] The entry-pressure transition function R in Eq. (23) depends on the smoothing parameter ϑ, but no numerical test of independence with respect to ϑ is reported. Please include such a test or state the range of ϑ for which the results are verified.
  5. [Figure 3] The curve labels in Fig. 3 are difficult to distinguish at printed size; using distinct line styles or markers in addition to color would improve readability.
  6. [Section II.A.2] The neglect of gas transit time through the seals is a reasonable approximation for thin seals, but its effect on the time at which gas arrives in the upper aquifer should be mentioned in the Sleipner discussion, where the seismic images show vertically stacked plumes.

Circularity Check

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No circularity found: the gas-leakage model is derived within the paper from Darcy's law and mass conservation, and the Sleipner estimate is explicitly conditional on the unconstrained parameter k*_rw.

full rationale

The derivation is self-contained. The governing equations for gas flow (Eqs. 36–44) are obtained by vertical integration of the two-phase Darcy equations, with a capillary-threshold closure (Eqs. 21–23) that is not imported from the authors' prior work. The water-flow framework is taken from Jenkins et al. [25], but that is an extension, not a reduction: the paper states, 'Unlike in Jenkins et al. [25], we now also allow for gas flow across the seals, subject to an appropriate capillary entry threshold,' and [25] itself assumed no gas leakage. The Sleipner estimate pc ≈ 3.2 MPa is presented as an end-member calculation: 'Assuming that the gas region completely obstructs vertical water flow, k*_rw ≈ 0... this capillary pressure... is sufficiently high to suggest that gas leakage through the sealing layers at Sleipner is entirely plausible.' No parameter is fitted to the target leakage outcome, and the entry-pressure range 0.5–5 MPa is taken from external measurements (Chiquet et al.; Kuila and Prasad; Chadwick et al.). The paper explicitly flags the weak constraint on k*_rw: 'the appropriate value of k*_rw [is] very poorly constrained. The most likely scenario is that k*_rw << 1.' This is an uncertainty/robustness limitation, not circular reasoning. There is minor self-citation to [25], but the central gas-leakage claim has independent content and would stand or fall with the unconstrained input, not with the citation.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The model rests on upscaled two-phase flow closures inherited from Jenkins et al. [25] and new closures for vertical gas leakage. The most important unconstrained input is k*_rw, which controls the headline result. No new physical entities are introduced.

free parameters (3)
  • k*_rw = reference 10^-3; varied from 10^-10 to 1
    Relative permeability of water in the gas region. Not measured; chosen by hand for the reference case and varied over the full range. The central results for capillary pressure and gas leakage are extremely sensitive to this parameter (Figs. 2, 3, 9).
  • pE_c = varied logarithmically; Sleipner estimate 0.5 to 5 MPa from Chiquet et al. and Kuila and Prasad
    Capillary entry pressure of the seal. Taken from literature estimates rather than fitted, but the leakage prediction depends on comparing the model's capillary pressure to this threshold.
  • theta (smoothing sharpness) = 300
    Sharpness parameter in the smoothed entry-pressure transition function R, Eq. (23). Chosen by hand; the paper asserts results are independent of this value for sufficiently large theta, but does not demonstrate convergence.
assumptions (6)
  • domain assumption Weakly compressible fluids with linear density-pressure relation, Eq. (1).
    Used throughout the derivation, Section II. For water, compressibility is neglected entirely; for gas, linear compressibility is retained.
  • domain assumption Strong gravity segregation: a coherent gas plume overlying water, with no gas in the water regions or seals, and no gas storage in seals.
    Invoked in Section II and used to derive the vertically integrated gas and water equations, Eqs. (36) and (37).
  • domain assumption Closure for vertical water flux: piecewise-linear profile through the aquifer, Eq. (5), and uniform vertical gas flux, Eq. (10).
    These closures allow vertical integration of the pressure field. They are asserted in Section II.A and are not validated against full 2D simulations or experiments.
  • domain assumption Seals have no horizontal flow and no storage, so vertical fluxes through each seal are uniform.
    Used in Section II.B to couple aquifers via water and gas leakage through seals.
  • domain assumption Gas leakage is controlled by a capillary entry threshold, represented by a smoothed step function R, Eq. (23).
    This is the new physical ingredient relative to Jenkins et al. [25]. The threshold model is standard for seal entry pressure but introduces the smoothing parameter theta.
  • domain assumption Leaked gas immediately appears in the overlying aquifer plume, neglecting transit time through the seal and water region.
    Stated in Section II.A.2, at the end of the derivation of the gas equation. This simplification is load-bearing for the multi-layer coupling.

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Cite this review

Pith. "Pith review of Gas injection and leakage in layered aquifers." pith.science (2026). https://pith.science/paper/AFXVIUBU

@misc{pith2026190808137,
  author       = {Pith},
  title        = {Pith review of: Gas injection and leakage in layered aquifers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AFXVIUBU}},
  note         = {Machine review of arXiv:1908.08137}
}
read the original abstract

Carbon dioxide (CO2) injection into saline aquifers is one method of mitigating anthropogenic climate change. To ensure secure storage of this CO2, it is important to understand the interaction of CO2 injection and migration with geological layering. For example, seismic monitoring at the Sleipner pilot project suggests that the injected CO2 is ponding against, and leaking across, a series of thin, intermediate seals. Here, we develop a gravity-current model for weakly compressible, two-phase fluid migration in a system of layered aquifers. Our model includes vertical leakage of both water and gas across seals, where the latter is subject to a capillary entry threshold. We demonstrate that the buildup of capillary pressure is very sensitive to the conductivity and connectivity of water films in the gas region. We identify two associated limiting cases, where gas obstructs water flow either completely or not at all. We then explore the parameters that govern gas leakage and the resulting fluid distributions---demonstrating that this problem involves a complex interplay between pressure dissipation, capillary pressure buildup, and fluid migration. We show that decreasing the relative permeability of water in the gas region can initiate gas leakage or significantly increase the amount of gas leakage. Finally, we apply our model to rock properties expected for Sleipner and show that CO2 injection may build up sufficient capillary pressure to invade the seals---suggesting that, contrary to conventional wisdom, CO2 may be able to leak across the intermediate seals at Sleipner in the absence of a focused conduit.

Figures

Figures reproduced from arXiv: 1908.08137 by the authors.

Figure 1
Figure 1. FIG. 1. A section of our model system, which comprises a sequence of aquifers of thickness [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Gas injection into the bottom-most aquifer of a two layer system with [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The maximum capillary pressure [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Mass fraction of gas in aquifer 2 at the end of injection, [PITH_FULL_IMAGE:figures/full_fig_p024_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The shape of the gas plume in aquifer 1 (bottom row) and in aquifer 2 (top row) the end of injection, [PITH_FULL_IMAGE:figures/full_fig_p025_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Plume width in aquifer 1 at the end of injection, [PITH_FULL_IMAGE:figures/full_fig_p026_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) The aspect ratio of the gas plume in aquifer 2, [PITH_FULL_IMAGE:figures/full_fig_p027_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. (a) Mass fraction of gas in the upper aquifer at the end of injection, [PITH_FULL_IMAGE:figures/full_fig_p028_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Mass of gas in the upper layer divided by total injected mass at the end of injection, as a function [PITH_FULL_IMAGE:figures/full_fig_p030_9.png]

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Works this paper leans on

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.