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REVIEW 4 major objections 5 minor 34 references

Impact of Time-Dependent Wettability Alteration on the Dynamics of Capillary Pressure

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Pith's one-line read A single rate parameter, derived from pore-scale contact-angle kinetics, describes how capillary pressure migrates from the initial to the final wetting state in a porous medium.

desk verdict Useful single-parameter interpolation model for dynamic capillarity, but the pore-to-macro scalings are fitted, not derived — worth refereeing with honest revision. read the letter →

arxiv 1908.06863 v1 pith:MJYVJFW3 submitted 2019-08-15 physics.flu-dyn

Abay M. Kassa , Sarah E. Gasda , K. Kumar , F. A. Radu This is my paper · ORCID
classification physics.flu-dyn PACS 47.56.+r68.08.Bc
keywords wettabilityalterationdynamiccapillarypressurebundle-of-tubesmodelcontactangleexposuretimeCO2storageinterpolationLangmuiradsorption
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

This paper argues that capillary pressure in a porous medium whose wettability is changing in time can be described by a weighted interpolation between the static initial- and final-wetting-state capillary pressure curves, with a single dynamic parameter controlling the shift. Using a bundle-of-tubes model in which each tube's contact angle evolves by a Langmuir-type law in the time-integrated non-wetting saturation (exposure time), the authors simulate multi-cycle drainage-imbibition experiments and show the dynamic coefficient collapses onto simple functions of exposure time and saturation. For uniform alteration the coefficient is $\omega = \chi/(2C+\chi)$; for non-uniform alteration it is $\omega = S_w\chi/(\beta_2 + S_w\chi)$ with $\beta_2 = b_1 C^{b_2}$. If correct, the model turns an observed months-long decline in capillary pressure—relevant for CO$_2$ storage and enhanced oil recovery—into a predictable function of the same rate constant that governs pore-scale contact-angle change.

What carries the argument

The load-bearing identity is the interpolation formula $P_c=(1-\omega) P_c^{st,i} + \omega P_c^{st,f}$, in which the dynamic coefficient $\omega$ carries all time dependence. The paper evaluates $\omega$ by simulating displacement in a bundle of non-interacting capillary tubes (a simplified pore-scale model of parallel cylindrical pores with a Weibull radius distribution), where each tube's contact angle obeys $\theta_m = \theta_{m,i} + \frac{\chi}{C+\chi}\Delta\Theta$, a Langmuir-type law in the local exposure time $\chi = (1/T)\int S_{nw}\,dt$. The bundle-of-tubes simulation generates $P_c$-$S$ data; fitting $\omega$ to those data produces the explicit forms $\omega=\chi/(2C+\chi)$ (uniform alteration) and $\omega=S_w\chi/(\beta_2+S_w\chi)$ (non-uniform), and the scalings $\beta_1=2C$, $\beta_2=b_1 C^{b_2}$ connect the pore-scale rate constant to the macroscale coefficient.

What would settle it

Run a multi-cycle drainage-imbibition experiment on a mineral substrate with a wettability-altering fluid while independently measuring contact angle and capillary pressure over time. Compute the exposure time $\chi$ from the recorded saturation history and check whether the normalized deviation $(P_c - P_c^{st,i})/(P_c^{st,f}-P_c^{st,i})$ collapses onto $\chi/(2C+\chi)$ for uniform alteration and whether the fitted $\beta_1$ equals $2C$ for several values of $C$. A systematic collapse failure or a non-constant ratio $\beta_1/C$ would contradict the central claim.

Watch

Extended reading notes

Core claim

The central claim is that the measured capillary pressure $P_c$ of a system undergoing wettability alteration is never an independent function of saturation but is always the static initial curve shifted by a fraction $\omega$ of the gap to the static final curve: $P_c = (1-\omega) P_c^{st,i} + \omega P_c^{st,f}$. The paper derives $\omega$ from pore-scale bundle-of-tubes simulations: when alteration is uniform, $\omega$ depends only on the non-dimensional exposure time $\chi$, taking $\omega = \chi/(2C+\chi)$; when alteration is non-uniform and local, $\omega$ also depends on saturation, $\omega = S_w \chi/(\beta_2 + S_w \chi)$ with $\beta_2 = b_1 C^{b_2}$. The macroscale parameter is therefore a direct function of the pore-scale rate constant $C$, so the dynamic capillary pressure can be predicted a priori once the static end states and the contact-angle kinetics are known. The simulations also show that wettability alteration alone can produce apparent hysteresis in a geometry that otherwise has none.

Load-bearing premise

The model stands on the assumption that a pore's contact angle changes along the smooth Langmuir-type path $\theta = \theta_i + (\chi/(C+\chi))\Delta\Theta$ driven by time-integrated non-wetting saturation; if laboratory measurements show a different kinetic law, the specific functional forms of $\omega$ and the $C$-scalings derived here would not apply.

Editorial extensions

If this is right

  • Reservoir simulators can replace cycle-dependent or hysteresis-tabulated capillary pressure curves for wettability-altering fluids with the static end curves plus a single dynamic parameter that depends on exposure time.
  • For CO$_2$ storage, a months-long decrease in capillary pressure—and the associated risk of reduced caprock sealing capacity—becomes predictable from batch contact-angle measurements rather than requiring years of core-flood experiments.
  • Laboratory protocols for reactive fluid pairs should report saturation history and exposure time, because the same saturation can correspond to different capillary pressures depending on how long the rock has been exposed.
  • Distinguishing uniform from non-uniform alteration matters: dissolution of a wettability-altering agent into the wetting phase and direct contact with the non-wetting phase lead to different functional forms of the dynamic coefficient.
  • Calibration of the dynamic coefficient against a single saturation-time path is sufficient to predict capillary pressure along arbitrary paths in the saturation-exposure-time domain, as demonstrated by the simulated surface comparisons.

Reading between the lines

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

  • A natural extension the authors leave implicit: the same interpolation logic should apply to relative permeability, since the pore-scale contact-angle model changes the mobility of phases; a bundle-of-tubes or pore-network study could test whether a single dynamic coefficient again collapses the curves.
  • If real contact-angle kinetics deviate from the Langmuir law, the interpolation identity may still hold but the coefficient $\omega$ would take a different form; the interpolation structure is more robust than the specific fitted scalings.
  • The appearance of apparent hysteresis in a non-hysteretic bundle of tubes suggests that in real porous media, part of the hysteresis observed with reactive fluids may be caused by time-dependent wettability rather than pore geometry or trapping—a distinction experiments could quantify by comparing inert and reactive cycles.
  • Because standard multi-step outflow experiments assume equilibrium, published capillary pressure data for reactive fluid pairs may contain hidden path dependence; re-analyzing historical data with saturation-history integration could reveal whether reported scatter collapses onto the proposed $\omega$ surfaces.
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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

4 major / 5 minor

Summary. The manuscript develops a dynamic capillary-pressure model for porous media subjected to time-dependent wettability alteration. The model interpolates between initial and final static Brooks-Corey curves through a dynamic coefficient ω: Pc = (1−ω) Pc^st,i + ω Pc^st,f. Using a bundle-of-tubes (BoT) pore-scale model with a Langmuir-type contact-angle law θ_m = θ_i + [χ/(C+χ)] ΔΘ, where χ is the integrated non-wetting saturation, the authors simulate drainage-imbibition cycles for uniform and non-uniform alteration, correlate ω to χ and saturation, and propose the pore-to-macroscale scaling laws β1 = 2C and β2 = b1 C^b2. They conclude that a single-parameter interpolation model captures WA-induced capillary-pressure dynamics and that the macroscale dynamics can be quantified 'a priori' from the pore-scale parameter C.

Significance. The topic is practically important for CO2 storage and enhanced oil recovery, where wettability alteration occurs on experimental and reservoir timescales. The paper's simulation framework is transparent, the BoT algorithm is clearly specified, and the authors report excellent fits to their simulated curves (R² = 0.9921 for the uniform case). The paper is also honest in stating that the pore-scale kinetic model is 'a convenient mathematical form' and that 'detailed laboratory work would needed to further justify the use of this model.' If the proposed pore-to-macroscale mappings were validated against independent simulations or experiments, the resulting single-parameter closure would be a useful ingredient for reservoir-scale simulators. The main novelty is the systematic attempt to connect a pore-scale contact-angle rate constant to a macroscale dynamic coefficient.

major comments (4)
  1. [§2.2, Eqs. (9)–(11)] The entire upscaling chain is conditional on the assumed Langmuir-type kinetics θ_m = θ_i + [χ/(C+χ)] ΔΘ. The text itself concedes that this model 'is not intended to capture the full complexity at the pore-scale' and that 'detailed laboratory work would needed to further justify the use of this model.' Consequently the functional forms of ω in Eqs. (14) and (16) are not general results; they are predictions only for this assumed kinetics. The Discussion should explicitly state this conditionality wherever the term 'a priori' is used.
  2. [§3.3.1, Eq. (15) and Fig. 10] The proportionality β1 = 2C is an empirical fit over C ∈ [3,8] × 10^-3, not a derivation. Moreover, an exact consequence of the pore-scale Young–Laplace law (Eq. 7) in the uniform case is Pc(Sw,θ) = cos θ Pc^st,i(Sw) (for θ_i = 0), which gives ω = (cos θ − 1)/(cos θ_f − 1); this is not identically equal to χ/(2C + χ) under Eq. (10). Thus Eq. (15) is an approximate closure calibrated on the same BoT data, and the Discussion's statement that the macroscale dynamics can be quantified 'a priori' overstates what has been demonstrated.
  3. [§3.4.1, Eqs. (16)–(18) and Fig. 19] For the non-uniform case, both α(χ) = β2/χ and the power-law β2 = b1 C^b2 are chosen from the shape of the data, and the latter is fitted to only four values of C over approximately one order of magnitude (Fig. 19) for a single pore-size distribution and fluid pair. The paper provides no out-of-sample test of these scalings for other distributions or fluid properties; therefore the claim that β1 and β2 can be predicted 'directly from the pore scale phenomenon' is not yet supported. Please reframe these as empirical correlations and report their uncertainty and range of validity.
  4. [§3.3.2 and §3.4.2, Figs. 11 and 18] The path-robustness tests in Figs. 11 and 18 do not validate the scaling laws across C; they show that a coefficient calibrated from one saturation path works for other paths with the same C. While this is a useful property, it is not evidence for 'a priori' prediction of the macroscale coefficient from C, which is the paper's strongest claim.
minor comments (5)
  1. [§2.2, text below Eq. (9)] The sentence 'Detailed laboratory work would needed to further justify the use of this model' should read 'would be needed.'
  2. [Fig. 12 caption] The word 'approximatly' should be 'approximately.'
  3. [§3.4.1, Eq. (16)] The function is written as ω(Snw,χ) but is defined in terms of Sw = 1 − Snw; please use the same saturation variable throughout the equation and surrounding text.
  4. [Discussion, first paragraph] The phrase 'single value parameter' is ambiguous; 'single-valued, single-parameter model' would be clearer.
  5. [Figs. 11 and 18] The color bars showing the difference between the model and the simulated data lack labels and units; adding them would make the magnitude of the mismatch easier to assess.

Circularity Check

2 steps flagged · score 6.0 of 10

The 'a priori' macroscale predictions are fitted re-expressions of the assumed Langmuir contact-angle law; the dynamic coefficient is calibrated to the same BoT simulations and then declared predictable from C.

  1. fitted input called prediction [Section 3.3.1, Eqs. (14)-(15), Fig. 10]
    "Given this insight, we propose an adsorption-type model to fit the interpolation coefficient ω to the average exposure time: ω = χ/(β1+χ), where β1 is a fitting parameter obtained from the best fit to simulated data in Figure 8b. ... Figure 10 shows that the interpolation model parameter is directly proportional to the pore-scale model parameter, with a proportionality constant of 2. Thus, the relationship β1 = 2C can be used to predict the macroscale parameter directly from knowledge of the pore-scale process."

    β1 is fitted to BoT simulations whose only time-dependent input is the assumed Langmuir contact-angle law θ = θ_i + [χ/(C+χ)] ΔΘ (Eq. 10). The same χ-dependence is then imposed on the dynamic coefficient ω (Eq. 14), and β1 is mapped to C by a second fit over simulations (Fig. 10). Consequently Eq. 15, Pc = χ/(2C+χ)(Pc^st,f − Pc^st,i) + Pc^st,i, is not an independently predicted macroscale law; it is the input pore-scale kinetics re-expressed with a fitted proportionality constant. The validation in Figs. 9 and 11 compares the model with the same simulated data from which β1 was fitted, so the 'a priori' prediction claim is not supported by an out-of-sample test.

  2. fitted input called prediction [Section 3.4.1, Eqs. (16)-(18), Fig. 19]
    "α(χ)=β2/χ, where β2 is non-dimensional fitting parameter. ... A power law model, β2 = b1C^b2 is observed between these parameters and the model parameters are estimated to be b1 = 3.3 × 10^6 and b2 = 1.8. The model for β2 can be substituted into model (18) to characterize the dynamics of the capillary pressure directly from the pore scale phenomenon."

    The non-uniform dynamic coefficient is built from fitting α to each cycle's ω−Snw data, then setting α = β2/χ, which turns Eq. 16 into ω = χSw/(β2+χSw), an adsorption form in the product χSw. β2 is then fit over simulations with varying C via a power law in C, and the resulting Eq. 18 is compared with the same simulation data used for calibration (Fig. 17). Thus the claimed relationship 'directly from the pore scale phenomenon' is a curve fit over four C values to an unvalidated kinetic ansatz, not an independent prediction.

full rationale

The paper is transparent that the pore-scale contact-angle model is a convenient mathematical ansatz rather than a validated mechanistic law: it states the model 'is not intended to capture the full complexity at the pore-scale' and that 'Detailed laboratory work would needed to further justify the use of this model.' That limitation is acknowledged, so the circularity is not hidden. The central overreach is in the upscaling claim. The dynamic coefficient ω is not derived from the pore-scale physics; it is proposed to have the same sorption form as the assumed θ(χ) law, and the scaling constants β1 = 2C and β2 = b1C^b2 are obtained by fitting to the same BoT simulations that take C as an input. These fitted scalings are then described as 'a priori' predictions of macroscale dynamics from knowledge of the pore-scale process. Moreover, the model validation is in-sample: Figs. 9, 11, 17, and 18 compare the calibrated model to the simulation data that generated the fitting parameters, rather than to independent experimental or out-of-sample simulation data. No load-bearing self-citation chain is present; the prior interpolation and Langmuir references are external and not used to justify the present model's predictions. Because the functional forms are not exact identities—for example, uniform ω would be (cosθ−1)/(cosθ_f−1) rather than exactly χ/(2C+χ)—there is genuine approximation content, so the work is not wholly definitional. However, the central 'single-parameter a priori prediction' claim reduces to a calibration of the assumed kinetic law, which is a partial circularity: one or more predictions reduce to fitted inputs.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The model does not introduce new physical entities; the dynamic coefficient ω is a mathematical fitting construct. The central dependencies are the assumed pore-scale kinetics (C, χ) and the fitted macroscale parameters (β1, β2, b1, b2).

free parameters (7)
  • C (pore-scale wettability alteration rate) = 0.005 (uniform), 1e-5 (non-uniform); varied in 0.003-0.008 and 1e-5 to 7e-5
    Chosen by hand to control the speed of contact angle change; the paper's scaling laws are fitted as functions of C, and C must ultimately be measured in batch experiments.
  • θ_f (final contact angle) = 80 degrees
    Chosen based on literature where contact angle increased from 0 to 75 degrees over 6 months of CO2 exposure; sets the final static capillary pressure curve.
  • β1 (uniform dynamic coefficient parameter) = 0.01 for C=0.005; then β1 = 2C
    Fitted to simulated ω-χ data (Eq. 14) for the uniform WA case; the proportionality constant 2 is fitted in Figure 10.
  • β2 (non-uniform dynamic coefficient parameter) = 0.004 for C=1e-5
    Fitted to simulated ω-Sw data (Eqs. 16-17) for the non-uniform WA case.
  • b1, b2 (scaling law for β2(C)) = b1=3.3e6, b2=1.8
    Fitted power law β2 = b1 C^b2 from Figure 19, using a small number of simulation points.
  • Brooks-Corey parameters cw, aw = cw: 360 Pa (initial), 56 Pa (final); aw: 0.2778 (both)
    Fitted to the simulated static Pc-S curves for the two end wetting states (Table 2).
  • Weibull pore-size distribution parameters = Rmin=10 µm, Rmax=40 µm, rav=23 µm, η=1.5
    Chosen by hand to define the bundle-of-tubes geometry; these inputs shape the static curves and the dynamics.
assumptions (6)
  • standard math Washburn equation for interface velocity in a capillary tube (Eq. 8)
    Standard low-Reynolds, quasi-static two-fluid flow model used to advance interfaces in each tube.
  • domain assumption Bundle-of-tubes representation of pore space, without pore interactions, converging-diverging geometry, or residual trapping
    Acknowledged in Sections 1 and 2.1 as a simplification; the authors note that real pore networks are interacting and can trap phases.
  • ad hoc to paper Langmuir-type contact angle evolution θ_m = θ_i + [χ/(C+χ)] ΔΘ with exposure time χ defined by Eq. (11)
    The mechanistic model for time-dependent wettability alteration is assumed as a convenient mathematical form; the paper states it is not intended to capture surface chemistry and needs laboratory justification.
  • ad hoc to paper Dynamic capillary pressure interpolates linearly between initial and final static Brooks-Corey curves (Eq. 4)
    The interpolation form is taken from prior reservoir simulation models [27,25,3,26] and is assumed to hold for time-dependent WA; it is not derived from pore-scale physics.
  • ad hoc to paper The dynamic coefficient ω is a unique function of χ in the uniform case and of χ and Sw in the non-uniform case
    The paper hypothesizes that Pc becomes a unique function of exposure time χ (Figures 7, 15) and uses this to justify the proposed functional forms for ω.
  • domain assumption Exposure time is proportional to the time-integrated non-wetting saturation
    Eqs. (11)-(12) assume WA agent exposure scales with integrated saturation, ignoring concentration gradients, diffusion, and adsorption capacity details.

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Cite this review

Pith. "Pith review of Impact of Time-Dependent Wettability Alteration on the Dynamics of Capillary Pressure." pith.science (2026). https://pith.science/paper/MJYVJFW3

@misc{pith2026190806863,
  author       = {Pith},
  title        = {Pith review of: Impact of Time-Dependent Wettability Alteration on the Dynamics of Capillary Pressure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MJYVJFW3}},
  note         = {Machine review of arXiv:1908.06863}
}
abstract

Wettability is a pore-scale property that has an important impact on capillarity, residual trapping, and hysteresis in porous media systems. In many applications, the wettability of the rock surface is assumed to be constant in time and uniform in space. However, many fluids are capable of altering the wettability of rock surfaces permanently and dynamically in time. Experiments have shown wettability alteration can significantly decrease capillarity in CO$_2$ storage applications. For these systems, the standard capillary-pressure model that assumes static wettability is insufficient to describe the physics. In this paper, we develop a new dynamic capillary-pressure model that takes into account changes in wettability at the pore-level by adding a dynamic term to the standard capillary pressure function. We simulate the dynamic system using a bundle-of-tubes (BoT) approach, where a mechanistic model for time-dependent contact angle change is introduced at the pore scale. The resulting capillary pressure curves are then used to quantify the dynamic component of the capillary pressure function. This study shows the importance of time-dependent wettability for determining capillary pressure over timescales of months to years. The impact of wettability has implications for experimental methodology as well as macroscale simulation of wettability-altering fluids.

Figures

Figures reproduced from arXiv: 1908.06863 by the authors.

Figure 1
Figure 1. Fluid displacement in non-interactive bundle of tubes (BoT). Here, the left reservoir [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Algorithm for wettability alteration and capillary pressure simulation following drainage [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Simulated Pc-S data for the initial and final wetting states compared to a Brooks-Corey model with calibrated parameters given in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: Simulation results for WA-induced dynamics of capillary pressure as a function of wetting [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Uniform contact angle θ change across the bundle as a function of drainage-imbibition fluid history paths. The color of each data point indicates the time elapsed in months. The dynamics in capillarity are coupled to a continuous change in contact angle between the two…
Figure 6
Figure 6. Figure 6: Saturation history for the simulated Pc-S data over two drainage-imbibition cycles as shown in [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: The capillary pressure data (a) and contact angle (b) as a function of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Plot of the dynamic coefficient ω against wetting phase saturation (a) and χ (b) for the uniform wettability alteration case. The data points are color-coded with exposure time in months. phase saturation but with values that are continuously increasing as the dynamic …
Figure 9
Figure 9. Figure 9: Comparison of the dynamic capillary pressure model for uniform wettability alteration [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: The relation between pore-scale wettability model parameter [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: (a) Simulated capillary pressure under uniform WA obtained by taking multiple paths [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 12
Figure 12. Figure 12: Simulated capillary pressure curves for the case of non-uniform WA over four drainage [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]
Figure 13
Figure 13. Figure 13: Dynamic contact angle evolution as a function of exposure time to the WA agent per [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]
Figure 14
Figure 14. Figure 14: Non-wetting fluid history paths over the four displacement cycles (a) and the averaged [PITH_FULL_IMAGE:figures/full_fig_p016_14.png]
Figure 15
Figure 15. Figure 15: Simulated capillary pressure curves for the case of non-uniform WA over four drainage [PITH_FULL_IMAGE:figures/full_fig_p017_15.png]
Figure 16
Figure 16. Figure 16: The dynamic coefficient obtained by applying equation (3): as a function of saturation [PITH_FULL_IMAGE:figures/full_fig_p017_16.png]
Figure 17
Figure 17. Figure 17: Comparison of the dynamic model (18) with the simulated [PITH_FULL_IMAGE:figures/full_fig_p018_17.png]
Figure 18
Figure 18. Figure 18: (a) Simulated capillary pressure under non-uniform WA obtained by taking multiple [PITH_FULL_IMAGE:figures/full_fig_p019_18.png]
Figure 19
Figure 19. Figure 19: The relation between pore-scale wettability model parameter [PITH_FULL_IMAGE:figures/full_fig_p019_19.png]

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Pith tools

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