{"id":"a5a4cc01-a493-49ef-8c1a-abb1a9e15c21","arxiv_id":"1908.06863","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A single-parameter interpolation model is shown to capture time-dependent capillary pressure caused by wettability alteration in bundle-of-tube simulations.","lead":"This paper derives a formula for how capillary pressure in rocks changes slowly as fluids alter the wetting properties of pore surfaces, using a simplified bundle-of-tubes simulation. The result gives reservoir modelers a single adjustable parameter to capture months-long wettability effects in CO2 storage and oil recovery.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'a priori' pore-to-macro scaling laws are fitted to one untested kinetic law and one BoT parameter set; the central claim is conditional, not established.","rationale":"The reader's CONDITIONAL verdict is appropriate. I find no internal inconsistency in the BoT simulations; the fitted models reproduce the simulated surfaces in Figs. 11 and 18, which is genuine in-sample support. The load-bearing weakness is external and quantitative: the a priori pore-to-macro map (β1=2C, β2=3.3×10^6 C^1.8) is fit to simulations generated under a particular Langmuir contact-angle law and a single BoT parameter set, without experimental calibration or sensitivity analysis over geometry, final contact angle, viscosity ratio, or characteristic time T. This does not warrant rejection—the paper is an honest modeling study with explicitly stated limitations—but it does require conditional acceptance pending the proposed sensitivity and experimental checks. I partially agree with the reader's weakest assumption: the pore-scale kinetics is the root of the uncertainty, but I would additionally emphasize that even under the assumed kinetics the macroscale scaling laws are empirical fits, not derived identities, so the 'a priori' claim is weaker than the discussion suggests.","tokens_in":15209,"tokens_out":11992,"duration_ms":126248,"concrete_test":"Re-run the uniform and non-uniform BoT simulations with the same C values, geometry, and χ histories, but replace the Langmuir law Eq. (10) with the first-order expression θ=θ_i+(1−e^{−χ/C})ΔΘ (and its local-χ analogue). Refit β1 and β2 from the new ω data. If Eqs. (14) and (16) no longer collapse the data, or if the best-fit β1(C)/β2(C) scalings depart from β1=2C and β2=3.3×10^6 C^1.8, then the single-parameter interpolation and its pore-to-macro scaling are specific to the Langmuir kinetics, not a general consequence of WA dynamics.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that a single-parameter interpolation model can be predicted a priori from the pore-scale constant C—has two load-bearing supports, and both are fitted rather than derived. First, the pore-scale kinetics, Eqs. (9)-(11), is a Langmuir ansatz in integrated saturation; the paper itself calls it 'a convenient mathematical form' and concedes that 'detailed laboratory work would needed to further justify the use of this model.' If real contact-angle evolution is not Langmuir in χ, the functional forms Eq. (14) and Eq. (16) are not implied. Second, even accepting that kinetics, the macroscale scaling laws are empirical fits over narrow ranges (C=3-8e-3 in Fig. 10; C=1-7e-5 in Fig. 19) for one BoT geometry and fluid pair. For the uniform case, the exact consequence of Eq. (10) is Pc(Sw,θ)=Pc_st,i(Sw)cosθ, hence ω=(cosθ−1)/(cosθf−1), which is not identically χ/(2C+χ); the β1=2C relation is an approximation, not a derivation. The non-uniform β2=b1 C^b2 is fit to four points. The paper's own Discussion states that 'further study is needed to calibrate the macroscale dynamic parameter to actual data.' Thus the strongest claim is not internally contradictory, but its quantitative predictive reach is unestablished.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":15660,"tokens_out":5467,"duration_ms":50826,"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":[{"comment":"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.","section":"§2.2, Eqs. (9)–(11)"},{"comment":"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.","section":"§3.3.1, Eq. (15) and Fig. 10"},{"comment":"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.","section":"§3.4.1, Eqs. (16)–(18) and Fig. 19"},{"comment":"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.","section":"§3.3.2 and §3.4.2, Figs. 11 and 18"}],"minor_comments":[{"comment":"The sentence 'Detailed laboratory work would needed to further justify the use of this model' should read 'would be needed.'","section":"§2.2, text below Eq. (9)"},{"comment":"The word 'approximatly' should be 'approximately.'","section":"Fig. 12 caption"},{"comment":"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.","section":"§3.4.1, Eq. (16)"},{"comment":"The phrase 'single value parameter' is ambiguous; 'single-valued, single-parameter model' would be clearer.","section":"Discussion, first paragraph"},{"comment":"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.","section":"Figs. 11 and 18"}],"recommendation":"major_revision","confidential_remarks":"The manuscript has a plausible and clearly presented core: a dynamic interpolation model for capillary pressure under wettability alteration, supported by BoT simulations. My main reservation is that the strongest claim—that the macroscale dynamic coefficient can be predicted 'a priori' from the pore-scale parameter C—is supported only by least-squares scaling laws fitted to one pore-scale model and one parameter set. A revision that reframes these results as calibrated empirical correlations, adds explicit out-of-sample checks, and softens the predictive language would bring the claims in line with the evidence. I do not see a fundamental internal inconsistency in the central idea."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper does something genuinely useful — it turns time-dependent wettability alteration into a single-parameter interpolation model for capillary pressure, with a plausible pore-scale story — but the scaling laws that connect pore-scale C to macroscale β are fitted to a handful of simulations under one assumed kinetic law, not derived. Treat the quantitative claims as provisional.\n\nWhat's new and good: previous reservoir-simulator work treated wettability alteration as instantaneous. This paper adds exposure time explicitly via χ, the time-integrated non-wetting saturation, and shows in a bundle-of-tubes model that a Langmuir-type contact angle law (Eq. 10) leads to an equally simple macroscale interpolation coefficient. The uniform case ω = χ/(2C+χ) fits simulated Pc-S curves with R²=0.992 and the non-uniform case ω = χSw/(β2+χSw) captures the cycle-by-cycle hysteresis-like behavior with one parameter. They also test both models over multiple arbitrary saturation-time paths after calibrating on a single path, and report small differences (Figs 11, 18). That is a real, reproducible-in-principle modeling contribution, and the paper is honest about the BoT limitations and the need for lab work.\n\nSoft spots: The pore-scale kinetics is an ansatz. The paper says so. If real contact angle evolution is not Langmuir in integrated saturation, then the functional forms of ω do not follow. More importantly, the 'a priori' predictions β1=2C and β2=b1C^b2 are empirically fitted over narrow ranges (C=3–8e-3 and 1–7e-5) for one geometry and fluid pair. They are convenient correlations, not derivations. The stress-test note is right that uniform-case ω from cosθ is not identically χ/(2C+χ); β1=2C is an approximation that happens to work for the simulated data. And because the model is validated against the same simulator and the same assumed kinetics, the agreement is internal consistency, not external validation. No code or data are provided in the arXiv version, so others cannot check the fits independently.\n\nBottom line: The model is plausible and potentially useful for reservoir simulators, and the paper is clearly written. The overreach is in calling the scaling laws predictions from pore-scale mechanism. A good referee should ask for softened claims, for code/data, and ideally for one experimental or direct-simulation-anchored test (e.g., contact angle kinetics from batch experiments) before the correlations are used quantitatively. That is a standard conditional accept path for a modeling paper.\n\nRecommendation: send to peer review. It would be a shame to desk-reject something that, with honest editing and supplementary material, could be a useful reference for CO2 storage and EOR modeling.","headline":"Useful single-parameter interpolation model for dynamic capillarity, but the pore-to-macro scalings are fitted, not derived — worth refereeing with honest revision.","tokens_in":16108,"tokens_out":2696,"would_cite":true,"duration_ms":26057,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["47.56.+r","68.08.Bc"],"model":"deepseek-v4-flash","headline":"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.","keywords":["wettability alteration","dynamic capillary pressure","bundle-of-tubes model","contact angle","exposure time","CO2 storage","interpolation model","Langmuir adsorption"],"falsifier":"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.","tokens_in":15021,"feed_emoji":"💧","tokens_out":8698,"duration_ms":79133,"temperature":0.7,"pith_summary":"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.","feed_headline":"One rate constant predicts capillary-pressure decline over months","feed_subtitle":"Interpolating between initial and final wetting states reproduces simulated CO2-storage capillary pressures with one parameter.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the experimental evidence that capillary pressure decreases over six months of CO$_2$-brine exposure while contact angle rises from 0 to 75 degrees, motivating the dynamic model.","marker":"[18]"},{"why":"Provides the instantaneous wettability-alteration interpolation model used in reservoir simulation that this paper generalizes to exposure-time dependence.","marker":"[27]"},{"why":"Gives the contact-angle-based Langmuir adsorption model that the paper adopts as the pore-scale mechanism for contact angle change.","marker":"[26]"},{"why":"Supplies the bundle-of-tubes methodology for computing dynamic capillary pressure-saturation behavior, extended here to time-dependent wettability.","marker":"[22]"},{"why":"Provides the bundle-of-tubes capillary pressure correlation and pore-size distribution approach used to define the static end-state curves.","marker":"[31]"},{"why":"Anchors the static curve reduction through the prediction that entry pressure scales with $\\cos\\theta$, matching the simulated decrease from 0 to 80 degrees.","marker":"[34]"},{"why":"Serves as the alternative mixed-wet capillary pressure correlation considered for comparison, showing why a single-parameter model is preferred.","marker":"[33]"},{"why":"Identifies the only prior study that included exposure time in wettability-alteration constitutive relations, highlighting the missing pore-to-macroscale upscaling that this paper addresses.","marker":"[29]"}],"fun_headline_variants":["One rate constant forecasts months of capillary pressure decline","Dynamic capillary pressure is a linear mix of wetting states","Pore-scale rate constant predicts dynamic capillary pressure","Wettability alone can create apparent capillary hysteresis","Wettability shift simplifies capillary pressure to a single constant"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["One rate constant forecasts months of capillary pressure decline","Dynamic capillary pressure is a linear mix of wetting states","Pore-scale rate constant predicts dynamic capillary pressure","Wettability alone can create apparent capillary hysteresis","Wettability shift simplifies capillary pressure to a single constant"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001694,"raw_usage":{"total_tokens":6734,"prompt_tokens":991,"completion_tokens":5743,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":607,"completion_tokens_details":{"reasoning_tokens":5668}},"tokens_in":607,"tokens_out":5743,"duration_ms":42022,"temperature":1.0,"reasoning_tokens":5668,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:09:52.373261+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"& Tokunaga, T","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental evidence that capillary pressure decreases over six months of CO$_2$-brine exposure while contact angle rises from 0 to 75 degrees, motivating the dynamic model."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the instantaneous wettability-alteration interpolation model used in reservoir simulation that this paper generalizes to exposure-time dependence."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the contact-angle-based Langmuir adsorption model that the paper adopts as the pore-scale mechanism for contact angle change."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the bundle-of-tubes methodology for computing dynamic capillary pressure-saturation behavior, extended here to time-dependent wettability."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the bundle-of-tubes capillary pressure correlation and pore-size distribution approach used to define the static end-state curves."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Anchors the static curve reduction through the prediction that entry pressure scales with $\\cos\\theta$, matching the simulated decrease from 0 to 80 degrees."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Serves as the alternative mixed-wet capillary pressure correlation considered for comparison, showing why a single-parameter model is preferred."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Identifies the only prior study that included exposure time in wettability-alteration constitutive relations, highlighting the missing pore-to-macroscale upscaling that this paper addresses."}],"review_version":1}