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arxiv: 2512.21990 · v2 · submitted 2025-12-26 · ⚛️ physics.flu-dyn · physics.chem-ph

Bridging scales in porous media: cDFT-informed pore network modelling for fluid transport with nanoconfined phase behavior

Irina Nesterova , Rustem Sirazov , Aleksey Khlyupin This is my paper

Pith reviewed 2026-05-16 19:55 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.chem-ph
keywords pore network modellingclassical density functional theorycapillary condensationnanoporous mediapermeabilitymultiscale modelingcapillary hysteresis
0
0 comments X

The pith

Pore network models that remove condensate-blocked nanopores show permeability depending on pore sizes and pressure direction.

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

This paper develops a multiscale model combining classical density functional theory for nanoconfined capillary condensation with quasi-static pore network modeling. Blocked pores are excluded from flow, leading to reduced permeability. The reduction depends strongly on pore and throat size distributions, sample geometry, size, structure, and whether pressure increases or decreases. A sympathetic reader would care because this provides a method to account for nanoscale effects in larger-scale fluid transport predictions in porous media.

Core claim

The central claim is that incorporating classical density functional theory calculations of capillary condensation and hysteresis into quasi-static pore network models allows prediction of permeability reduction by excluding blocked pores, with the resulting permeability depending on porous space geometry including pore and throat size distributions, sample size and structure, and on thermodynamic processes such as pressure growth or decrease.

What carries the argument

Quasi-static pore network model informed by classical density functional theory for capillary condensation with hysteresis, where blocked pores are excluded to compute permeability.

If this is right

  • Permeability falls as more pores become blocked by condensate under nanoconfinement.
  • The size of the permeability reduction changes with the particular pore size distribution and throat sizes.
  • Different sample sizes and internal structures produce different permeability values under the same conditions.
  • The direction of pressure change affects hysteresis and therefore the final permeability.

Where Pith is reading between the lines

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

  • Standard pore network models ignoring nanoconfined condensation may overestimate permeability.
  • The method could be applied to real rock samples to refine predictions for tight reservoirs.
  • Similar effects may occur in other confined geometries like membranes.

Load-bearing premise

Pores fully blocked by condensate can be excluded from the flow network without residual film flow, and quasi-static cDFT calculations represent phase behavior in the connected network.

What would settle it

Compare model-predicted permeability changes with experimental measurements on a sample with known pore size distribution during pressure cycles across the condensation threshold.

Figures

Figures reproduced from arXiv: 2512.21990 by Aleksey Khlyupin, Irina Nesterova, Rustem Sirazov.

Figure 1
Figure 1. Figure 1: Schematic illustration of fluid properties in nanoporous media. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Mock-up of the image, where the channels with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Density profiles of carbon dioxide at T = 298 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: PVT for 𝐶𝑂2 at T = 298 K during pressure increase up to 10 MPa in the bulk and in the pores H = 3, 5, and 8 nm [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Pressures of capillary condensation for 𝐶𝑂2 in the pores H = 3-20 nm at T = 298 K during pressure increase and decrease. Inset: PVT hysteresis at H = 8 nm. values. As illustrated in Fig.4, the PVT characteristics of carbon dioxide at T = 298 K in the pores H = 3,5,8 nm deviate from the bulk PVT behavior. As one can see, PVT depends on the pore size, and wider pores provide fluid PVT properties closer to it… view at source ↗
Figure 6
Figure 6. Figure 6: Permeability drop for 𝐶𝑂2 filtration in the sample ’lin-300’ at T = 298 K. condensation in the pores occurs at lower pressure values than the pressure of phase transition in the bulk, and for smaller pores, it happens at lower pressure values. After that, we collect the results of the pressures for capillary condensation during pressure increase and cap￾illary recondensation during pressure decrease to inv… view at source ↗
Figure 7
Figure 7. Figure 7: Capillary hysteresis for carbon dioxide at T = 273 K (left) and T = 298 K (right) and corresponding [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Permeability drop for ’lin’ samples with various [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Pore and throat size distribution alongside the results of permeability drops at T = 298 K in the samples: [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Permeability drop for 6 samples with artificially generated structure from one PSD at T = 273 K along [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: At the top: pore PVT for carbon dioxide at [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
read the original abstract

The simulation of fluid flow in real, multiscale porous media remains challenging due to the complexity of nanoscale phenomena and the difficulty of developing upscaling methodologies. In this study, we introduce a multiscale filtration framework based on quasi-static Pore Network Modelling, incorporating the effects of pore blockage resulting from capillary condensation of fluid in the nanoporous space. To accurately predict capillary condensation in nanoconfinement, we apply classical Density Functional Theory calculations considering capillary hysteresis. The pores blocked by condensate are excluded from the fluid flow, resulting in a decrease in permeability of the porous space. Our findings demonstrate that the resulting permeability is strongly dependent on the geometry of the porous space, including pore size distribution, throat size distribution, sample size, and the particular structure of the sample, as well as thermodynamic conditions and processes, specifically pressure growth or decrease. Overall, the presented research contributes valuable insights into multiscale transport phenomena and facilitates the advancement of upscaling techniques.

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

3 major / 2 minor

Summary. The paper introduces a multiscale framework that couples quasi-static classical Density Functional Theory (cDFT) calculations of capillary condensation (including hysteresis) in nanopores with Pore Network Modelling (PNM) to simulate fluid transport. Blocked pores are removed from the network, and the resulting permeability is reported to depend strongly on pore/throat size distributions, sample size, network structure, and whether pressure is increasing or decreasing.

Significance. If the quantitative predictions are validated, the approach could offer a computationally tractable route to incorporate nanoconfined phase behavior into upscaling of transport properties for applications such as filtration and subsurface flows. The work correctly identifies that geometry and thermodynamic path matter, but the current lack of direct validation against experiments or full simulations limits its immediate utility for predictive modeling.

major comments (3)
  1. [Abstract / methodology description] Abstract and methodology: the central claim that permeability is strongly reduced by excluding condensate-blocked pores rests on the assumption that such pores contribute zero residual flow. Quasi-static cDFT typically predicts a condensed core plus thin adsorbed films; these films can sustain surface diffusion or film flow, especially near molecular scales. No quantitative estimate of the error introduced by complete exclusion is supplied, which directly affects the reported sensitivity to geometry and pressure history.
  2. [Abstract] Abstract: the findings are stated as demonstrating strong dependence on pore/throat distributions, sample size, structure, and pressure path, yet no error bars, sensitivity coefficients, or direct comparisons to experiments or pore-scale DNS are provided. This leaves the quantitative strength of the dependence unsupported.
  3. [Methodology] The quasi-static cDFT treatment is applied to individual pores or throats and then mapped onto the network; no analysis is given of how flow-induced perturbations or network connectivity might alter the local phase distribution relative to the isolated-pore cDFT solutions.
minor comments (2)
  1. [Methodology] Clarify the precise criterion used to declare a pore 'blocked' (e.g., filling fraction threshold) and whether throat blockage is treated independently or coupled to adjacent pores.
  2. [Abstract] The abstract refers to 'sample size' dependence; specify whether this is a finite-size effect in the network realization or a scaling with physical domain size.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address each major comment below, clarifying our modeling assumptions and outlining targeted revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract / methodology description] Abstract and methodology: the central claim that permeability is strongly reduced by excluding condensate-blocked pores rests on the assumption that such pores contribute zero residual flow. Quasi-static cDFT typically predicts a condensed core plus thin adsorbed films; these films can sustain surface diffusion or film flow, especially near molecular scales. No quantitative estimate of the error introduced by complete exclusion is supplied, which directly affects the reported sensitivity to geometry and pressure history.

    Authors: We acknowledge that the complete exclusion of condensate-blocked pores is an approximation. Quasi-static cDFT solutions do retain thin adsorbed films, which can support limited surface diffusion or film flow. In our framework the dominant permeability reduction arises from the sharp drop in effective cross-section once a condensed core forms; film contributions are secondary for the pore sizes and pressures examined. In revision we will add a dedicated paragraph in the methodology section that (i) states the approximation explicitly, (ii) cites literature values for film-flow conductivity in nanopores, and (iii) supplies an order-of-magnitude error estimate (typically <15 % for the conditions studied). This will also qualify the reported sensitivities to geometry and pressure history. revision: partial

  2. Referee: [Abstract] Abstract: the findings are stated as demonstrating strong dependence on pore/throat distributions, sample size, structure, and pressure path, yet no error bars, sensitivity coefficients, or direct comparisons to experiments or pore-scale DNS are provided. This leaves the quantitative strength of the dependence unsupported.

    Authors: The present work is a methodological demonstration that employs parametric sweeps to reveal trends rather than a validated predictive tool. We will revise the abstract to temper the wording and will augment the results section with sensitivity coefficients (partial derivatives of permeability with respect to key distribution parameters) together with error bars derived from ensemble runs over randomized network realizations. Direct experimental or DNS benchmarks lie outside the scope of this initial paper; we will add a short forward-looking paragraph indicating how such validation could be structured. revision: partial

  3. Referee: [Methodology] The quasi-static cDFT treatment is applied to individual pores or throats and then mapped onto the network; no analysis is given of how flow-induced perturbations or network connectivity might alter the local phase distribution relative to the isolated-pore cDFT solutions.

    Authors: Our model adopts the quasi-static approximation on the premise that capillary condensation equilibrates on timescales much shorter than advective transport. We will insert a new paragraph in the methodology section that (i) justifies the isolated-pore cDFT mapping via timescale estimates, (ii) discusses the expected magnitude of flow-induced perturbations (small for low Reynolds number and moderate pressure gradients), and (iii) explicitly flags network-connectivity effects as a limitation to be addressed in future dynamic-cDFT extensions. revision: yes

Circularity Check

0 steps flagged

No circularity: cDFT phase calculations and PNM exclusion are independent inputs to permeability

full rationale

The derivation applies classical Density Functional Theory (cDFT) as an external quasi-static solver for nanoconfined capillary condensation and hysteresis, then removes fully blocked pores from the pore-network flow graph. Permeability is computed from the resulting network geometry and pressure conditions. No equation reduces the output permeability to a parameter fitted from the same permeability data, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in via prior work by the same authors. The reported sensitivity to pore/throat distributions, sample size, and pressure path follows directly from the network simulation once the cDFT-derived blockage map is supplied; the steps remain non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard domain assumptions of quasi-static PNM and mean-field cDFT without introducing new fitted parameters or entities in the abstract description.

axioms (2)
  • domain assumption Quasi-static approximation holds for the filtration process
    Invoked to allow equilibrium cDFT calculations at each pressure step without dynamic effects.
  • domain assumption Blocked pores are fully excluded from the flow network
    Stated directly as the mechanism linking condensation to permeability drop.

pith-pipeline@v0.9.0 · 5478 in / 1264 out tokens · 34371 ms · 2026-05-16T19:55:54.704698+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The pores blocked by condensate are excluded from the fluid flow, resulting in a decrease in permeability... permeability is strongly dependent on the geometry of the porous space, including pore size distribution, throat size distribution, sample size, and the particular structure of the sample, as well as thermodynamic conditions and processes, specifically pressure growth or decrease.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We perform DFT calculations of fluid density in the pore during pressure increase and decrease and calculate average density in the pore... capillary hysteresis

What do these tags mean?
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extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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