pith. sign in

arxiv: 2504.05920 · v1 · submitted 2025-04-08 · ⚛️ physics.flu-dyn

Local Thermal Non-Equilibrium Models in Porous Media: A Comparative Study of Conduction Effects

Anna Mareike Kostelecky , Ivar Stefansson , Carina Bringedal , Tufan Ghosh , Helge K. Dahle , Rainer Helmig This is my paper

Pith reviewed 2026-05-22 20:55 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords local thermal non-equilibriumporous mediahomogenizationREV-scale modeldual-network modelconductioninterfacial heat transferpore-resolved simulation
0
0 comments X

The pith

The REV-scale model with homogenization-derived effective parameters reproduces pore-resolved LTNE temperature profiles in conductive porous media, unlike dual-network models.

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

The paper compares three continuum models for heat transfer between fluid and solid phases in fully saturated porous media under conditions where local thermal equilibrium may fail. It evaluates dual-network and REV-scale models against a detailed pore-resolved simulation used as reference. The central result is that only the REV-scale formulation whose parameters come from homogenization matches the reference temperatures, because that route alone includes the interfacial heat transfer coefficient. A reader would care because many technical systems operate in conduction-dominated regimes where accurate yet computationally cheap models are needed to predict whether the two phases stay at different temperatures.

Core claim

In purely conductive systems with one fluid and one solid phase, the local thermal equilibrium assumption holds only when interfacial resistance is low; when resistance is high the phases develop distinct temperatures. Among the tested upscaled models the REV-scale version supplied with effective parameters obtained by homogenization produces temperature fields close to the pore-resolved reference, while the dual-network model deviates more because of its fixed spatial resolution. Only the homogenization route among the effective-parameter choices captures the LTNE regime, since it alone incorporates the interfacial heat transfer coefficient.

What carries the argument

Homogenization-derived effective parameters for the REV-scale model, which embed the interfacial heat transfer coefficient.

If this is right

  • Local thermal equilibrium holds for low interfacial resistances in conduction-only systems.
  • Solid and fluid temperatures diverge when interfacial resistances become large.
  • The REV-scale model supplied with homogenization parameters produces results close to the pore-resolved reference.
  • The dual-network model deviates further from the reference because of its fixed spatial resolution.
  • Only the homogenization-based effective-parameter set captures LTNE behavior by including the interfacial heat transfer coefficient.

Where Pith is reading between the lines

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

  • The same homogenization route may remain the preferred upscaling method once convection is added, as the follow-up study plans to examine.
  • Engineering codes for geothermal or filtration systems could adopt the homogenization-based REV model to obtain phase-specific temperatures without resolving every pore.
  • The finding underscores that accurate treatment of the solid-fluid interface is decisive for model selection in any LTNE problem, even when flow is absent.
  • The comparison framework could be tested on different pore geometries or material pairs to check whether the advantage of homogenization persists.

Load-bearing premise

The pore-resolved simulation is accepted as a reliable reference for judging the continuum models even though no experimental data are available.

What would settle it

Laboratory measurements of separate solid and fluid temperature profiles inside a saturated porous specimen with deliberately high interfacial thermal resistance, under pure conduction, would show whether the homogenization-based REV model matches reality while the alternatives do not.

Figures

Figures reproduced from arXiv: 2504.05920 by Anna Mareike Kostelecky, Carina Bringedal, Helge K. Dahle, Ivar Stefansson, Rainer Helmig, Tufan Ghosh.

Figure 1
Figure 1. Figure 1: Overview of the different continuum-scale modeling approaches for taking LTNE [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Geometrical setup of the simulation domain with [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Averaged REV-scale temperatures for three different model classes, which are [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Averaged REV-scale temperatures for three different model classes, which are [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Averaged REV-scale temperatures for three different effective conductivity mod [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
read the original abstract

Instantaneous heat transfer between different phases is a common assumption for modeling heat transfer in porous media, known as Local Thermal Equilibrium (LTE). This assumption may not hold in certain technical and environmental applications, especially in systems with large temperature gradients, large differences in thermal properties, or high velocities. Local Thermal Non-Equilibrium (LTNE) models aim to describe heat transfer processes when the LTE assumption may fail. In this work, we compare three continuum-scale models from the pore to the representative elementary volume (REV) scale. Specifically, dual-network and REV-scale models are evaluated against a pore-resolved model, which we perceive as a reference in the absence of experimental results. Different effective models are used to obtain upscaled properties on the REV scale and to compare resulting temperature profiles. The systems investigated are fully saturated, consisting of one fluid and one solid phase. This study focuses on purely conductive systems without significant differences in thermal properties. Results show that LTE holds then for low interfacial resistances. However, for large interfacial resistances, solid and fluid temperatures differ. The REV-scale model with effective parameters obtained by homogenization leads to similar results as the pore-resolved model, whereas the dual-network model shows greater deviation due to its fixed spatial resolution. Among the evaluated effective parameter formulations for the REV-scale model, only the homogenization-based approach captures the LTNE behavior, as it incorporates the interfacial heat transfer coefficient. Convection is relevant for most practical applications, and its impact will be addressed in a follow-up article.

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

1 major / 0 minor

Summary. The manuscript compares three models for conductive heat transfer in fully saturated porous media (one fluid, one solid phase) under conditions where local thermal equilibrium (LTE) may fail: a pore-resolved model (treated as reference in the absence of experiments), a dual-network model, and REV-scale models using different effective parameter sets. It reports that LTE holds at low interfacial resistances but solid-fluid temperature differences emerge at high resistances; the homogenization-based REV model produces temperature profiles similar to the pore-resolved reference while the dual-network deviates due to fixed spatial resolution; and only the homogenization formulation captures LTNE because it incorporates the interfacial heat transfer coefficient. Convection effects are deferred to a follow-up.

Significance. If the numerical comparisons are reliable, the work provides concrete guidance on selecting upscaled models for LTNE in conduction-dominated porous-media applications by showing which effective-parameter choices reproduce pore-scale behavior. The explicit multi-model comparison and focus on interfacial resistance as the driver of LTNE constitute a useful contribution to the literature on homogenization versus network approaches.

major comments (1)
  1. [Abstract] Abstract (and the systems-investigated paragraph): the central ranking—that the homogenization-based REV-scale model matches the pore-resolved reference while the dual-network deviates, and that only homogenization captures LTNE—depends on the pore-resolved simulation being an accurate ground truth. No mesh-convergence study, residual norms, grid-refinement data, or domain-size sensitivity analysis is supplied to quantify discretization error, particularly in the high-resistance cases where LTNE is observed. Without such evidence the reported similarity and model ranking remain inconclusive.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and the opportunity to strengthen the manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the systems-investigated paragraph): the central ranking—that the homogenization-based REV-scale model matches the pore-resolved reference while the dual-network deviates, and that only homogenization captures LTNE—depends on the pore-resolved simulation being an accurate ground truth. No mesh-convergence study, residual norms, grid-refinement data, or domain-size sensitivity analysis is supplied to quantify discretization error, particularly in the high-resistance cases where LTNE is observed. Without such evidence the reported similarity and model ranking remain inconclusive.

    Authors: We agree that explicit quantification of discretization error is necessary to substantiate the pore-resolved model as reference. In the revised manuscript we will add a dedicated mesh-convergence section that reports residual norms, successive grid-refinement results, and temperature-profile convergence metrics, with emphasis on the high interfacial-resistance cases. These additions will directly support the model ranking and the claim that only the homogenization-based REV formulation captures LTNE. revision: yes

Circularity Check

0 steps flagged

No circularity: independent model formulations compared against pore-resolved reference

full rationale

The paper compares three distinct continuum-scale models (pore-resolved as reference, dual-network, and REV-scale with varying effective-parameter formulations) in purely conductive saturated systems. The homogenization-based REV model is shown to match the pore-resolved results more closely and to capture LTNE via the interfacial coefficient, while other formulations deviate. These are separately derived models whose outputs are compared numerically; no equation reduces a reported outcome to a fitted quantity defined by the same data, no self-definition occurs, and no load-bearing premise collapses to a self-citation chain. The explicit choice to treat the pore-resolved simulation as reference in the absence of experiments is a methodological assumption, not a circular derivation step.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review supplies insufficient detail to enumerate specific free parameters or invented entities; the work relies on standard continuum assumptions for porous media and treats the pore-resolved simulation as ground truth without external benchmarks.

axioms (1)
  • domain assumption Continuum-scale modeling via representative elementary volume is valid for the systems studied
    Invoked when moving from pore-resolved to REV-scale descriptions (abstract).

pith-pipeline@v0.9.0 · 5828 in / 1242 out tokens · 33696 ms · 2026-05-22T20:55:55.197808+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

17 extracted references · 17 canonical work pages

  1. [1]

    Elsevier

    The effective thermal conductivity of sat- urated porous media, in: Advances in Heat Transfer. Elsevier. volume 39, pp. 377–460. doi: 10.1016/S0065-2717(06)39004-1. Auriault, J.L., Boutin, C., Geindreau, C.,

    work page doi:10.1016/s0065-2717(06)39004-1

  2. [2]

    doi: 10.18419/DARUS-4771

    Netgen/ngsolve code for pore-resolved simulations for: ”local thermal non-equilibrium models in porous media: A comparative study of conduction effects”. doi: 10.18419/DARUS-4771. Dahmen, W., Gotzen, T., M¨ uller, S., Rom, M.,

    work page doi:10.18419/darus-4771

  3. [3]

    International journal for numerical methods in fluids 76, 331–365

    Numerical simulation of transpiration cooling through porous material. International journal for numerical methods in fluids 76, 331–365. doi: 10.1002/fld.3935. Dullien, F.A.,

    work page doi:10.1002/fld.3935

  4. [4]

    Surfaces and Interfaces 50 33, 102188

    Interfacial thermal resistance between nanoconfined water and sil- icon: Impact of temperature and silicon phase. Surfaces and Interfaces 50 33, 102188. URL: https://www.sciencedirect.com/science/article/ pii/S2468023022004540, doi:10.1016/j.surfin.2022.102188. Gostick, J.T., Khan, Z.A., Tranter, T.G., Kok, M.D., Agnaou, M., Sadeghi, M., Jervis, R.,

    work page doi:10.1016/j.surfin.2022.102188 2022

  5. [5]

    International journal of heat and mass transfer 49, 2315–2327

    Heat/mass transfer in porous electrodes of fuel cells. International journal of heat and mass transfer 49, 2315–2327. doi:10.1016/j.ijheatmasstransfer.2005.11.021. Keilegavlen, E., Berge, R., Fumagalli, A., Starnoni, M., Stefansson, I., Varela, J., Berre, I.,

    work page doi:10.1016/j.ijheatmasstransfer.2005.11.021 2005

  6. [6]

    Computational Geosciences 25, 243–265

    Porepy: An open-source software for simu- lation of multiphysics processes in fractured porous media. Computational Geosciences 25, 243–265. doi: 10.1007/s10596-020-10002-5 . Koch, T., Gl¨ aser, D., Weishaupt, K., Ackermann, S., Beck, M., Becker, B., Burbulla, S., Class, H., Coltman, E., Emmert, S., Fetzer, T., Gr¨ uninger, C., Heck, K., Hommel, J., Kurz,...

    work page doi:10.1007/s10596-020-10002-5 2020

  7. [7]

    doi: 10.1007/978-3-319-49562-0

    Springer. doi: 10.1007/978-3-319-49562-0 . Nuske, P., Ronneberger, O., Karadimitriou, N.K., Helmig, R., Has- sanizadeh, S.M.,

    work page doi:10.1007/978-3-319-49562-0

  8. [8]

    International Journal of Heat and Mass Transfer 88, 822–835

    Modeling two-phase flow in a micro-model with local thermal non-equilibrium on the darcy scale. International Journal of Heat and Mass Transfer 88, 822–835. URL: https:// www.sciencedirect.com/science/article/pii/S0017931015004275, doi:10.1016/j.ijheatmasstransfer.2015.04.057. Pati, S., Borah, A., Boruah, M.P., Randive, P.R.,

    work page doi:10.1016/j.ijheatmasstransfer.2015.04.057 2015

  9. [9]

    Pollack, G.L.,

    doi:10.1016/j.icheatmasstransfer.2022.105889. Pollack, G.L.,

    work page doi:10.1016/j.icheatmasstransfer.2022.105889 2022

  10. [10]

    Kapitza resistance. Rev. Mod. Phys. 41, 48–81. URL: https://link.aps.org/doi/10.1103/RevModPhys.41.48, doi:10.1103/ RevModPhys.41.48. Quintard, M., Whitaker, S.,

    work page doi:10.1103/revmodphys.41.48

  11. [11]

    Elsevier

    One-and two-equation models for transient diffusion processes in two-phase systems, in: Advances in heat transfer. Elsevier. volume 23, pp. 369–464. doi: 10.1016/S0065-2717(08)70009-1. Sch¨ oberl, J.,

    work page doi:10.1016/s0065-2717(08)70009-1

  12. [12]

    Transport in Porous Media 141, 737–769

    A three-dimensional homogenization ap- proach for effective heat transport in thin porous media. Transport in Porous Media 141, 737–769. doi: 10.1007/s11242-022-01746-y . Shahraeeni, E., Or, D.,

    work page doi:10.1007/s11242-022-01746-y

  13. [13]

    Stefansson, I.,

    doi: 10.1029/2009WR008455. Stefansson, I.,

    work page doi:10.1029/2009wr008455

  14. [14]

    doi: 10.18419/DARUS-4785

    Porepy code for rev simulations for: ”local thermal non- equilibrium models in porous media: A comparative study of conduction effects”. doi: 10.18419/DARUS-4785. Stefansson, I., Varela, J., Keilegavlen, E., Berre, I.,

    work page doi:10.18419/darus-4785

  15. [15]

    Wakao, N., Kagei, S.,

    1016/j.rinam.2023.100428. Wakao, N., Kagei, S.,

    work page arXiv 2023

  16. [16]

    Drying Technology 40, 697–718

    A fully implicit cou- pled pore-network/free-flow model for the pore-scale simulation of dry- ing processes. Drying Technology 40, 697–718. URL: https://www. tandfonline.com/doi/full/10.1080/07373937.2021.1955706, doi:10. 1080/07373937.2021.1955706. Xu, X.Y., Hu, N., Qian, Z.K., Wang, Q., Fan, L.W., Song, X.,

    work page doi:10.1080/07373937.2021.1955706 2021

  17. [17]

    Garai, S

    Un- derstanding of co-boiling between organic contaminants and water during thermal remediation: Effects of nonequilibrium heat and mass transport. Environmental Science & Technology 57, 16043–16052. doi: 10.1021/acs. est.3c04259. Yang, B., Wu, W., Li, M., Zhai, W.,

    work page doi:10.1021/acs